Research ArticlePerformance Analysis of Energy Harvesting-Based Full-DuplexDecode-and-Forward Vehicle-to-Vehicle Relay Networks withNonorthogonal Multiple Access

Ba Cao Nguyen1 Tran Manh Hoang1 Xuan Nghia Pham1 and Phuong T Tran 2

1Faculty of Radio Electronics Le Quy Don Technical University Hanoi Vietnam2Wireless Communications Research Group Faculty of Electrical and Electronics Engineering Ton Duc ang UniversityHo Chi Minh City Vietnam

Correspondence should be addressed to Phuong T Tran tranthanhphuongtdtueduvn

Received 3 July 2019 Revised 24 September 2019 Accepted 15 October 2019 Published 3 November 2019

Academic Editor Miguel Lopez-Benıtez

Copyright copy 2019 BaCaoNguyen et alis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper a combination of energy harvesting (EH) and cooperative nonorthogonal multiple access (NOMA) has beenproposed for full-duplex (FD) relaying vehicle-to-vehicle (V2V) networks with two destination nodes over a Rayleigh fadingchannel Dierent from previous studies here both source and relay nodes are supplied with the energy from a power beacon (PB)via RF signals and then use the harvested energy for transmitting the information For the extensive performance analysis theclosed-form expressions for the performance indicators including outage probability (OP) and ergodic capacity of both usershave been derived rigorously Additionally the eect of various parameters such as EH time duration residual self-interference(RSI) level and power allocation coecients on the system performance has also been investigated Furthermore all mathe-matical analytical results are conrmed by Monte-Carlo simulations which also demonstrate the optimal value of EH timeduration to minimize the OP and maximize the ergodic capacity of the proposed system

1 Introduction

Under the fast development of Internet of ings (IoT)devices and future wireless networks eg the fth gener-ation (5G) of mobile communications and numerous so-lutions to improve the spectrum eciency have beenproposed and experimented Among those solutions theadvanced techniques such as full-duplex (FD) relayingnonorthogonal multiple access (NOMA) and massivemultiple-input multiple-output (MIMO) have been arisingas the most promising candidates [1ndash3] erefore a lot ofstudies and experiments have been conducted to investigatethose systems in practical scenarios to verify the potential ofcapacity increasing Due to the fact that the FD commu-nication can achieve double of system capacity compared tohalf-duplex (HD) with perfect self-interference (SI) can-cellation the study of FD systems becomes a hot topic Onthe contrary NOMA can improve the average system ca-pacity in comparison with the traditional orthogonal

multiple access (OMA) because it can help exchange in-formation among multiple users at the same time in thesame frequency band only with dierent power allocationcoecients

e combination between FD communication andNOMA technique has been studied in the literature such as[4ndash7] In [4] the authors analyzed the down-link NOMAsystem with a FD amplify-and-forward (AF) relay In thatwork the direct link from the source node to near user hasbeen considered rough numerical calculation the au-thors obtained the analytical expressions to indicate thesystem performance including outage probabilities (OPs)and ergodic capacities of both users Based on that theimpact of residual self-interference (RSI) and power allo-cation coecients were also investigated In another aspectYue et al [6] have utilized a cooperative NOMA systemwhere the near user was employed as a relay which canoperate in either HD or FD mode and with decode-and-forward (DF) protocol e authors considered two cases

HindawiWireless Communications and Mobile ComputingVolume 2019 Article ID 6097686 11 pageshttpsdoiorg10115520196097686

ie with or without a direct link from the base station (BS) tothe far user OP expressions ergodic rate and energy effi-ciency have been derived for system performance analysisSimilar to [6] Zhang et al [7] also considered a NOMAsystem in which the near user operated as a FD relay toforward the signal to the far user1e authors derived the OPexpressions of both users and compared with the conven-tional NOMA and OMA schemes

Recently various techniques have been applied for en-ergy supply for wireless networks including RF energyharvesting (EH) [5 8ndash11] Specifically wireless devices firstharvest energy from radio frequency signals and then use theharvested energy for exchanging data 1erefore the EHtechnique is a promising solution for battery-limited devicesDue to the advantage of wireless charging EH becomespopular in real-world applications such as personal mobilephones Furthermore to increase the amount of harvestedenergy at the transmitters power beacon (PB) may beutilized to supply energy wirelessly to both source and relaybefore information transmission [10 12ndash14]

In the literature there have been several studies onthe combination of EH FD and NOMA [5 9 15ndash17] In[9] the authors considered a down-link NOMA systemwhere the source node transmits two signals to two usersvia a FD decode-and-forward relay node In this modelthe relay node has constrained power supply and mustharvest energy through RF signals transmitted by thesource Based on the theoretical analysis the authorsderived OP of the considered system over Nakagami-mfading channel Additionally the optimal harvestingtime and optimal power allocation coefficients to mini-mize OP were also obtained In 2018 Alsaba et al [5]investigated a cooperative NOMA system where a stronguser operated at the FD mode and forwarded the signal toa weak user 1e authors successfully derived OP ex-pressions for both users and studied the impact of im-perfect self-interference and EH circuit on the systemperformance Wang and Wu [15] and Guo et al [16]investigated a similar system where the strong user(which is an EH-FD relay node) harvested energy fromthe source node for transmitting information messagesFurthermore [17] extended this model to M relay nodesand K users Different from [5 9 15 16] the work in [17]investigated the case that the users harvest energy fromthe source In summary the previous studies consideredeither only FD relay (strong user) or weak user canharvest energy from the source 1e case that both sourceand relay harvest energy from the power beacon has notbeen investigated

Although the EH FD and NOMA are advanced tech-niques that play a key role for future wireless networks thecoexistence of these techniques in a unique system raises thecomplexity of processing to a very high level However withthe fast development of circuit design as well as analog anddigital processing techniques hopefully the proposed systemcan be implemented in very near future On the contrary inpractical networks not only the relay node but also thesource node has limited power supply 1at leads to the ideaof providing the energy to the source node before message

transmission by using the power beacon (PB) With tre-mendous number of applications in many areas [18] FDcommunication has been considered particularly for vehi-cle-to-vehicle (V2V) communication networks When ve-hicles move on the road the end-to-end delay of theinformation transmission among them can be reducedsignificantly by applying FD communication Moreoverwith the ability to send and receive data simultaneously theinnovative technologies such as cooperative semi-autonomous and autonomous driving can be supported Asa result road and passenger safety is enhanced and trafficcongestion is reduced Because of the mobility of vehicles itis difficult to supply energy to the wireless devices on thevehicle To maintain the connectivity to other devices theyneed to harvest energy from the RF signals for powering thedata transmission 1erefore EH is a promising solution forV2V networks

Motivated by all these above facts in this paper weinvestigate an EH-FD-NOMA system in which bothsource and relay nodes harvest energy from PB After thatthey utilize suitable circuits to transform the harvestedenergy to power for transmitting information Further-more the relay node operates in the FD mode while thesource node and two users operate in the half-duplex(HD) mode Two users are located in different locationfrom the relay In particular there is a strong user and theother is a weak user Based on the analytical expressions ofoutage probability and ergodic capacities at both users weinvestigate the system performance of the proposedsystem 1e contributions of this paper can be summa-rized as follows

(i) We proposed a novel combination of EH FD andNOMA techniques in V2V networks It is noted thatin the previous studies about the similar combi-nation only the case that a strong user acts as a relayhas been considered In addition only the relay canharvest the energy from the source node In ourmodel we assume that both the source node and theFD relay node which is not any one of the receivingusers harvest the energy from the power beaconthrough RF signals 1is assumption leads to thecomplexity in mathematical derivations of theproposed system performance compared withprevious works However our model can be appliedfor V2V communication systems and future wire-less networks thus it is vital to investigate

(ii) We derive the exact theoretical expressions for thesystem performance in terms of outage probabilitythroughput and ergodic capacity of both users inthe case of imperfect self-interference cancellationat the FD relay node over Rayleigh fading channel

(iii) We analyze the system performance throughanalysis and simulation1e numerical results showthat with the suitable power allocation coefficientsfor both users the performance measures of bothusers are the same On the contrary the impact ofimperfect self-interference cancellation and the timefor harvesting are also analyzed In fact there exists

2 Wireless Communications and Mobile Computing

an optimal time duration for EH tominimize outageprobability and maximize ergodic capacity Finallywe conduct Monte-Carlo simulations to validate theanalytical results

1e rest of this paper is organized as follows Section 2presents the system model while Section 3 derives thesystem performance in terms of OP and capacity Section 4discusses about the numerical results and finally Section 5concludes this paper

2 System Model

In this section we introduce a system model that combinesthree techniques EH FD and NOMA as illustrated inFigure 1 Here the source node (S) simultaneously transmitstwo messages to both users (D1 and D2) under the assistanceof relay node (R) We assume that S and R do not have theirall power supplies due to their inconvenient locations Asa result they must harvest the energy from RF signals Tosupply enough power for S and R we use a power beacon(PB) to transmit energy to them After the energy harvestingphase S and R convert the received energy to the power fortransmitting signals As shown in Figure 1 PB S D1 and D2are single-antenna devices while R is equipped with twoantennas In this system only R operates at the FD modewhile other devices operate in the HD mode In manyanalytical studies and experiments R can use one shared-antenna for transmittingreceiving the signal However inthis work we deploy two-antenna relay to identify clearly theSI and get the better SI cancellation To transmit simulta-neously two messages to two users S applies the NOMAtechnique in the power domain Assume that the distancesfrom two users to R are different In particular D1 is a faruser and D2 is a near user

1e operation of the EH-FD-NOMA system of interest isdivided into two stages During the first stage PB transmitsa RF signal to S and R S and R harvest the energy throughthis RF signal and then convert it to the supply powerDuring the second stage by using the harvested energy Stransmits a message to R and at the same time R transmitsthe decoded message from the previous block to D1 and D2Let T be the length of the entire transmission block1e timeduration for the first stage is αT while the time duration forthe second stage is (1 minus α)T where α is called time-switchingratio 0le αle 1 Figure 2 illustrates the time duration for EHand for information transmission

Let ESh and ER

h denote the harvested energies at S and Rduring the EH phase αT 1erefore ES

h and ERh are given as

[19]

ESh ηαTP hBS

111386811138681113868111386811138681113868111386811138682

ERh ηαTP hBR

111386811138681113868111386811138681113868111386811138682

(1)

where η is a constant that represents the energy conversionefficiency Its value depends on the converting hardware andmethod (0le ηle 1) P is the average transmit power of PBand hBS and hBR are respectively the fading coefficients ofthe channels from PB to S and from PB to R As illustrated in

Figure 1 in this paper we investigate the case that R onlyuses one antenna for EH In practical systems R can use allantennas for harvesting energy by using suitable hardwareresources [20] Furthermore S and R have a super capacitorto store the harvested energy After the time duration αT ofEH S and R can fully use the harvested energy for trans-mitting information during the time (1 minus α)T1erefore thetransmit power at S and R can be calculated as [21]

PS ηαP hBS

111386811138681113868111386811138681113868111386811138682

1 minus αηαPρ11 minus α

PR ηαP hBR

111386811138681113868111386811138681113868111386811138682

1 minus αηαPρ21 minus α

(2)

where ρ1 |hBS|2 and ρ2 |hBR|2 are channel gains of the

links PB⟶ S and PB⟶ R respectivelyDuring the time duration (1 minus α)T S transmits a signal

to R Simultaneously R forwards a signal to both users D1and D2 on the same frequency band1at results in SI at R Itis also noted that the message that is transmitted by S are thecombination of two messages for two users D1 and D2 1emessages transmitted by R are the decoded messages at Rduring the previous symbol block (as long as R decodessuccessfully the received message) 1e received signal at Rcan be calculated as

yR hSRa1PS

1113968x1 +

a2PS

1113968x2( 1113857 + 1113957hRR

PR

1113968xR + zR (3)

where hSR and 1113957hRR are respectively the fading coefficients ofthe channels from S⟶ R and from the transmitting to thereceiving circuits of R a1 and a2 are NOMA coefficients witha1 gt a2 PS and PR are average transmit powers at S and Rrespectively x1 andx2 are two messages for two users D1and D2 respectively xR is the transmitted signals at R andzR is the additive white Gaussian noise (AWGN) with zero-mean and variance of σ2 ie zRsimCN(0 σ2)

D2

D1

RS

PB

RX

RX

TX

TX

RX hRD2hSR

hBS hBR

h~RR

hRD1

RXTX

Figure 1 System model of the proposed EH-FD-NOMA system

Energy harvestingPB to S and R

Information transmissionS to R R to D1 and D2

T

αT (1 ndash α)T

Figure 2 Data frame structure of the time duration for EH andinformation

Wireless Communications and Mobile Computing 3

From (3) the SI at R is calculated by

E 1113957hRR1113868111386811138681113868

11138681113868111386811138682PR1113882 1113883

ηαP

1 minus αE 1113957hRR

111386811138681113868111386811138681113868111386811138682ρ21113882 1113883 (4)

In FD devices various SI cancellation techniques canbe applied to reduce the effect of RSI on the systemperformance such as isolation propagation domain anddigital and analog cancellation In fact the relay defi-nitely knows the transmit signal xR so by using theresults of SI channel estimation of 1113957hRR it can apply digitalprocessing methods to subtract the SI from the receivedsignals [22ndash25] However due to the hardware impairmentand the imperfect estimation of the SI channel SI may stillexist in the system after applying various SI cancellationmethods and degrade the system performance Typically theRSI which is denoted by IR can be modeled by the complexGaussian distribution [23 25ndash28] with zero-mean and var-iance cRSI where cRSI 1113957Ω(ηαP)(1 minus α) It is also noted that1113957Ω denotes the SI cancellation capability of the relay nodeAfter SI cancellation (3) becomes

yR hSRa1PS

1113968x1 +

a2PS

1113968x2( 1113857 + IR + zR (5)

From (5) SINR (signal-to-interference-plus-noise ra-tio) to detect the message x1 at R (denoted by c

x1R ) is

calculated as

cx1R

hSR1113868111386811138681113868

11138681113868111386811138682a1PS

hSR1113868111386811138681113868

11138681113868111386811138682a2PS + cRSI + σ2

a1ηαPρ1ρ3

a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

(6)

where ρ3 |hSR|2 is the channel gain from S⟶ RAfter detecting x1 R removes all x1rsquos components from

received signals and then detect x2 1us SINR to detectmessage x2 at R (denoted by c

x2R ) is given by

cx2R

a2ηαPρ1ρ3cRSI + σ2( 1113857(1 minus α)

middot (7)

Due to the FD mode during the time duration of(1 minus α)T R transmits the signals to both destinations D1 andD2 We assume that the delay caused by signal processing atthe relay is equal to one symbol period 1erefore thetransmitted signals at R are the received signals in theprevious period after processing 1en the received signalsat D1 and D2 are respectively given by

yD1 hRD1

a1PR

1113968x1 +

a2PR

1113968x2( 1113857 + z1 (8)

yD2 hRD2

a1PR

1113968x1 +

a2PR

1113968x2( 1113857 + z2 (9)

where hRD1and hRD2

are fading coefficients of channels fromR⟶ D1 and R⟶ D1 respectively and z1 and z2 are theAWGN terms with zero-mean and variance of σ2 iez1simCN(0 σ2) and z2simCN(0 σ2)

By the principle of NOMA systems the far user (user 1denoted by D1 in our paper) decodes its own message whileuser 2rsquos message is considered as interference 1e near user(user 2 or D2 in this paper) first subtracts the signal of the

user D1 through successive interference cancellation (SIC) toremove the interference from the far user D1 1en it de-codes its own message In this paper we assume that D2 canperfectly remove interference After that the received signalat D2 from (9) can be rewritten as

yD2 hRD2

a2PR

1113968x2 + z2 (10)

From equations (8)ndash(10) SINRs at D1 and D2 can becalculated as

cx1D1

hRD1

11138681113868111386811138681113868

111386811138681113868111386811138682a1PR

hRD1

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR + σ2

a1ηαPρ2ρ4

a2ηαPρ2ρ4 + σ2(1 minus α)

cSICx1D2

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a1PR

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR + σ2

a1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)

cx2D2

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR

σ2

a2ηαPρ2ρ5σ2(1 minus α)

(11)

where ρ4 |hRD1|2 and ρ5 |hRD2

|2 are the channel gains ofthe links R⟶ D1 and R⟶ D2 respectively

It is also noted that for DF relaying protocol the end-to-end SINR is calculated as

ce2e min cR cD1113864 1113865 (12)

1erefore the end-to-end SINRs at D1 and D2 can bewritten as follows

cD1 min c

x1R c

x1D1

1113966 1113967 (13)

cD2 min c

x1R c

x2R c

SICx1D2

cx2D2

1113882 1113883 (14)

3 Performance Analysis

31 Outage Probability Analysis In this section the outageprobability of the considered EH-FD-NOMA system is de-rived to evaluate the system performance 1e system OP isthe probability that makes the instantaneous SINR fallingbelow a predefined threshold [29] To derive OPs for thissystem let R1 and R2 (bitsHz) be the minimum requireddata rates for the users D1 and D2 respectively By assumingthe fairness of the users in this systems we setR1 R2 R1en OP at D1 denoted by P

D1out can be calculated as

PD1out Pr (1 minus α)log2 1 + cD1

1113872 1113873ltR1113966 1113967 Pr cD1lt 2R(1minus α)

minus 11113966 1113967

(15)

where cD1is derived in (13) Let x 2R(1minus α) minus 1 be the SINR

threshold 1en the expression (15) can be rewritten as

PD1out Pr cD1

ltx1113966 1113967 (16)

At destination D2 the outage occurs when it does notdecode successfully the signal x1 or its own message x21erefore we have

4 Wireless Communications and Mobile Computing

PD2out Pr cD2

ltx1113966 1113967 Pr min cx1R c

x2R c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

Pr min min cx1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877ltx1113882 1113883

(17)

Theorem 1 e OPs at D1 (PD1out) and D2 (P

D2out) of the

cooperative EH-FD-NOMA system under the impact of RSIover Rayleigh fading channel are determined respectively asfollows

PD1out

1 minus

XYx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xlta1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(18)

PD2out

1 minus

XZx2

a22

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

1 minus

XZx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠a1

a2minus 1le xlt

a1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)

where X (4(cRSI + σ2)(1 minus α))(Ω1Ω3ηαP) Y (4σ2(1minus

α))(Ω2Ω4ηαP) and Z (4σ2(1 minus α))(Ω2Ω5ηαP) HereΩi E ρi1113864 1113865 where Ωi and ρi denote the average and in-stantaneous channel gains of the Rayleigh fading channelrespectively (i 1 2 5) E denotes the expectation op-erator and K1(middot) is the first-order modified Bessel function ofthe second kind [30]

Proof of eorem 1 To calculate PD1out and P

D2out from

equations (16) and (17) we apply the probability rule in [31]to get

PD1out Pr min c

x1R c

x1D1

1113872 1113873ltx1113966 1113967 Pr cx1R ltx1113864 1113865 + Pr c

x1D1ltx1113966 1113967

minus Pr cx1R ltx1113864 1113865Pr c

x1D1ltx1113966 1113967

(20)

PD2out Pr min min c

x1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877lt x1113882 1113883

Pr min cx1R c

x2R( 1113857lt x1113864 1113865 + Pr min c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

minus Pr min cx1R c

x2R( 1113857lt x1113864 1113865Pr min c

SICx1D2

cx2D2

1113874 1113875ltx1113882 1113883

(21)

On the contrary the cumulative distribution functions(CDFs) Fρi

(x) and probability distribution functions (PDFs)of the Rayleigh distribution fρi

(x) can be determined asfollows

Fρi(x) 1 minus exp minus

x

Ωi

1113888 1113889 xge 0 (22)

fρi(x)

1Ωi

exp minusx

Ωi

1113888 1113889 xge 0 (23)

By using equations (20)ndash(23) and doing some algebraswe can derive (18) and (19) in 1eorem 1 For details of theproof see in appendix A

32 Ergodic Capacity Analysis 1e ergodic capacity of theFD relay system is calculated by

C E log2(1 + c)1113864 1113865 1113946infin

0log2(1 + c)fc(c)dc (24)

where c is the end-to-end SINR of the considered systemand fc(c) is the PDF of c To derive the closed-form ex-pression of the ergodic capacity of the system we rewrite(24) after some algebras as

C 1ln 2

1113946infin

0

1 minus F(x)

1 + xdx (25)

where F(x) is the CDF of the end-to-end SINR of theconsidered system

Theorem 2 e ergodic capacities of both users D1 and D2are respectively given by

Wireless Communications and Mobile Computing 5

CD1

a1π2Na2ln 2

1113944N

n1

1 minus ϕ2n1113969

G1(u) (26)

CD2

π2Nln2

1113876a1 minus a2

a21113944

N

n1

1 minus ϕ2n1113969

G21 v1( 1113857

+ 1113944N

n1

1 minus ϕ2n

1113969

G22 v2( 11138571113877

(27)

where N is the complexity-accuracy trade-off parameterϕn cos((2n minus 1)π2N) u (a12a2)(ϕn + 1) v1 ((a1minus

a2)2a2)(ϕn + 1) and v2 ((2a1 minus a2)2a2) + ((12)ϕn)

G1(u) 1

1 + u

XYu2

a1 minus a2u( 11138572

1113971

middot K1

Xu

a1 minus a2u

1113971

⎛⎝ ⎞⎠K1

middot

Yu

a1 minus a2u

1113971

⎛⎝ ⎞⎠

G21 v1( 1113857 1

1 + v1

XZv21

a22

1113971

K1

Xv1

a2

1113971

⎛⎝ ⎞⎠K1

Zv1

a2

1113971

⎛⎝ ⎞⎠

G22 v2( 1113857 1

1 + v2

XZv22

a1 minus a2v2( 11138572

1113971

middot K1

Xv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠K1

middot

Zv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠

(28)

Proof of eorem 2 From (25) we calculate the ergodiccapacities at D1 (CD1

) and D2 (CD2) by replacing F(x) in (25)

by PD1out and P

D2out in (18) and (19) respectively 1erefore CD1

and CD2are calculated as

CD1

1ln 2

1113946infin

0

1 minus PD1out(x)

1 + xdx (29)

CD2

1ln 2

1113946infin

0

1 minus PD2out(x)

1 + xdx (30)

By applying the integral formulas in [32] we obtain theergodic capacities at D1 and D2 in (26) and (27) after somemathematical transforms In appendix B we provide thedetails of proof

4 Numerical Results

In this section the EH-FD-NOMA system performance interms of OP and ergodic capacity is plotted by using theexpressions in1eorem 1 and1eorem 2 In addition we alsoconduct the Monte-Carlo simulations on OP and ergodiccapacity to demonstrate the correctness of theoretical formulas1e system performance is evaluated for different values of theaverage SNR where SNR is the ratio between the transmit

power of PB and the variance of AWGN ie SNR Pσ2 Inour simulations we choose parameters for evaluating thesystem performance as follows the power allocation co-efficients are a1 065 and a2 035 the energy harvestingefficiency at each node is η 085 the average channel gainsΩ1 Ω2 Ω3 Ω5 1 andΩ4 071e simulation resultswere obtained by using 106 channel realizations

In Figure 3 we consider the OPs of both users D1 andD2 versus the average SNR In this figure we use theresults of 1eorem 1 to plot theoretical curves ((18) for D1and (19) for D2) with α 05 R 03 bitsHz and SIcancellation capability 1113957Ω minus 30 dB It is obvious that thesimulation curves exactly match with the theoretical onesAs can be seen from the figure OPs of both users have thesame performance and diversity order 1ey decreasewhen SNR increases On the contrary at high SNR regime(SNR gt 35 dB) the OPs of both users decrease slowly If wecontinuously increase SNR the OPs will go to outage floordue to the RSI and NOMA coefficients It is easy to seethat even if the RSI is very small and with high transmitpower at PB from (6) we have c

x1R ⟶ (a1a2) If the RSI is

larger the outage floor will be reached sooner 1ereforeit is necessary to apply various SI cancellation techniquesfor the FD mode to avoid performance loss of the FDcommunication systems

Figure 4 illustrates the throughput of the EH-FD-NOMAsystem versus average SNR with various data transmissionrates R 03 05 07 bitsHz It is also noted that thesystem throughput is defined by TD1

≜R(1 minus PD1out) and

TD2≜R(1 minus P

D2out) 1e other simulation parameters are the

same as those in Figure 3 Figure 4 shows that at low SNRregime (ie SNRlt 10 dB) with low data transmission rateieR 03 the throughput will reach the best value amongthree considered cases When SNR increases such as from14 to 26 dB the optimal throughput is obtained whenR 05 In the case of SNRgt 26 dB the system throughputreaches the maximal value with R 07 1ereforedepending on the transmit power at PB we can suitablychoose the data transmission rate for the considered systemto get the optimal throughput and improve the overallsystem performance

Figure 5 shows the impact of EH time-switching ratioα on the OPs of the considered system with R 03 bitsHz and 1113957Ω minus 30 dB As can be seen from the figure thereis an optimal value of α corresponding to a pretransmitpower of PB For example with SNR 20 dB the optimalvalue is α asymp 06 In the case of SNR 30 dB the value isα asymp 05 and in the case of SNR 40 dB α asymp 03 Conse-quently based on the transmit power at PB we can adjustthe EH time-switching ratio in order to improve thesystem performance

Figure 6 illustrates the ergodic capacity of both usersunder the impact of SI cancellation capability with1113957Ω minus 30 minus 20 and minus 10 dB In this figure the theoreticalcurves are plotted by using equations (26) and (27) in1eorem 2 while the marker symbols are plotted byMonte-Carlo simulations It is obvious that the ergodiccapacity increases when SNR increases especially when

6 Wireless Communications and Mobile Computing

RSI is small such as 1113957Ω minus 30 dB In the case of 1113957Ω minus 30 dBthe ergodic capacity at both users increases about 06 bitsHz comparing with the case of 1113957Ω minus 10 dB 1e gain forthe system capacity is about 12 bitsHz Figure 6 showsthe strong impact of RSI on the capacity of the consideredsystem 1us to deploy this system in realistic scenarioswireless researchers and designers need to design circuitsand build algorithms in order to improve the SIcancellation

Finally Figure 7 plots the ergodic capacities of theEH-FD-NOMA system with various time durations of αin the case of 1113957Ω minus 30 dB 1is figure shows that the

ergodic capacities of users D1 and D2 increase when αincreases For example the ergodic capacity in the case ofα 07 is the best capacity compared with the case of α

03 and α 05 However at high SNR such asSNR 40 dB the ergodic capacities of three consideredcases are the same 1e results in Figure 7 are compatiblewith those in Figure 5 By combining Figures 5 and 7 wecan clearly see that when SNRlt 30 dB we choose α 07to get the best performance and best capacity of theconsidered system

5 10 15 20 250 35 4030Average SNR (dB)

0

01

02

03

04

05

06

Thro

ughp

ut (b

its

Hz)

R = 07

R = 05

R = 03

Simulation D1Theory D1

Simulation D2Theory D2

Figure 4 1roughput of the EH-FD-NOMA system with variousdata transmission rates R 03 05 07 bitsHz

5 10 15 20 250 35 4030Average SNR (dB)

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

Simulation D1Theory D1

Simulation D2Theory D2

Figure 3 1e OPs at D1 and D2 versus the average SNR whenR 03 bitsHz 1113957Ω minus 30 dB and α 05

10ndash3

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

104 06 08020α

SNR = 20 30 40 dB

Simulation D1Theory D1

Simulation D2Theory D2

Figure 51e impact of EH time duration on the OPs at both userswith SNR 20 30 40 dB R 03 bitsHz and 1113957Ω minus 30 dB

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

Ω~ = ndash30 ndash20 ndash10dB

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 6 1e ergodic capacities of both users under the impact ofSI cancellation capability with α 05 and various levels of RSI

Wireless Communications and Mobile Computing 7

5 Conclusion

In this paper we propose a novel combination of threeadvanced techniques namely EH FD and NOMA in a so-

called EH-FD-NOMA communication system which can beapplied for V2V communication networks By mathematicalanalysis we derive exact expressions of outage probabilityand ergodic capacity at both users under the impact ofresidual self-interference at the FD relay node Our resultsshow that the two users can obtain the same performanceand capacity ie the fairness is guaranteed Depending onthe transmit power at the power beacon there is an optimalvalue for EH time-switching ratio to minimize the outageprobability and maximize the capacity Furthermore theimpact of data transmission rate residual self-interferencelevel and time-switching factor α is also investigated Nu-merical results demonstrate the importance of self-and-successive-interference cancellation on the performance ofthe considered system 1ose results serve as importantreferences for wireless researchers and designers in de-ployment of the EH-FD-NOMA system in practice

Appendix

A Proof of Theorem 1

In this appendix we provide step-by-step procedure of howto derive the expressions of outage probability at both usersof the proposed EH-FD-NOMA system over Rayleigh fadingchannels

For PD1out from (20) we calculate Pr c

x1R lt x1113864 1113865 in (A1) and

Pr cx1D1ltx1113966 1113967 in (A2) as follows

Pr cx1R lt x1113864 1113865 Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

1113946infin

0Fρ1

cRSI + σ2( 1113857(1 minus α)x

ηαP a1 minus a2x( 1113857ρ31113888 1113889fρ3 ρ3( 1113857dρ3 1113946

infin

01 minus exp minus

cRSI + σ2( 1113857(1 minus α)x

Ω1ηαP a1 minus a2x( 1113857ρ31113888 11138891113890 1113891

1Ω3

exp minusρ3Ω3

1113888 1113889dρ3

1 minus

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

K1

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A1)

Pr cx1D1ltx1113966 1113967 Pr ηαP a1 minus a2x( 1113857ρ2ρ4 lt σ

2(1 minus α)x1113966 1113967

1113946infin

0Fρ2

σ2(1 minus α)x

ηαP a1 minus a2x( 1113857ρ41113888 1113889fρ4 ρ4( 1113857dρ4 1113946

infin

01 minus exp minus

σ2(1 minus α)x

Ω2ηαP a1 minus a2x( 1113857ρ41113888 11138891113890 1113891

1Ω4

exp minusρ4Ω4

1113888 1113889dρ4

1 minus

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

K1

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Yx

a1 minus a2x

1113971

K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A2)

It is noted that in the case of a1 minus a2xle 0 the proba-bilities in (A1) and (A2) always occur 1ereforePr c

x1R lt x1113864 1113865 1 and Pr c

x1D1ltx1113966 1113967 1 which lead to P

D1out 1

After doing some algebras and applying [30 33241] wederive Pr c

x1R ltx1113864 1113865 and Pr c

x1D1lt x1113966 1113967 at the end of (A1) and

(A2) By substituting (A1) and (A2) into (20) we obtainPD1out in (18) in 1eorem 1For P

D2out based on the equation (21) we can calculate

Pr min(cx1R c

x2R )lt x1113864 1113865 as in (A3) and Pr min(c

SICx1D2

1113882 cx2D2

)

lt x as in (A4)

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

α = 03 05 07

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 7 1e impact of the EH time duration on the ergodicperformance of the EH-FD-NOMA system versus the average SNRfor different values of α α 03 05 07 and 1113957Ω minus 30 dB

8 Wireless Communications and Mobile Computing

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

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an optimal time duration for EH tominimize outageprobability and maximize ergodic capacity Finallywe conduct Monte-Carlo simulations to validate theanalytical results

1e rest of this paper is organized as follows Section 2presents the system model while Section 3 derives thesystem performance in terms of OP and capacity Section 4discusses about the numerical results and finally Section 5concludes this paper

2 System Model

In this section we introduce a system model that combinesthree techniques EH FD and NOMA as illustrated inFigure 1 Here the source node (S) simultaneously transmitstwo messages to both users (D1 and D2) under the assistanceof relay node (R) We assume that S and R do not have theirall power supplies due to their inconvenient locations Asa result they must harvest the energy from RF signals Tosupply enough power for S and R we use a power beacon(PB) to transmit energy to them After the energy harvestingphase S and R convert the received energy to the power fortransmitting signals As shown in Figure 1 PB S D1 and D2are single-antenna devices while R is equipped with twoantennas In this system only R operates at the FD modewhile other devices operate in the HD mode In manyanalytical studies and experiments R can use one shared-antenna for transmittingreceiving the signal However inthis work we deploy two-antenna relay to identify clearly theSI and get the better SI cancellation To transmit simulta-neously two messages to two users S applies the NOMAtechnique in the power domain Assume that the distancesfrom two users to R are different In particular D1 is a faruser and D2 is a near user

1e operation of the EH-FD-NOMA system of interest isdivided into two stages During the first stage PB transmitsa RF signal to S and R S and R harvest the energy throughthis RF signal and then convert it to the supply powerDuring the second stage by using the harvested energy Stransmits a message to R and at the same time R transmitsthe decoded message from the previous block to D1 and D2Let T be the length of the entire transmission block1e timeduration for the first stage is αT while the time duration forthe second stage is (1 minus α)T where α is called time-switchingratio 0le αle 1 Figure 2 illustrates the time duration for EHand for information transmission

Let ESh and ER

h denote the harvested energies at S and Rduring the EH phase αT 1erefore ES

h and ERh are given as

[19]

ESh ηαTP hBS

111386811138681113868111386811138681113868111386811138682

ERh ηαTP hBR

111386811138681113868111386811138681113868111386811138682

(1)

where η is a constant that represents the energy conversionefficiency Its value depends on the converting hardware andmethod (0le ηle 1) P is the average transmit power of PBand hBS and hBR are respectively the fading coefficients ofthe channels from PB to S and from PB to R As illustrated in

Figure 1 in this paper we investigate the case that R onlyuses one antenna for EH In practical systems R can use allantennas for harvesting energy by using suitable hardwareresources [20] Furthermore S and R have a super capacitorto store the harvested energy After the time duration αT ofEH S and R can fully use the harvested energy for trans-mitting information during the time (1 minus α)T1erefore thetransmit power at S and R can be calculated as [21]

PS ηαP hBS

111386811138681113868111386811138681113868111386811138682

1 minus αηαPρ11 minus α

PR ηαP hBR

111386811138681113868111386811138681113868111386811138682

1 minus αηαPρ21 minus α

(2)

where ρ1 |hBS|2 and ρ2 |hBR|2 are channel gains of the

links PB⟶ S and PB⟶ R respectivelyDuring the time duration (1 minus α)T S transmits a signal

to R Simultaneously R forwards a signal to both users D1and D2 on the same frequency band1at results in SI at R Itis also noted that the message that is transmitted by S are thecombination of two messages for two users D1 and D2 1emessages transmitted by R are the decoded messages at Rduring the previous symbol block (as long as R decodessuccessfully the received message) 1e received signal at Rcan be calculated as

yR hSRa1PS

1113968x1 +

a2PS

1113968x2( 1113857 + 1113957hRR

PR

1113968xR + zR (3)

where hSR and 1113957hRR are respectively the fading coefficients ofthe channels from S⟶ R and from the transmitting to thereceiving circuits of R a1 and a2 are NOMA coefficients witha1 gt a2 PS and PR are average transmit powers at S and Rrespectively x1 andx2 are two messages for two users D1and D2 respectively xR is the transmitted signals at R andzR is the additive white Gaussian noise (AWGN) with zero-mean and variance of σ2 ie zRsimCN(0 σ2)

D2

D1

RS

PB

RX

RX

TX

TX

RX hRD2hSR

hBS hBR

h~RR

hRD1

RXTX

Figure 1 System model of the proposed EH-FD-NOMA system

Energy harvestingPB to S and R

Information transmissionS to R R to D1 and D2

T

αT (1 ndash α)T

Figure 2 Data frame structure of the time duration for EH andinformation

Wireless Communications and Mobile Computing 3

From (3) the SI at R is calculated by

E 1113957hRR1113868111386811138681113868

11138681113868111386811138682PR1113882 1113883

ηαP

1 minus αE 1113957hRR

111386811138681113868111386811138681113868111386811138682ρ21113882 1113883 (4)

In FD devices various SI cancellation techniques canbe applied to reduce the effect of RSI on the systemperformance such as isolation propagation domain anddigital and analog cancellation In fact the relay defi-nitely knows the transmit signal xR so by using theresults of SI channel estimation of 1113957hRR it can apply digitalprocessing methods to subtract the SI from the receivedsignals [22ndash25] However due to the hardware impairmentand the imperfect estimation of the SI channel SI may stillexist in the system after applying various SI cancellationmethods and degrade the system performance Typically theRSI which is denoted by IR can be modeled by the complexGaussian distribution [23 25ndash28] with zero-mean and var-iance cRSI where cRSI 1113957Ω(ηαP)(1 minus α) It is also noted that1113957Ω denotes the SI cancellation capability of the relay nodeAfter SI cancellation (3) becomes

yR hSRa1PS

1113968x1 +

a2PS

1113968x2( 1113857 + IR + zR (5)

From (5) SINR (signal-to-interference-plus-noise ra-tio) to detect the message x1 at R (denoted by c

x1R ) is

calculated as

cx1R

hSR1113868111386811138681113868

11138681113868111386811138682a1PS

hSR1113868111386811138681113868

11138681113868111386811138682a2PS + cRSI + σ2

a1ηαPρ1ρ3

a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

(6)

where ρ3 |hSR|2 is the channel gain from S⟶ RAfter detecting x1 R removes all x1rsquos components from

received signals and then detect x2 1us SINR to detectmessage x2 at R (denoted by c

x2R ) is given by

cx2R

a2ηαPρ1ρ3cRSI + σ2( 1113857(1 minus α)

middot (7)

Due to the FD mode during the time duration of(1 minus α)T R transmits the signals to both destinations D1 andD2 We assume that the delay caused by signal processing atthe relay is equal to one symbol period 1erefore thetransmitted signals at R are the received signals in theprevious period after processing 1en the received signalsat D1 and D2 are respectively given by

yD1 hRD1

a1PR

1113968x1 +

a2PR

1113968x2( 1113857 + z1 (8)

yD2 hRD2

a1PR

1113968x1 +

a2PR

1113968x2( 1113857 + z2 (9)

where hRD1and hRD2

are fading coefficients of channels fromR⟶ D1 and R⟶ D1 respectively and z1 and z2 are theAWGN terms with zero-mean and variance of σ2 iez1simCN(0 σ2) and z2simCN(0 σ2)

By the principle of NOMA systems the far user (user 1denoted by D1 in our paper) decodes its own message whileuser 2rsquos message is considered as interference 1e near user(user 2 or D2 in this paper) first subtracts the signal of the

user D1 through successive interference cancellation (SIC) toremove the interference from the far user D1 1en it de-codes its own message In this paper we assume that D2 canperfectly remove interference After that the received signalat D2 from (9) can be rewritten as

yD2 hRD2

a2PR

1113968x2 + z2 (10)

From equations (8)ndash(10) SINRs at D1 and D2 can becalculated as

cx1D1

hRD1

11138681113868111386811138681113868

111386811138681113868111386811138682a1PR

hRD1

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR + σ2

a1ηαPρ2ρ4

a2ηαPρ2ρ4 + σ2(1 minus α)

cSICx1D2

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a1PR

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR + σ2

a1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)

cx2D2

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR

σ2

a2ηαPρ2ρ5σ2(1 minus α)

(11)

where ρ4 |hRD1|2 and ρ5 |hRD2

|2 are the channel gains ofthe links R⟶ D1 and R⟶ D2 respectively

It is also noted that for DF relaying protocol the end-to-end SINR is calculated as

ce2e min cR cD1113864 1113865 (12)

1erefore the end-to-end SINRs at D1 and D2 can bewritten as follows

cD1 min c

x1R c

x1D1

1113966 1113967 (13)

cD2 min c

x1R c

x2R c

SICx1D2

cx2D2

1113882 1113883 (14)

3 Performance Analysis

31 Outage Probability Analysis In this section the outageprobability of the considered EH-FD-NOMA system is de-rived to evaluate the system performance 1e system OP isthe probability that makes the instantaneous SINR fallingbelow a predefined threshold [29] To derive OPs for thissystem let R1 and R2 (bitsHz) be the minimum requireddata rates for the users D1 and D2 respectively By assumingthe fairness of the users in this systems we setR1 R2 R1en OP at D1 denoted by P

D1out can be calculated as

PD1out Pr (1 minus α)log2 1 + cD1

1113872 1113873ltR1113966 1113967 Pr cD1lt 2R(1minus α)

minus 11113966 1113967

(15)

where cD1is derived in (13) Let x 2R(1minus α) minus 1 be the SINR

threshold 1en the expression (15) can be rewritten as

PD1out Pr cD1

ltx1113966 1113967 (16)

At destination D2 the outage occurs when it does notdecode successfully the signal x1 or its own message x21erefore we have

4 Wireless Communications and Mobile Computing

PD2out Pr cD2

ltx1113966 1113967 Pr min cx1R c

x2R c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

Pr min min cx1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877ltx1113882 1113883

(17)

Theorem 1 e OPs at D1 (PD1out) and D2 (P

D2out) of the

cooperative EH-FD-NOMA system under the impact of RSIover Rayleigh fading channel are determined respectively asfollows

PD1out

1 minus

XYx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xlta1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(18)

PD2out

1 minus

XZx2

a22

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

1 minus

XZx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠a1

a2minus 1le xlt

a1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)

where X (4(cRSI + σ2)(1 minus α))(Ω1Ω3ηαP) Y (4σ2(1minus

α))(Ω2Ω4ηαP) and Z (4σ2(1 minus α))(Ω2Ω5ηαP) HereΩi E ρi1113864 1113865 where Ωi and ρi denote the average and in-stantaneous channel gains of the Rayleigh fading channelrespectively (i 1 2 5) E denotes the expectation op-erator and K1(middot) is the first-order modified Bessel function ofthe second kind [30]

Proof of eorem 1 To calculate PD1out and P

D2out from

equations (16) and (17) we apply the probability rule in [31]to get

PD1out Pr min c

x1R c

x1D1

1113872 1113873ltx1113966 1113967 Pr cx1R ltx1113864 1113865 + Pr c

x1D1ltx1113966 1113967

minus Pr cx1R ltx1113864 1113865Pr c

x1D1ltx1113966 1113967

(20)

PD2out Pr min min c

x1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877lt x1113882 1113883

Pr min cx1R c

x2R( 1113857lt x1113864 1113865 + Pr min c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

minus Pr min cx1R c

x2R( 1113857lt x1113864 1113865Pr min c

SICx1D2

cx2D2

1113874 1113875ltx1113882 1113883

(21)

On the contrary the cumulative distribution functions(CDFs) Fρi

(x) and probability distribution functions (PDFs)of the Rayleigh distribution fρi

(x) can be determined asfollows

Fρi(x) 1 minus exp minus

x

Ωi

1113888 1113889 xge 0 (22)

fρi(x)

1Ωi

exp minusx

Ωi

1113888 1113889 xge 0 (23)

By using equations (20)ndash(23) and doing some algebraswe can derive (18) and (19) in 1eorem 1 For details of theproof see in appendix A

32 Ergodic Capacity Analysis 1e ergodic capacity of theFD relay system is calculated by

C E log2(1 + c)1113864 1113865 1113946infin

0log2(1 + c)fc(c)dc (24)

where c is the end-to-end SINR of the considered systemand fc(c) is the PDF of c To derive the closed-form ex-pression of the ergodic capacity of the system we rewrite(24) after some algebras as

C 1ln 2

1113946infin

0

1 minus F(x)

1 + xdx (25)

where F(x) is the CDF of the end-to-end SINR of theconsidered system

Theorem 2 e ergodic capacities of both users D1 and D2are respectively given by

Wireless Communications and Mobile Computing 5

CD1

a1π2Na2ln 2

1113944N

n1

1 minus ϕ2n1113969

G1(u) (26)

CD2

π2Nln2

1113876a1 minus a2

a21113944

N

n1

1 minus ϕ2n1113969

G21 v1( 1113857

+ 1113944N

n1

1 minus ϕ2n

1113969

G22 v2( 11138571113877

(27)

where N is the complexity-accuracy trade-off parameterϕn cos((2n minus 1)π2N) u (a12a2)(ϕn + 1) v1 ((a1minus

a2)2a2)(ϕn + 1) and v2 ((2a1 minus a2)2a2) + ((12)ϕn)

G1(u) 1

1 + u

XYu2

a1 minus a2u( 11138572

1113971

middot K1

Xu

a1 minus a2u

1113971

⎛⎝ ⎞⎠K1

middot

Yu

a1 minus a2u

1113971

⎛⎝ ⎞⎠

G21 v1( 1113857 1

1 + v1

XZv21

a22

1113971

K1

Xv1

a2

1113971

⎛⎝ ⎞⎠K1

Zv1

a2

1113971

⎛⎝ ⎞⎠

G22 v2( 1113857 1

1 + v2

XZv22

a1 minus a2v2( 11138572

1113971

middot K1

Xv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠K1

middot

Zv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠

(28)

Proof of eorem 2 From (25) we calculate the ergodiccapacities at D1 (CD1

) and D2 (CD2) by replacing F(x) in (25)

by PD1out and P

D2out in (18) and (19) respectively 1erefore CD1

and CD2are calculated as

CD1

1ln 2

1113946infin

0

1 minus PD1out(x)

1 + xdx (29)

CD2

1ln 2

1113946infin

0

1 minus PD2out(x)

1 + xdx (30)

By applying the integral formulas in [32] we obtain theergodic capacities at D1 and D2 in (26) and (27) after somemathematical transforms In appendix B we provide thedetails of proof

4 Numerical Results

In this section the EH-FD-NOMA system performance interms of OP and ergodic capacity is plotted by using theexpressions in1eorem 1 and1eorem 2 In addition we alsoconduct the Monte-Carlo simulations on OP and ergodiccapacity to demonstrate the correctness of theoretical formulas1e system performance is evaluated for different values of theaverage SNR where SNR is the ratio between the transmit

power of PB and the variance of AWGN ie SNR Pσ2 Inour simulations we choose parameters for evaluating thesystem performance as follows the power allocation co-efficients are a1 065 and a2 035 the energy harvestingefficiency at each node is η 085 the average channel gainsΩ1 Ω2 Ω3 Ω5 1 andΩ4 071e simulation resultswere obtained by using 106 channel realizations

In Figure 3 we consider the OPs of both users D1 andD2 versus the average SNR In this figure we use theresults of 1eorem 1 to plot theoretical curves ((18) for D1and (19) for D2) with α 05 R 03 bitsHz and SIcancellation capability 1113957Ω minus 30 dB It is obvious that thesimulation curves exactly match with the theoretical onesAs can be seen from the figure OPs of both users have thesame performance and diversity order 1ey decreasewhen SNR increases On the contrary at high SNR regime(SNR gt 35 dB) the OPs of both users decrease slowly If wecontinuously increase SNR the OPs will go to outage floordue to the RSI and NOMA coefficients It is easy to seethat even if the RSI is very small and with high transmitpower at PB from (6) we have c

x1R ⟶ (a1a2) If the RSI is

larger the outage floor will be reached sooner 1ereforeit is necessary to apply various SI cancellation techniquesfor the FD mode to avoid performance loss of the FDcommunication systems

Figure 4 illustrates the throughput of the EH-FD-NOMAsystem versus average SNR with various data transmissionrates R 03 05 07 bitsHz It is also noted that thesystem throughput is defined by TD1

≜R(1 minus PD1out) and

TD2≜R(1 minus P

D2out) 1e other simulation parameters are the

same as those in Figure 3 Figure 4 shows that at low SNRregime (ie SNRlt 10 dB) with low data transmission rateieR 03 the throughput will reach the best value amongthree considered cases When SNR increases such as from14 to 26 dB the optimal throughput is obtained whenR 05 In the case of SNRgt 26 dB the system throughputreaches the maximal value with R 07 1ereforedepending on the transmit power at PB we can suitablychoose the data transmission rate for the considered systemto get the optimal throughput and improve the overallsystem performance

Figure 5 shows the impact of EH time-switching ratioα on the OPs of the considered system with R 03 bitsHz and 1113957Ω minus 30 dB As can be seen from the figure thereis an optimal value of α corresponding to a pretransmitpower of PB For example with SNR 20 dB the optimalvalue is α asymp 06 In the case of SNR 30 dB the value isα asymp 05 and in the case of SNR 40 dB α asymp 03 Conse-quently based on the transmit power at PB we can adjustthe EH time-switching ratio in order to improve thesystem performance

Figure 6 illustrates the ergodic capacity of both usersunder the impact of SI cancellation capability with1113957Ω minus 30 minus 20 and minus 10 dB In this figure the theoreticalcurves are plotted by using equations (26) and (27) in1eorem 2 while the marker symbols are plotted byMonte-Carlo simulations It is obvious that the ergodiccapacity increases when SNR increases especially when

6 Wireless Communications and Mobile Computing

RSI is small such as 1113957Ω minus 30 dB In the case of 1113957Ω minus 30 dBthe ergodic capacity at both users increases about 06 bitsHz comparing with the case of 1113957Ω minus 10 dB 1e gain forthe system capacity is about 12 bitsHz Figure 6 showsthe strong impact of RSI on the capacity of the consideredsystem 1us to deploy this system in realistic scenarioswireless researchers and designers need to design circuitsand build algorithms in order to improve the SIcancellation

Finally Figure 7 plots the ergodic capacities of theEH-FD-NOMA system with various time durations of αin the case of 1113957Ω minus 30 dB 1is figure shows that the

ergodic capacities of users D1 and D2 increase when αincreases For example the ergodic capacity in the case ofα 07 is the best capacity compared with the case of α

03 and α 05 However at high SNR such asSNR 40 dB the ergodic capacities of three consideredcases are the same 1e results in Figure 7 are compatiblewith those in Figure 5 By combining Figures 5 and 7 wecan clearly see that when SNRlt 30 dB we choose α 07to get the best performance and best capacity of theconsidered system

5 10 15 20 250 35 4030Average SNR (dB)

0

01

02

03

04

05

06

Thro

ughp

ut (b

its

Hz)

R = 07

R = 05

R = 03

Simulation D1Theory D1

Simulation D2Theory D2

Figure 4 1roughput of the EH-FD-NOMA system with variousdata transmission rates R 03 05 07 bitsHz

5 10 15 20 250 35 4030Average SNR (dB)

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

Simulation D1Theory D1

Simulation D2Theory D2

Figure 3 1e OPs at D1 and D2 versus the average SNR whenR 03 bitsHz 1113957Ω minus 30 dB and α 05

10ndash3

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

104 06 08020α

SNR = 20 30 40 dB

Simulation D1Theory D1

Simulation D2Theory D2

Figure 51e impact of EH time duration on the OPs at both userswith SNR 20 30 40 dB R 03 bitsHz and 1113957Ω minus 30 dB

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

Ω~ = ndash30 ndash20 ndash10dB

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 6 1e ergodic capacities of both users under the impact ofSI cancellation capability with α 05 and various levels of RSI

Wireless Communications and Mobile Computing 7

5 Conclusion

In this paper we propose a novel combination of threeadvanced techniques namely EH FD and NOMA in a so-

called EH-FD-NOMA communication system which can beapplied for V2V communication networks By mathematicalanalysis we derive exact expressions of outage probabilityand ergodic capacity at both users under the impact ofresidual self-interference at the FD relay node Our resultsshow that the two users can obtain the same performanceand capacity ie the fairness is guaranteed Depending onthe transmit power at the power beacon there is an optimalvalue for EH time-switching ratio to minimize the outageprobability and maximize the capacity Furthermore theimpact of data transmission rate residual self-interferencelevel and time-switching factor α is also investigated Nu-merical results demonstrate the importance of self-and-successive-interference cancellation on the performance ofthe considered system 1ose results serve as importantreferences for wireless researchers and designers in de-ployment of the EH-FD-NOMA system in practice

Appendix

A Proof of Theorem 1

In this appendix we provide step-by-step procedure of howto derive the expressions of outage probability at both usersof the proposed EH-FD-NOMA system over Rayleigh fadingchannels

For PD1out from (20) we calculate Pr c

x1R lt x1113864 1113865 in (A1) and

Pr cx1D1ltx1113966 1113967 in (A2) as follows

Pr cx1R lt x1113864 1113865 Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

1113946infin

0Fρ1

cRSI + σ2( 1113857(1 minus α)x

ηαP a1 minus a2x( 1113857ρ31113888 1113889fρ3 ρ3( 1113857dρ3 1113946

infin

01 minus exp minus

cRSI + σ2( 1113857(1 minus α)x

Ω1ηαP a1 minus a2x( 1113857ρ31113888 11138891113890 1113891

1Ω3

exp minusρ3Ω3

1113888 1113889dρ3

1 minus

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

K1

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A1)

Pr cx1D1ltx1113966 1113967 Pr ηαP a1 minus a2x( 1113857ρ2ρ4 lt σ

2(1 minus α)x1113966 1113967

1113946infin

0Fρ2

σ2(1 minus α)x

ηαP a1 minus a2x( 1113857ρ41113888 1113889fρ4 ρ4( 1113857dρ4 1113946

infin

01 minus exp minus

σ2(1 minus α)x

Ω2ηαP a1 minus a2x( 1113857ρ41113888 11138891113890 1113891

1Ω4

exp minusρ4Ω4

1113888 1113889dρ4

1 minus

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

K1

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Yx

a1 minus a2x

1113971

K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A2)

It is noted that in the case of a1 minus a2xle 0 the proba-bilities in (A1) and (A2) always occur 1ereforePr c

x1R lt x1113864 1113865 1 and Pr c

x1D1ltx1113966 1113967 1 which lead to P

D1out 1

After doing some algebras and applying [30 33241] wederive Pr c

x1R ltx1113864 1113865 and Pr c

x1D1lt x1113966 1113967 at the end of (A1) and

(A2) By substituting (A1) and (A2) into (20) we obtainPD1out in (18) in 1eorem 1For P

D2out based on the equation (21) we can calculate

Pr min(cx1R c

x2R )lt x1113864 1113865 as in (A3) and Pr min(c

SICx1D2

1113882 cx2D2

)

lt x as in (A4)

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

α = 03 05 07

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 7 1e impact of the EH time duration on the ergodicperformance of the EH-FD-NOMA system versus the average SNRfor different values of α α 03 05 07 and 1113957Ω minus 30 dB

8 Wireless Communications and Mobile Computing

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

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Submit your manuscripts atwwwhindawicom

From (3) the SI at R is calculated by

E 1113957hRR1113868111386811138681113868

11138681113868111386811138682PR1113882 1113883

ηαP

1 minus αE 1113957hRR

111386811138681113868111386811138681113868111386811138682ρ21113882 1113883 (4)

In FD devices various SI cancellation techniques canbe applied to reduce the effect of RSI on the systemperformance such as isolation propagation domain anddigital and analog cancellation In fact the relay defi-nitely knows the transmit signal xR so by using theresults of SI channel estimation of 1113957hRR it can apply digitalprocessing methods to subtract the SI from the receivedsignals [22ndash25] However due to the hardware impairmentand the imperfect estimation of the SI channel SI may stillexist in the system after applying various SI cancellationmethods and degrade the system performance Typically theRSI which is denoted by IR can be modeled by the complexGaussian distribution [23 25ndash28] with zero-mean and var-iance cRSI where cRSI 1113957Ω(ηαP)(1 minus α) It is also noted that1113957Ω denotes the SI cancellation capability of the relay nodeAfter SI cancellation (3) becomes

yR hSRa1PS

1113968x1 +

a2PS

1113968x2( 1113857 + IR + zR (5)

From (5) SINR (signal-to-interference-plus-noise ra-tio) to detect the message x1 at R (denoted by c

x1R ) is

calculated as

cx1R

hSR1113868111386811138681113868

11138681113868111386811138682a1PS

hSR1113868111386811138681113868

11138681113868111386811138682a2PS + cRSI + σ2

a1ηαPρ1ρ3

a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

(6)

where ρ3 |hSR|2 is the channel gain from S⟶ RAfter detecting x1 R removes all x1rsquos components from

received signals and then detect x2 1us SINR to detectmessage x2 at R (denoted by c

x2R ) is given by

cx2R

a2ηαPρ1ρ3cRSI + σ2( 1113857(1 minus α)

middot (7)

Due to the FD mode during the time duration of(1 minus α)T R transmits the signals to both destinations D1 andD2 We assume that the delay caused by signal processing atthe relay is equal to one symbol period 1erefore thetransmitted signals at R are the received signals in theprevious period after processing 1en the received signalsat D1 and D2 are respectively given by

yD1 hRD1

a1PR

1113968x1 +

a2PR

1113968x2( 1113857 + z1 (8)

yD2 hRD2

a1PR

1113968x1 +

a2PR

1113968x2( 1113857 + z2 (9)

where hRD1and hRD2

are fading coefficients of channels fromR⟶ D1 and R⟶ D1 respectively and z1 and z2 are theAWGN terms with zero-mean and variance of σ2 iez1simCN(0 σ2) and z2simCN(0 σ2)

By the principle of NOMA systems the far user (user 1denoted by D1 in our paper) decodes its own message whileuser 2rsquos message is considered as interference 1e near user(user 2 or D2 in this paper) first subtracts the signal of the

user D1 through successive interference cancellation (SIC) toremove the interference from the far user D1 1en it de-codes its own message In this paper we assume that D2 canperfectly remove interference After that the received signalat D2 from (9) can be rewritten as

yD2 hRD2

a2PR

1113968x2 + z2 (10)

From equations (8)ndash(10) SINRs at D1 and D2 can becalculated as

cx1D1

hRD1

11138681113868111386811138681113868

111386811138681113868111386811138682a1PR

hRD1

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR + σ2

a1ηαPρ2ρ4

a2ηαPρ2ρ4 + σ2(1 minus α)

cSICx1D2

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a1PR

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR + σ2

a1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)

cx2D2

hRD2

11138681113868111386811138681113868

111386811138681113868111386811138682a2PR

σ2

a2ηαPρ2ρ5σ2(1 minus α)

(11)

where ρ4 |hRD1|2 and ρ5 |hRD2

|2 are the channel gains ofthe links R⟶ D1 and R⟶ D2 respectively

It is also noted that for DF relaying protocol the end-to-end SINR is calculated as

ce2e min cR cD1113864 1113865 (12)

1erefore the end-to-end SINRs at D1 and D2 can bewritten as follows

cD1 min c

x1R c

x1D1

1113966 1113967 (13)

cD2 min c

x1R c

x2R c

SICx1D2

cx2D2

1113882 1113883 (14)

3 Performance Analysis

31 Outage Probability Analysis In this section the outageprobability of the considered EH-FD-NOMA system is de-rived to evaluate the system performance 1e system OP isthe probability that makes the instantaneous SINR fallingbelow a predefined threshold [29] To derive OPs for thissystem let R1 and R2 (bitsHz) be the minimum requireddata rates for the users D1 and D2 respectively By assumingthe fairness of the users in this systems we setR1 R2 R1en OP at D1 denoted by P

D1out can be calculated as

PD1out Pr (1 minus α)log2 1 + cD1

1113872 1113873ltR1113966 1113967 Pr cD1lt 2R(1minus α)

minus 11113966 1113967

(15)

where cD1is derived in (13) Let x 2R(1minus α) minus 1 be the SINR

threshold 1en the expression (15) can be rewritten as

PD1out Pr cD1

ltx1113966 1113967 (16)

At destination D2 the outage occurs when it does notdecode successfully the signal x1 or its own message x21erefore we have

4 Wireless Communications and Mobile Computing

PD2out Pr cD2

ltx1113966 1113967 Pr min cx1R c

x2R c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

Pr min min cx1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877ltx1113882 1113883

(17)

Theorem 1 e OPs at D1 (PD1out) and D2 (P

D2out) of the

cooperative EH-FD-NOMA system under the impact of RSIover Rayleigh fading channel are determined respectively asfollows

PD1out

1 minus

XYx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xlta1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(18)

PD2out

1 minus

XZx2

a22

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

1 minus

XZx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠a1

a2minus 1le xlt

a1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)

where X (4(cRSI + σ2)(1 minus α))(Ω1Ω3ηαP) Y (4σ2(1minus

α))(Ω2Ω4ηαP) and Z (4σ2(1 minus α))(Ω2Ω5ηαP) HereΩi E ρi1113864 1113865 where Ωi and ρi denote the average and in-stantaneous channel gains of the Rayleigh fading channelrespectively (i 1 2 5) E denotes the expectation op-erator and K1(middot) is the first-order modified Bessel function ofthe second kind [30]

Proof of eorem 1 To calculate PD1out and P

D2out from

equations (16) and (17) we apply the probability rule in [31]to get

PD1out Pr min c

x1R c

x1D1

1113872 1113873ltx1113966 1113967 Pr cx1R ltx1113864 1113865 + Pr c

x1D1ltx1113966 1113967

minus Pr cx1R ltx1113864 1113865Pr c

x1D1ltx1113966 1113967

(20)

PD2out Pr min min c

x1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877lt x1113882 1113883

Pr min cx1R c

x2R( 1113857lt x1113864 1113865 + Pr min c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

minus Pr min cx1R c

x2R( 1113857lt x1113864 1113865Pr min c

SICx1D2

cx2D2

1113874 1113875ltx1113882 1113883

(21)

On the contrary the cumulative distribution functions(CDFs) Fρi

(x) and probability distribution functions (PDFs)of the Rayleigh distribution fρi

(x) can be determined asfollows

Fρi(x) 1 minus exp minus

x

Ωi

1113888 1113889 xge 0 (22)

fρi(x)

1Ωi

exp minusx

Ωi

1113888 1113889 xge 0 (23)

By using equations (20)ndash(23) and doing some algebraswe can derive (18) and (19) in 1eorem 1 For details of theproof see in appendix A

32 Ergodic Capacity Analysis 1e ergodic capacity of theFD relay system is calculated by

C E log2(1 + c)1113864 1113865 1113946infin

0log2(1 + c)fc(c)dc (24)

where c is the end-to-end SINR of the considered systemand fc(c) is the PDF of c To derive the closed-form ex-pression of the ergodic capacity of the system we rewrite(24) after some algebras as

C 1ln 2

1113946infin

0

1 minus F(x)

1 + xdx (25)

where F(x) is the CDF of the end-to-end SINR of theconsidered system

Theorem 2 e ergodic capacities of both users D1 and D2are respectively given by

Wireless Communications and Mobile Computing 5

CD1

a1π2Na2ln 2

1113944N

n1

1 minus ϕ2n1113969

G1(u) (26)

CD2

π2Nln2

1113876a1 minus a2

a21113944

N

n1

1 minus ϕ2n1113969

G21 v1( 1113857

+ 1113944N

n1

1 minus ϕ2n

1113969

G22 v2( 11138571113877

(27)

where N is the complexity-accuracy trade-off parameterϕn cos((2n minus 1)π2N) u (a12a2)(ϕn + 1) v1 ((a1minus

a2)2a2)(ϕn + 1) and v2 ((2a1 minus a2)2a2) + ((12)ϕn)

G1(u) 1

1 + u

XYu2

a1 minus a2u( 11138572

1113971

middot K1

Xu

a1 minus a2u

1113971

⎛⎝ ⎞⎠K1

middot

Yu

a1 minus a2u

1113971

⎛⎝ ⎞⎠

G21 v1( 1113857 1

1 + v1

XZv21

a22

1113971

K1

Xv1

a2

1113971

⎛⎝ ⎞⎠K1

Zv1

a2

1113971

⎛⎝ ⎞⎠

G22 v2( 1113857 1

1 + v2

XZv22

a1 minus a2v2( 11138572

1113971

middot K1

Xv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠K1

middot

Zv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠

(28)

Proof of eorem 2 From (25) we calculate the ergodiccapacities at D1 (CD1

) and D2 (CD2) by replacing F(x) in (25)

by PD1out and P

D2out in (18) and (19) respectively 1erefore CD1

and CD2are calculated as

CD1

1ln 2

1113946infin

0

1 minus PD1out(x)

1 + xdx (29)

CD2

1ln 2

1113946infin

0

1 minus PD2out(x)

1 + xdx (30)

By applying the integral formulas in [32] we obtain theergodic capacities at D1 and D2 in (26) and (27) after somemathematical transforms In appendix B we provide thedetails of proof

4 Numerical Results

In this section the EH-FD-NOMA system performance interms of OP and ergodic capacity is plotted by using theexpressions in1eorem 1 and1eorem 2 In addition we alsoconduct the Monte-Carlo simulations on OP and ergodiccapacity to demonstrate the correctness of theoretical formulas1e system performance is evaluated for different values of theaverage SNR where SNR is the ratio between the transmit

power of PB and the variance of AWGN ie SNR Pσ2 Inour simulations we choose parameters for evaluating thesystem performance as follows the power allocation co-efficients are a1 065 and a2 035 the energy harvestingefficiency at each node is η 085 the average channel gainsΩ1 Ω2 Ω3 Ω5 1 andΩ4 071e simulation resultswere obtained by using 106 channel realizations

In Figure 3 we consider the OPs of both users D1 andD2 versus the average SNR In this figure we use theresults of 1eorem 1 to plot theoretical curves ((18) for D1and (19) for D2) with α 05 R 03 bitsHz and SIcancellation capability 1113957Ω minus 30 dB It is obvious that thesimulation curves exactly match with the theoretical onesAs can be seen from the figure OPs of both users have thesame performance and diversity order 1ey decreasewhen SNR increases On the contrary at high SNR regime(SNR gt 35 dB) the OPs of both users decrease slowly If wecontinuously increase SNR the OPs will go to outage floordue to the RSI and NOMA coefficients It is easy to seethat even if the RSI is very small and with high transmitpower at PB from (6) we have c

x1R ⟶ (a1a2) If the RSI is

larger the outage floor will be reached sooner 1ereforeit is necessary to apply various SI cancellation techniquesfor the FD mode to avoid performance loss of the FDcommunication systems

Figure 4 illustrates the throughput of the EH-FD-NOMAsystem versus average SNR with various data transmissionrates R 03 05 07 bitsHz It is also noted that thesystem throughput is defined by TD1

≜R(1 minus PD1out) and

TD2≜R(1 minus P

D2out) 1e other simulation parameters are the

same as those in Figure 3 Figure 4 shows that at low SNRregime (ie SNRlt 10 dB) with low data transmission rateieR 03 the throughput will reach the best value amongthree considered cases When SNR increases such as from14 to 26 dB the optimal throughput is obtained whenR 05 In the case of SNRgt 26 dB the system throughputreaches the maximal value with R 07 1ereforedepending on the transmit power at PB we can suitablychoose the data transmission rate for the considered systemto get the optimal throughput and improve the overallsystem performance

Figure 5 shows the impact of EH time-switching ratioα on the OPs of the considered system with R 03 bitsHz and 1113957Ω minus 30 dB As can be seen from the figure thereis an optimal value of α corresponding to a pretransmitpower of PB For example with SNR 20 dB the optimalvalue is α asymp 06 In the case of SNR 30 dB the value isα asymp 05 and in the case of SNR 40 dB α asymp 03 Conse-quently based on the transmit power at PB we can adjustthe EH time-switching ratio in order to improve thesystem performance

Figure 6 illustrates the ergodic capacity of both usersunder the impact of SI cancellation capability with1113957Ω minus 30 minus 20 and minus 10 dB In this figure the theoreticalcurves are plotted by using equations (26) and (27) in1eorem 2 while the marker symbols are plotted byMonte-Carlo simulations It is obvious that the ergodiccapacity increases when SNR increases especially when

6 Wireless Communications and Mobile Computing

RSI is small such as 1113957Ω minus 30 dB In the case of 1113957Ω minus 30 dBthe ergodic capacity at both users increases about 06 bitsHz comparing with the case of 1113957Ω minus 10 dB 1e gain forthe system capacity is about 12 bitsHz Figure 6 showsthe strong impact of RSI on the capacity of the consideredsystem 1us to deploy this system in realistic scenarioswireless researchers and designers need to design circuitsand build algorithms in order to improve the SIcancellation

Finally Figure 7 plots the ergodic capacities of theEH-FD-NOMA system with various time durations of αin the case of 1113957Ω minus 30 dB 1is figure shows that the

ergodic capacities of users D1 and D2 increase when αincreases For example the ergodic capacity in the case ofα 07 is the best capacity compared with the case of α

03 and α 05 However at high SNR such asSNR 40 dB the ergodic capacities of three consideredcases are the same 1e results in Figure 7 are compatiblewith those in Figure 5 By combining Figures 5 and 7 wecan clearly see that when SNRlt 30 dB we choose α 07to get the best performance and best capacity of theconsidered system

5 10 15 20 250 35 4030Average SNR (dB)

0

01

02

03

04

05

06

Thro

ughp

ut (b

its

Hz)

R = 07

R = 05

R = 03

Simulation D1Theory D1

Simulation D2Theory D2

Figure 4 1roughput of the EH-FD-NOMA system with variousdata transmission rates R 03 05 07 bitsHz

5 10 15 20 250 35 4030Average SNR (dB)

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

Simulation D1Theory D1

Simulation D2Theory D2

Figure 3 1e OPs at D1 and D2 versus the average SNR whenR 03 bitsHz 1113957Ω minus 30 dB and α 05

10ndash3

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

104 06 08020α

SNR = 20 30 40 dB

Simulation D1Theory D1

Simulation D2Theory D2

Figure 51e impact of EH time duration on the OPs at both userswith SNR 20 30 40 dB R 03 bitsHz and 1113957Ω minus 30 dB

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

Ω~ = ndash30 ndash20 ndash10dB

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 6 1e ergodic capacities of both users under the impact ofSI cancellation capability with α 05 and various levels of RSI

Wireless Communications and Mobile Computing 7

5 Conclusion

In this paper we propose a novel combination of threeadvanced techniques namely EH FD and NOMA in a so-

called EH-FD-NOMA communication system which can beapplied for V2V communication networks By mathematicalanalysis we derive exact expressions of outage probabilityand ergodic capacity at both users under the impact ofresidual self-interference at the FD relay node Our resultsshow that the two users can obtain the same performanceand capacity ie the fairness is guaranteed Depending onthe transmit power at the power beacon there is an optimalvalue for EH time-switching ratio to minimize the outageprobability and maximize the capacity Furthermore theimpact of data transmission rate residual self-interferencelevel and time-switching factor α is also investigated Nu-merical results demonstrate the importance of self-and-successive-interference cancellation on the performance ofthe considered system 1ose results serve as importantreferences for wireless researchers and designers in de-ployment of the EH-FD-NOMA system in practice

Appendix

A Proof of Theorem 1

In this appendix we provide step-by-step procedure of howto derive the expressions of outage probability at both usersof the proposed EH-FD-NOMA system over Rayleigh fadingchannels

For PD1out from (20) we calculate Pr c

x1R lt x1113864 1113865 in (A1) and

Pr cx1D1ltx1113966 1113967 in (A2) as follows

Pr cx1R lt x1113864 1113865 Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

1113946infin

0Fρ1

cRSI + σ2( 1113857(1 minus α)x

ηαP a1 minus a2x( 1113857ρ31113888 1113889fρ3 ρ3( 1113857dρ3 1113946

infin

01 minus exp minus

cRSI + σ2( 1113857(1 minus α)x

Ω1ηαP a1 minus a2x( 1113857ρ31113888 11138891113890 1113891

1Ω3

exp minusρ3Ω3

1113888 1113889dρ3

1 minus

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

K1

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A1)

Pr cx1D1ltx1113966 1113967 Pr ηαP a1 minus a2x( 1113857ρ2ρ4 lt σ

2(1 minus α)x1113966 1113967

1113946infin

0Fρ2

σ2(1 minus α)x

ηαP a1 minus a2x( 1113857ρ41113888 1113889fρ4 ρ4( 1113857dρ4 1113946

infin

01 minus exp minus

σ2(1 minus α)x

Ω2ηαP a1 minus a2x( 1113857ρ41113888 11138891113890 1113891

1Ω4

exp minusρ4Ω4

1113888 1113889dρ4

1 minus

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

K1

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Yx

a1 minus a2x

1113971

K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A2)

It is noted that in the case of a1 minus a2xle 0 the proba-bilities in (A1) and (A2) always occur 1ereforePr c

x1R lt x1113864 1113865 1 and Pr c

x1D1ltx1113966 1113967 1 which lead to P

D1out 1

After doing some algebras and applying [30 33241] wederive Pr c

x1R ltx1113864 1113865 and Pr c

x1D1lt x1113966 1113967 at the end of (A1) and

(A2) By substituting (A1) and (A2) into (20) we obtainPD1out in (18) in 1eorem 1For P

D2out based on the equation (21) we can calculate

Pr min(cx1R c

x2R )lt x1113864 1113865 as in (A3) and Pr min(c

SICx1D2

1113882 cx2D2

)

lt x as in (A4)

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

α = 03 05 07

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 7 1e impact of the EH time duration on the ergodicperformance of the EH-FD-NOMA system versus the average SNRfor different values of α α 03 05 07 and 1113957Ω minus 30 dB

8 Wireless Communications and Mobile Computing

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

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PD2out Pr cD2

ltx1113966 1113967 Pr min cx1R c

x2R c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

Pr min min cx1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877ltx1113882 1113883

(17)

Theorem 1 e OPs at D1 (PD1out) and D2 (P

D2out) of the

cooperative EH-FD-NOMA system under the impact of RSIover Rayleigh fading channel are determined respectively asfollows

PD1out

1 minus

XYx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xlta1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(18)

PD2out

1 minus

XZx2

a22

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

1 minus

XZx2

a1 minus a2x( 11138572

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠a1

a2minus 1le xlt

a1

a2

1 xgea1

a2

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(19)

where X (4(cRSI + σ2)(1 minus α))(Ω1Ω3ηαP) Y (4σ2(1minus

α))(Ω2Ω4ηαP) and Z (4σ2(1 minus α))(Ω2Ω5ηαP) HereΩi E ρi1113864 1113865 where Ωi and ρi denote the average and in-stantaneous channel gains of the Rayleigh fading channelrespectively (i 1 2 5) E denotes the expectation op-erator and K1(middot) is the first-order modified Bessel function ofthe second kind [30]

Proof of eorem 1 To calculate PD1out and P

D2out from

equations (16) and (17) we apply the probability rule in [31]to get

PD1out Pr min c

x1R c

x1D1

1113872 1113873ltx1113966 1113967 Pr cx1R ltx1113864 1113865 + Pr c

x1D1ltx1113966 1113967

minus Pr cx1R ltx1113864 1113865Pr c

x1D1ltx1113966 1113967

(20)

PD2out Pr min min c

x1R c

x2R( 1113857min c

SICx1D2

cx2D2

1113874 11138751113876 1113877lt x1113882 1113883

Pr min cx1R c

x2R( 1113857lt x1113864 1113865 + Pr min c

SICx1D2

cx2D2

1113874 1113875lt x1113882 1113883

minus Pr min cx1R c

x2R( 1113857lt x1113864 1113865Pr min c

SICx1D2

cx2D2

1113874 1113875ltx1113882 1113883

(21)

On the contrary the cumulative distribution functions(CDFs) Fρi

(x) and probability distribution functions (PDFs)of the Rayleigh distribution fρi

(x) can be determined asfollows

Fρi(x) 1 minus exp minus

x

Ωi

1113888 1113889 xge 0 (22)

fρi(x)

1Ωi

exp minusx

Ωi

1113888 1113889 xge 0 (23)

By using equations (20)ndash(23) and doing some algebraswe can derive (18) and (19) in 1eorem 1 For details of theproof see in appendix A

32 Ergodic Capacity Analysis 1e ergodic capacity of theFD relay system is calculated by

C E log2(1 + c)1113864 1113865 1113946infin

0log2(1 + c)fc(c)dc (24)

where c is the end-to-end SINR of the considered systemand fc(c) is the PDF of c To derive the closed-form ex-pression of the ergodic capacity of the system we rewrite(24) after some algebras as

C 1ln 2

1113946infin

0

1 minus F(x)

1 + xdx (25)

where F(x) is the CDF of the end-to-end SINR of theconsidered system

Theorem 2 e ergodic capacities of both users D1 and D2are respectively given by

Wireless Communications and Mobile Computing 5

CD1

a1π2Na2ln 2

1113944N

n1

1 minus ϕ2n1113969

G1(u) (26)

CD2

π2Nln2

1113876a1 minus a2

a21113944

N

n1

1 minus ϕ2n1113969

G21 v1( 1113857

+ 1113944N

n1

1 minus ϕ2n

1113969

G22 v2( 11138571113877

(27)

where N is the complexity-accuracy trade-off parameterϕn cos((2n minus 1)π2N) u (a12a2)(ϕn + 1) v1 ((a1minus

a2)2a2)(ϕn + 1) and v2 ((2a1 minus a2)2a2) + ((12)ϕn)

G1(u) 1

1 + u

XYu2

a1 minus a2u( 11138572

1113971

middot K1

Xu

a1 minus a2u

1113971

⎛⎝ ⎞⎠K1

middot

Yu

a1 minus a2u

1113971

⎛⎝ ⎞⎠

G21 v1( 1113857 1

1 + v1

XZv21

a22

1113971

K1

Xv1

a2

1113971

⎛⎝ ⎞⎠K1

Zv1

a2

1113971

⎛⎝ ⎞⎠

G22 v2( 1113857 1

1 + v2

XZv22

a1 minus a2v2( 11138572

1113971

middot K1

Xv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠K1

middot

Zv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠

(28)

Proof of eorem 2 From (25) we calculate the ergodiccapacities at D1 (CD1

) and D2 (CD2) by replacing F(x) in (25)

by PD1out and P

D2out in (18) and (19) respectively 1erefore CD1

and CD2are calculated as

CD1

1ln 2

1113946infin

0

1 minus PD1out(x)

1 + xdx (29)

CD2

1ln 2

1113946infin

0

1 minus PD2out(x)

1 + xdx (30)

By applying the integral formulas in [32] we obtain theergodic capacities at D1 and D2 in (26) and (27) after somemathematical transforms In appendix B we provide thedetails of proof

4 Numerical Results

In this section the EH-FD-NOMA system performance interms of OP and ergodic capacity is plotted by using theexpressions in1eorem 1 and1eorem 2 In addition we alsoconduct the Monte-Carlo simulations on OP and ergodiccapacity to demonstrate the correctness of theoretical formulas1e system performance is evaluated for different values of theaverage SNR where SNR is the ratio between the transmit

power of PB and the variance of AWGN ie SNR Pσ2 Inour simulations we choose parameters for evaluating thesystem performance as follows the power allocation co-efficients are a1 065 and a2 035 the energy harvestingefficiency at each node is η 085 the average channel gainsΩ1 Ω2 Ω3 Ω5 1 andΩ4 071e simulation resultswere obtained by using 106 channel realizations

In Figure 3 we consider the OPs of both users D1 andD2 versus the average SNR In this figure we use theresults of 1eorem 1 to plot theoretical curves ((18) for D1and (19) for D2) with α 05 R 03 bitsHz and SIcancellation capability 1113957Ω minus 30 dB It is obvious that thesimulation curves exactly match with the theoretical onesAs can be seen from the figure OPs of both users have thesame performance and diversity order 1ey decreasewhen SNR increases On the contrary at high SNR regime(SNR gt 35 dB) the OPs of both users decrease slowly If wecontinuously increase SNR the OPs will go to outage floordue to the RSI and NOMA coefficients It is easy to seethat even if the RSI is very small and with high transmitpower at PB from (6) we have c

x1R ⟶ (a1a2) If the RSI is

larger the outage floor will be reached sooner 1ereforeit is necessary to apply various SI cancellation techniquesfor the FD mode to avoid performance loss of the FDcommunication systems

Figure 4 illustrates the throughput of the EH-FD-NOMAsystem versus average SNR with various data transmissionrates R 03 05 07 bitsHz It is also noted that thesystem throughput is defined by TD1

≜R(1 minus PD1out) and

TD2≜R(1 minus P

D2out) 1e other simulation parameters are the

same as those in Figure 3 Figure 4 shows that at low SNRregime (ie SNRlt 10 dB) with low data transmission rateieR 03 the throughput will reach the best value amongthree considered cases When SNR increases such as from14 to 26 dB the optimal throughput is obtained whenR 05 In the case of SNRgt 26 dB the system throughputreaches the maximal value with R 07 1ereforedepending on the transmit power at PB we can suitablychoose the data transmission rate for the considered systemto get the optimal throughput and improve the overallsystem performance

Figure 5 shows the impact of EH time-switching ratioα on the OPs of the considered system with R 03 bitsHz and 1113957Ω minus 30 dB As can be seen from the figure thereis an optimal value of α corresponding to a pretransmitpower of PB For example with SNR 20 dB the optimalvalue is α asymp 06 In the case of SNR 30 dB the value isα asymp 05 and in the case of SNR 40 dB α asymp 03 Conse-quently based on the transmit power at PB we can adjustthe EH time-switching ratio in order to improve thesystem performance

Figure 6 illustrates the ergodic capacity of both usersunder the impact of SI cancellation capability with1113957Ω minus 30 minus 20 and minus 10 dB In this figure the theoreticalcurves are plotted by using equations (26) and (27) in1eorem 2 while the marker symbols are plotted byMonte-Carlo simulations It is obvious that the ergodiccapacity increases when SNR increases especially when

6 Wireless Communications and Mobile Computing

RSI is small such as 1113957Ω minus 30 dB In the case of 1113957Ω minus 30 dBthe ergodic capacity at both users increases about 06 bitsHz comparing with the case of 1113957Ω minus 10 dB 1e gain forthe system capacity is about 12 bitsHz Figure 6 showsthe strong impact of RSI on the capacity of the consideredsystem 1us to deploy this system in realistic scenarioswireless researchers and designers need to design circuitsand build algorithms in order to improve the SIcancellation

Finally Figure 7 plots the ergodic capacities of theEH-FD-NOMA system with various time durations of αin the case of 1113957Ω minus 30 dB 1is figure shows that the

ergodic capacities of users D1 and D2 increase when αincreases For example the ergodic capacity in the case ofα 07 is the best capacity compared with the case of α

03 and α 05 However at high SNR such asSNR 40 dB the ergodic capacities of three consideredcases are the same 1e results in Figure 7 are compatiblewith those in Figure 5 By combining Figures 5 and 7 wecan clearly see that when SNRlt 30 dB we choose α 07to get the best performance and best capacity of theconsidered system

5 10 15 20 250 35 4030Average SNR (dB)

0

01

02

03

04

05

06

Thro

ughp

ut (b

its

Hz)

R = 07

R = 05

R = 03

Simulation D1Theory D1

Simulation D2Theory D2

Figure 4 1roughput of the EH-FD-NOMA system with variousdata transmission rates R 03 05 07 bitsHz

5 10 15 20 250 35 4030Average SNR (dB)

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

Simulation D1Theory D1

Simulation D2Theory D2

Figure 3 1e OPs at D1 and D2 versus the average SNR whenR 03 bitsHz 1113957Ω minus 30 dB and α 05

10ndash3

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

104 06 08020α

SNR = 20 30 40 dB

Simulation D1Theory D1

Simulation D2Theory D2

Figure 51e impact of EH time duration on the OPs at both userswith SNR 20 30 40 dB R 03 bitsHz and 1113957Ω minus 30 dB

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

Ω~ = ndash30 ndash20 ndash10dB

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 6 1e ergodic capacities of both users under the impact ofSI cancellation capability with α 05 and various levels of RSI

Wireless Communications and Mobile Computing 7

5 Conclusion

In this paper we propose a novel combination of threeadvanced techniques namely EH FD and NOMA in a so-

called EH-FD-NOMA communication system which can beapplied for V2V communication networks By mathematicalanalysis we derive exact expressions of outage probabilityand ergodic capacity at both users under the impact ofresidual self-interference at the FD relay node Our resultsshow that the two users can obtain the same performanceand capacity ie the fairness is guaranteed Depending onthe transmit power at the power beacon there is an optimalvalue for EH time-switching ratio to minimize the outageprobability and maximize the capacity Furthermore theimpact of data transmission rate residual self-interferencelevel and time-switching factor α is also investigated Nu-merical results demonstrate the importance of self-and-successive-interference cancellation on the performance ofthe considered system 1ose results serve as importantreferences for wireless researchers and designers in de-ployment of the EH-FD-NOMA system in practice

Appendix

A Proof of Theorem 1

In this appendix we provide step-by-step procedure of howto derive the expressions of outage probability at both usersof the proposed EH-FD-NOMA system over Rayleigh fadingchannels

For PD1out from (20) we calculate Pr c

x1R lt x1113864 1113865 in (A1) and

Pr cx1D1ltx1113966 1113967 in (A2) as follows

Pr cx1R lt x1113864 1113865 Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

1113946infin

0Fρ1

cRSI + σ2( 1113857(1 minus α)x

ηαP a1 minus a2x( 1113857ρ31113888 1113889fρ3 ρ3( 1113857dρ3 1113946

infin

01 minus exp minus

cRSI + σ2( 1113857(1 minus α)x

Ω1ηαP a1 minus a2x( 1113857ρ31113888 11138891113890 1113891

1Ω3

exp minusρ3Ω3

1113888 1113889dρ3

1 minus

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

K1

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A1)

Pr cx1D1ltx1113966 1113967 Pr ηαP a1 minus a2x( 1113857ρ2ρ4 lt σ

2(1 minus α)x1113966 1113967

1113946infin

0Fρ2

σ2(1 minus α)x

ηαP a1 minus a2x( 1113857ρ41113888 1113889fρ4 ρ4( 1113857dρ4 1113946

infin

01 minus exp minus

σ2(1 minus α)x

Ω2ηαP a1 minus a2x( 1113857ρ41113888 11138891113890 1113891

1Ω4

exp minusρ4Ω4

1113888 1113889dρ4

1 minus

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

K1

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Yx

a1 minus a2x

1113971

K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A2)

It is noted that in the case of a1 minus a2xle 0 the proba-bilities in (A1) and (A2) always occur 1ereforePr c

x1R lt x1113864 1113865 1 and Pr c

x1D1ltx1113966 1113967 1 which lead to P

D1out 1

After doing some algebras and applying [30 33241] wederive Pr c

x1R ltx1113864 1113865 and Pr c

x1D1lt x1113966 1113967 at the end of (A1) and

(A2) By substituting (A1) and (A2) into (20) we obtainPD1out in (18) in 1eorem 1For P

D2out based on the equation (21) we can calculate

Pr min(cx1R c

x2R )lt x1113864 1113865 as in (A3) and Pr min(c

SICx1D2

1113882 cx2D2

)

lt x as in (A4)

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

α = 03 05 07

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 7 1e impact of the EH time duration on the ergodicperformance of the EH-FD-NOMA system versus the average SNRfor different values of α α 03 05 07 and 1113957Ω minus 30 dB

8 Wireless Communications and Mobile Computing

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

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AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

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Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

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Shock and Vibration

Hindawiwwwhindawicom Volume 2018

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Electrical and Computer Engineering

Journal of

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CD1

a1π2Na2ln 2

1113944N

n1

1 minus ϕ2n1113969

G1(u) (26)

CD2

π2Nln2

1113876a1 minus a2

a21113944

N

n1

1 minus ϕ2n1113969

G21 v1( 1113857

+ 1113944N

n1

1 minus ϕ2n

1113969

G22 v2( 11138571113877

(27)

where N is the complexity-accuracy trade-off parameterϕn cos((2n minus 1)π2N) u (a12a2)(ϕn + 1) v1 ((a1minus

a2)2a2)(ϕn + 1) and v2 ((2a1 minus a2)2a2) + ((12)ϕn)

G1(u) 1

1 + u

XYu2

a1 minus a2u( 11138572

1113971

middot K1

Xu

a1 minus a2u

1113971

⎛⎝ ⎞⎠K1

middot

Yu

a1 minus a2u

1113971

⎛⎝ ⎞⎠

G21 v1( 1113857 1

1 + v1

XZv21

a22

1113971

K1

Xv1

a2

1113971

⎛⎝ ⎞⎠K1

Zv1

a2

1113971

⎛⎝ ⎞⎠

G22 v2( 1113857 1

1 + v2

XZv22

a1 minus a2v2( 11138572

1113971

middot K1

Xv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠K1

middot

Zv2

a1 minus a2v2

1113971

⎛⎝ ⎞⎠

(28)

Proof of eorem 2 From (25) we calculate the ergodiccapacities at D1 (CD1

) and D2 (CD2) by replacing F(x) in (25)

by PD1out and P

D2out in (18) and (19) respectively 1erefore CD1

and CD2are calculated as

CD1

1ln 2

1113946infin

0

1 minus PD1out(x)

1 + xdx (29)

CD2

1ln 2

1113946infin

0

1 minus PD2out(x)

1 + xdx (30)

By applying the integral formulas in [32] we obtain theergodic capacities at D1 and D2 in (26) and (27) after somemathematical transforms In appendix B we provide thedetails of proof

4 Numerical Results

In this section the EH-FD-NOMA system performance interms of OP and ergodic capacity is plotted by using theexpressions in1eorem 1 and1eorem 2 In addition we alsoconduct the Monte-Carlo simulations on OP and ergodiccapacity to demonstrate the correctness of theoretical formulas1e system performance is evaluated for different values of theaverage SNR where SNR is the ratio between the transmit

power of PB and the variance of AWGN ie SNR Pσ2 Inour simulations we choose parameters for evaluating thesystem performance as follows the power allocation co-efficients are a1 065 and a2 035 the energy harvestingefficiency at each node is η 085 the average channel gainsΩ1 Ω2 Ω3 Ω5 1 andΩ4 071e simulation resultswere obtained by using 106 channel realizations

In Figure 3 we consider the OPs of both users D1 andD2 versus the average SNR In this figure we use theresults of 1eorem 1 to plot theoretical curves ((18) for D1and (19) for D2) with α 05 R 03 bitsHz and SIcancellation capability 1113957Ω minus 30 dB It is obvious that thesimulation curves exactly match with the theoretical onesAs can be seen from the figure OPs of both users have thesame performance and diversity order 1ey decreasewhen SNR increases On the contrary at high SNR regime(SNR gt 35 dB) the OPs of both users decrease slowly If wecontinuously increase SNR the OPs will go to outage floordue to the RSI and NOMA coefficients It is easy to seethat even if the RSI is very small and with high transmitpower at PB from (6) we have c

x1R ⟶ (a1a2) If the RSI is

larger the outage floor will be reached sooner 1ereforeit is necessary to apply various SI cancellation techniquesfor the FD mode to avoid performance loss of the FDcommunication systems

Figure 4 illustrates the throughput of the EH-FD-NOMAsystem versus average SNR with various data transmissionrates R 03 05 07 bitsHz It is also noted that thesystem throughput is defined by TD1

≜R(1 minus PD1out) and

TD2≜R(1 minus P

D2out) 1e other simulation parameters are the

same as those in Figure 3 Figure 4 shows that at low SNRregime (ie SNRlt 10 dB) with low data transmission rateieR 03 the throughput will reach the best value amongthree considered cases When SNR increases such as from14 to 26 dB the optimal throughput is obtained whenR 05 In the case of SNRgt 26 dB the system throughputreaches the maximal value with R 07 1ereforedepending on the transmit power at PB we can suitablychoose the data transmission rate for the considered systemto get the optimal throughput and improve the overallsystem performance

Figure 5 shows the impact of EH time-switching ratioα on the OPs of the considered system with R 03 bitsHz and 1113957Ω minus 30 dB As can be seen from the figure thereis an optimal value of α corresponding to a pretransmitpower of PB For example with SNR 20 dB the optimalvalue is α asymp 06 In the case of SNR 30 dB the value isα asymp 05 and in the case of SNR 40 dB α asymp 03 Conse-quently based on the transmit power at PB we can adjustthe EH time-switching ratio in order to improve thesystem performance

Figure 6 illustrates the ergodic capacity of both usersunder the impact of SI cancellation capability with1113957Ω minus 30 minus 20 and minus 10 dB In this figure the theoreticalcurves are plotted by using equations (26) and (27) in1eorem 2 while the marker symbols are plotted byMonte-Carlo simulations It is obvious that the ergodiccapacity increases when SNR increases especially when

6 Wireless Communications and Mobile Computing

RSI is small such as 1113957Ω minus 30 dB In the case of 1113957Ω minus 30 dBthe ergodic capacity at both users increases about 06 bitsHz comparing with the case of 1113957Ω minus 10 dB 1e gain forthe system capacity is about 12 bitsHz Figure 6 showsthe strong impact of RSI on the capacity of the consideredsystem 1us to deploy this system in realistic scenarioswireless researchers and designers need to design circuitsand build algorithms in order to improve the SIcancellation

Finally Figure 7 plots the ergodic capacities of theEH-FD-NOMA system with various time durations of αin the case of 1113957Ω minus 30 dB 1is figure shows that the

ergodic capacities of users D1 and D2 increase when αincreases For example the ergodic capacity in the case ofα 07 is the best capacity compared with the case of α

03 and α 05 However at high SNR such asSNR 40 dB the ergodic capacities of three consideredcases are the same 1e results in Figure 7 are compatiblewith those in Figure 5 By combining Figures 5 and 7 wecan clearly see that when SNRlt 30 dB we choose α 07to get the best performance and best capacity of theconsidered system

5 10 15 20 250 35 4030Average SNR (dB)

0

01

02

03

04

05

06

Thro

ughp

ut (b

its

Hz)

R = 07

R = 05

R = 03

Simulation D1Theory D1

Simulation D2Theory D2

Figure 4 1roughput of the EH-FD-NOMA system with variousdata transmission rates R 03 05 07 bitsHz

5 10 15 20 250 35 4030Average SNR (dB)

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

Simulation D1Theory D1

Simulation D2Theory D2

Figure 3 1e OPs at D1 and D2 versus the average SNR whenR 03 bitsHz 1113957Ω minus 30 dB and α 05

10ndash3

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

104 06 08020α

SNR = 20 30 40 dB

Simulation D1Theory D1

Simulation D2Theory D2

Figure 51e impact of EH time duration on the OPs at both userswith SNR 20 30 40 dB R 03 bitsHz and 1113957Ω minus 30 dB

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

Ω~ = ndash30 ndash20 ndash10dB

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 6 1e ergodic capacities of both users under the impact ofSI cancellation capability with α 05 and various levels of RSI

Wireless Communications and Mobile Computing 7

5 Conclusion

In this paper we propose a novel combination of threeadvanced techniques namely EH FD and NOMA in a so-

called EH-FD-NOMA communication system which can beapplied for V2V communication networks By mathematicalanalysis we derive exact expressions of outage probabilityand ergodic capacity at both users under the impact ofresidual self-interference at the FD relay node Our resultsshow that the two users can obtain the same performanceand capacity ie the fairness is guaranteed Depending onthe transmit power at the power beacon there is an optimalvalue for EH time-switching ratio to minimize the outageprobability and maximize the capacity Furthermore theimpact of data transmission rate residual self-interferencelevel and time-switching factor α is also investigated Nu-merical results demonstrate the importance of self-and-successive-interference cancellation on the performance ofthe considered system 1ose results serve as importantreferences for wireless researchers and designers in de-ployment of the EH-FD-NOMA system in practice

Appendix

A Proof of Theorem 1

In this appendix we provide step-by-step procedure of howto derive the expressions of outage probability at both usersof the proposed EH-FD-NOMA system over Rayleigh fadingchannels

For PD1out from (20) we calculate Pr c

x1R lt x1113864 1113865 in (A1) and

Pr cx1D1ltx1113966 1113967 in (A2) as follows

Pr cx1R lt x1113864 1113865 Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

1113946infin

0Fρ1

cRSI + σ2( 1113857(1 minus α)x

ηαP a1 minus a2x( 1113857ρ31113888 1113889fρ3 ρ3( 1113857dρ3 1113946

infin

01 minus exp minus

cRSI + σ2( 1113857(1 minus α)x

Ω1ηαP a1 minus a2x( 1113857ρ31113888 11138891113890 1113891

1Ω3

exp minusρ3Ω3

1113888 1113889dρ3

1 minus

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

K1

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A1)

Pr cx1D1ltx1113966 1113967 Pr ηαP a1 minus a2x( 1113857ρ2ρ4 lt σ

2(1 minus α)x1113966 1113967

1113946infin

0Fρ2

σ2(1 minus α)x

ηαP a1 minus a2x( 1113857ρ41113888 1113889fρ4 ρ4( 1113857dρ4 1113946

infin

01 minus exp minus

σ2(1 minus α)x

Ω2ηαP a1 minus a2x( 1113857ρ41113888 11138891113890 1113891

1Ω4

exp minusρ4Ω4

1113888 1113889dρ4

1 minus

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

K1

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Yx

a1 minus a2x

1113971

K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A2)

It is noted that in the case of a1 minus a2xle 0 the proba-bilities in (A1) and (A2) always occur 1ereforePr c

x1R lt x1113864 1113865 1 and Pr c

x1D1ltx1113966 1113967 1 which lead to P

D1out 1

After doing some algebras and applying [30 33241] wederive Pr c

x1R ltx1113864 1113865 and Pr c

x1D1lt x1113966 1113967 at the end of (A1) and

(A2) By substituting (A1) and (A2) into (20) we obtainPD1out in (18) in 1eorem 1For P

D2out based on the equation (21) we can calculate

Pr min(cx1R c

x2R )lt x1113864 1113865 as in (A3) and Pr min(c

SICx1D2

1113882 cx2D2

)

lt x as in (A4)

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

α = 03 05 07

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 7 1e impact of the EH time duration on the ergodicperformance of the EH-FD-NOMA system versus the average SNRfor different values of α α 03 05 07 and 1113957Ω minus 30 dB

8 Wireless Communications and Mobile Computing

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

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Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

RSI is small such as 1113957Ω minus 30 dB In the case of 1113957Ω minus 30 dBthe ergodic capacity at both users increases about 06 bitsHz comparing with the case of 1113957Ω minus 10 dB 1e gain forthe system capacity is about 12 bitsHz Figure 6 showsthe strong impact of RSI on the capacity of the consideredsystem 1us to deploy this system in realistic scenarioswireless researchers and designers need to design circuitsand build algorithms in order to improve the SIcancellation

Finally Figure 7 plots the ergodic capacities of theEH-FD-NOMA system with various time durations of αin the case of 1113957Ω minus 30 dB 1is figure shows that the

ergodic capacities of users D1 and D2 increase when αincreases For example the ergodic capacity in the case ofα 07 is the best capacity compared with the case of α

03 and α 05 However at high SNR such asSNR 40 dB the ergodic capacities of three consideredcases are the same 1e results in Figure 7 are compatiblewith those in Figure 5 By combining Figures 5 and 7 wecan clearly see that when SNRlt 30 dB we choose α 07to get the best performance and best capacity of theconsidered system

5 10 15 20 250 35 4030Average SNR (dB)

0

01

02

03

04

05

06

Thro

ughp

ut (b

its

Hz)

R = 07

R = 05

R = 03

Simulation D1Theory D1

Simulation D2Theory D2

Figure 4 1roughput of the EH-FD-NOMA system with variousdata transmission rates R 03 05 07 bitsHz

5 10 15 20 250 35 4030Average SNR (dB)

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

Simulation D1Theory D1

Simulation D2Theory D2

Figure 3 1e OPs at D1 and D2 versus the average SNR whenR 03 bitsHz 1113957Ω minus 30 dB and α 05

10ndash3

10ndash2

10ndash1

100

Out

age p

roba

bilit

y (O

P)

104 06 08020α

SNR = 20 30 40 dB

Simulation D1Theory D1

Simulation D2Theory D2

Figure 51e impact of EH time duration on the OPs at both userswith SNR 20 30 40 dB R 03 bitsHz and 1113957Ω minus 30 dB

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

Ω~ = ndash30 ndash20 ndash10dB

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 6 1e ergodic capacities of both users under the impact ofSI cancellation capability with α 05 and various levels of RSI

Wireless Communications and Mobile Computing 7

5 Conclusion

In this paper we propose a novel combination of threeadvanced techniques namely EH FD and NOMA in a so-

called EH-FD-NOMA communication system which can beapplied for V2V communication networks By mathematicalanalysis we derive exact expressions of outage probabilityand ergodic capacity at both users under the impact ofresidual self-interference at the FD relay node Our resultsshow that the two users can obtain the same performanceand capacity ie the fairness is guaranteed Depending onthe transmit power at the power beacon there is an optimalvalue for EH time-switching ratio to minimize the outageprobability and maximize the capacity Furthermore theimpact of data transmission rate residual self-interferencelevel and time-switching factor α is also investigated Nu-merical results demonstrate the importance of self-and-successive-interference cancellation on the performance ofthe considered system 1ose results serve as importantreferences for wireless researchers and designers in de-ployment of the EH-FD-NOMA system in practice

Appendix

A Proof of Theorem 1

In this appendix we provide step-by-step procedure of howto derive the expressions of outage probability at both usersof the proposed EH-FD-NOMA system over Rayleigh fadingchannels

For PD1out from (20) we calculate Pr c

x1R lt x1113864 1113865 in (A1) and

Pr cx1D1ltx1113966 1113967 in (A2) as follows

Pr cx1R lt x1113864 1113865 Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

1113946infin

0Fρ1

cRSI + σ2( 1113857(1 minus α)x

ηαP a1 minus a2x( 1113857ρ31113888 1113889fρ3 ρ3( 1113857dρ3 1113946

infin

01 minus exp minus

cRSI + σ2( 1113857(1 minus α)x

Ω1ηαP a1 minus a2x( 1113857ρ31113888 11138891113890 1113891

1Ω3

exp minusρ3Ω3

1113888 1113889dρ3

1 minus

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

K1

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A1)

Pr cx1D1ltx1113966 1113967 Pr ηαP a1 minus a2x( 1113857ρ2ρ4 lt σ

2(1 minus α)x1113966 1113967

1113946infin

0Fρ2

σ2(1 minus α)x

ηαP a1 minus a2x( 1113857ρ41113888 1113889fρ4 ρ4( 1113857dρ4 1113946

infin

01 minus exp minus

σ2(1 minus α)x

Ω2ηαP a1 minus a2x( 1113857ρ41113888 11138891113890 1113891

1Ω4

exp minusρ4Ω4

1113888 1113889dρ4

1 minus

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

K1

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Yx

a1 minus a2x

1113971

K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A2)

It is noted that in the case of a1 minus a2xle 0 the proba-bilities in (A1) and (A2) always occur 1ereforePr c

x1R lt x1113864 1113865 1 and Pr c

x1D1ltx1113966 1113967 1 which lead to P

D1out 1

After doing some algebras and applying [30 33241] wederive Pr c

x1R ltx1113864 1113865 and Pr c

x1D1lt x1113966 1113967 at the end of (A1) and

(A2) By substituting (A1) and (A2) into (20) we obtainPD1out in (18) in 1eorem 1For P

D2out based on the equation (21) we can calculate

Pr min(cx1R c

x2R )lt x1113864 1113865 as in (A3) and Pr min(c

SICx1D2

1113882 cx2D2

)

lt x as in (A4)

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

α = 03 05 07

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 7 1e impact of the EH time duration on the ergodicperformance of the EH-FD-NOMA system versus the average SNRfor different values of α α 03 05 07 and 1113957Ω minus 30 dB

8 Wireless Communications and Mobile Computing

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

5 Conclusion

In this paper we propose a novel combination of threeadvanced techniques namely EH FD and NOMA in a so-

called EH-FD-NOMA communication system which can beapplied for V2V communication networks By mathematicalanalysis we derive exact expressions of outage probabilityand ergodic capacity at both users under the impact ofresidual self-interference at the FD relay node Our resultsshow that the two users can obtain the same performanceand capacity ie the fairness is guaranteed Depending onthe transmit power at the power beacon there is an optimalvalue for EH time-switching ratio to minimize the outageprobability and maximize the capacity Furthermore theimpact of data transmission rate residual self-interferencelevel and time-switching factor α is also investigated Nu-merical results demonstrate the importance of self-and-successive-interference cancellation on the performance ofthe considered system 1ose results serve as importantreferences for wireless researchers and designers in de-ployment of the EH-FD-NOMA system in practice

Appendix

A Proof of Theorem 1

In this appendix we provide step-by-step procedure of howto derive the expressions of outage probability at both usersof the proposed EH-FD-NOMA system over Rayleigh fadingchannels

For PD1out from (20) we calculate Pr c

x1R lt x1113864 1113865 in (A1) and

Pr cx1D1ltx1113966 1113967 in (A2) as follows

Pr cx1R lt x1113864 1113865 Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

1113946infin

0Fρ1

cRSI + σ2( 1113857(1 minus α)x

ηαP a1 minus a2x( 1113857ρ31113888 1113889fρ3 ρ3( 1113857dρ3 1113946

infin

01 minus exp minus

cRSI + σ2( 1113857(1 minus α)x

Ω1ηαP a1 minus a2x( 1113857ρ31113888 11138891113890 1113891

1Ω3

exp minusρ3Ω3

1113888 1113889dρ3

1 minus

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

K1

4 cRSI + σ2( 1113857(1 minus α)x

Ω1Ω3ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A1)

Pr cx1D1ltx1113966 1113967 Pr ηαP a1 minus a2x( 1113857ρ2ρ4 lt σ

2(1 minus α)x1113966 1113967

1113946infin

0Fρ2

σ2(1 minus α)x

ηαP a1 minus a2x( 1113857ρ41113888 1113889fρ4 ρ4( 1113857dρ4 1113946

infin

01 minus exp minus

σ2(1 minus α)x

Ω2ηαP a1 minus a2x( 1113857ρ41113888 11138891113890 1113891

1Ω4

exp minusρ4Ω4

1113888 1113889dρ4

1 minus

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

K1

4σ2(1 minus α)x

Ω2Ω4ηαP a1 minus a2x( 1113857

1113971

⎛⎝ ⎞⎠ 1 minus

Yx

a1 minus a2x

1113971

K1

Yx

a1 minus a2x

1113971

⎛⎝ ⎞⎠

(A2)

It is noted that in the case of a1 minus a2xle 0 the proba-bilities in (A1) and (A2) always occur 1ereforePr c

x1R lt x1113864 1113865 1 and Pr c

x1D1ltx1113966 1113967 1 which lead to P

D1out 1

After doing some algebras and applying [30 33241] wederive Pr c

x1R ltx1113864 1113865 and Pr c

x1D1lt x1113966 1113967 at the end of (A1) and

(A2) By substituting (A1) and (A2) into (20) we obtainPD1out in (18) in 1eorem 1For P

D2out based on the equation (21) we can calculate

Pr min(cx1R c

x2R )lt x1113864 1113865 as in (A3) and Pr min(c

SICx1D2

1113882 cx2D2

)

lt x as in (A4)

0

05

1

15

2

25

3

35

Ergo

dic c

apac

ity

0 10 20 30 40ndash10Average SNR (dB)

α = 03 05 07

Simulation D1Theory D1Simulation D2

Theory D2Simulation C1 + C2Theory C1 + C2

Figure 7 1e impact of the EH time duration on the ergodicperformance of the EH-FD-NOMA system versus the average SNRfor different values of α α 03 05 07 and 1113957Ω minus 30 dB

8 Wireless Communications and Mobile Computing

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

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Submit your manuscripts atwwwhindawicom

Pr min cx1R c

x2R( 1113857ltx1113864 1113865 Pr min

a1ηαPρ1ρ3a2ηαPρ1ρ3 + cRSI + σ2( 1113857(1 minus α)

a2ηαPρ1ρ3

cRSI + σ2( 1113857(1 minus α)1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ1ρ3 ηαPa2ρ1ρ3( 1113857lt cRSI + σ21113872 1113873(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ1ρ3 lt cRSI + σ2( 1113857(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

1 minus

Xx

a1 minus a2x

1113971

K1

Xx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Xx

a2

1113971

K1

Xx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A3)

Pr min cSICx1D2

cx2D2

1113874 1113875lt x1113882 1113883 Pr mina1ηαPρ2ρ5

a2ηαPρ2ρ5 + σ2(1 minus α)a2ηαPρ2ρ5σ2(1 minus α)

1113888 1113889ltx1113896 1113897

Pr min ηαP a1 minus a2x( 1113857ρ2ρ5 ηαPa2ρ2ρ5( 1113857lt σ2(1 minus α)x1113966 1113967

Pr ηαP a1 minus a2x( 1113857ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xgea1

a2minus 1

Pr ηαPa2ρ2ρ5 lt σ2(1 minus α)x1113864 1113865 xlta1

a2minus 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1 minus

Zx

a1 minus a2x

1113971

K1

Zx

a1 minus a2x

1113971

⎛⎝ ⎞⎠ xgea1

a2minus 1

1 minus

Zx

a2

1113971

K1

Zx

a2

1113971

⎛⎝ ⎞⎠ xlta1

a2minus 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(A4)

It is also noted that when a1 minus a2xle 0 we always havePD2out 1 In the case of a1 minus a2xle a2 we have

xge (a1a2) minus 1 that means min(ηαP(a1 minus a2x)ρ1ρ3ηαPa2ρ1ρ3) ηαP(a1 minus a2x)ρ1ρ3 Otherwise we havemin(ηαP(a1 minus a2x)ρ1ρ3 ηαPa2ρ1ρ3) ηαPa2ρ1ρ3 1ere-fore we can transform the second line to the third line of(A3) and (A4) After doing some algebraic manipulationsand using [30 33241] we obtain the final expressions ofPr min(c

x1R c

x2R )ltx1113864 1113865 in the last line of (A3) and

Pr min(cSICx1D2

cx2D2

)ltx1113882 1113883 in the last line of (A4) After thatwe can substitute (A3) and (A4) into (21) to achieve (19) asin 1eorem 1

1e proof is complete

B Proof of Theorem 2

1is appendix is used to provide the detailed proof of1eorem 2 From (29) and (30) we have

CD1

1ln 2

1113946a1a2

0

XYx2 a1 minus a2x( 11138572

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Yx a1 minus a2x( 1113857

1113969

1113874 1113875

1 + xdx

(B1)

CD2

1ln 2

1113946a1a2minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

+1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

(B2)

Wireless Communications and Mobile Computing 9

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Due to the complexity of equations (B1) and (B2) it isdifficult to derive the closed-form expressions for ergodiccapacity at both users In this case we apply the

GaussianndashChebyshev quadrature method in [32] to obtainthe ergodic capacity for both users

1e first and second terms in (B2) are respectivelycalculated as

1ln 2

1113946a1a2( )minus 1

0

XZx2a2

2( 1113857

1113969K1

Xxa2( 1113857

1113969

1113874 1113875K1

Zxa2( 1113857

1113969

1113874 1113875

1 + xdx

π a1 minus a2( 1113857

2Na2ln 21113944n1

N

1 minus ϕ2n1113969

G21 v1( 1113857 (B3)

1ln 2

1113946a1a2

a1a2( )minus 1

XZx2 a1 minus a2x( 11138572

1113872 1113873

1113969

K1

Xx a1 minus a2x( 1113857

1113969

1113874 1113875K1

Zx a1 minus a2x( 1113857( 1113857

1113969

1113874 1113875

1 + xdx

π2Nln 2

1113944n1

N

1 minus ϕ2n1113969

G22 v2( 1113857

(B4)

By substituting (B3) and (B4) into (B2) we obtain thecapacity of user D2 as in (27) Similarly the capacity of userD1 is obtained as in (26)

1e proof is complete

Data Availability

1e simulation data used to support the findings of thisstudy are included within the article

Conflicts of Interest

1e authors declare that they have no conflicts of interest

Acknowledgments

1is research is funded by the VietnamNational Foundationfor Science and Technology Development (NAFOSTED)under grant number 10204-2017317

References

[1] S Hong J Brand J Choi et al ldquoApplications of self-in-terference cancellation in 5G and beyondrdquo IEEE Communi-cations Magazine vol 52 no 2 pp 114ndash121 2014

[2] Q C Li H Niu A T Papathanassiou and G Wu ldquo5Gnetwork capacity key elements and technologiesrdquo IEEEVehicular Technology Magazine vol 9 no 1 pp 71ndash78 2014

[3] B C Nguyen T M Hoang and L T Dung ldquoPerformanceanalysis of vehicle-to-vehicle communication with full-duplexamplify-and-forward relay over double-Rayleigh fadingchannelsrdquo Vehicular Communications vol 19 Article ID100166 2019

[4] O Abbasi and A Ebrahimi ldquoCooperative noma with full-duplex amplify-and-forward relayingrdquo Transactions onEmerging Telecommunications Technologies vol 29 no 7p e3421 2018

[5] Y Alsaba C Y Leow and S K Abdul Rahim ldquoFull-duplexcooperative non-orthogonal multiple access with beam-forming and energy harvestingrdquo IEEE Access vol 6pp 19726ndash19738 2018

[6] X Yue Y Liu S Kang A Nallanathan and Z DingldquoExploiting fullhalf-duplex user relaying in noma systemsrdquoIEEE Transactions on Communications vol 66 no 2pp 560ndash575 2017

[7] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66no 5 pp 4467ndash4471 2017

[8] G Chen P Xiao J R Kelly B Li and R Tafazolli ldquoFull-duplex wireless-powered relay in two way cooperative net-worksrdquo IEEE Access vol 5 pp 1548ndash1558 2017

[9] T M Hoang V Van Son N C Dinh and P T HiepldquoOptimizing duration of energy harvesting for downlinknoma full-duplex over nakagami-m fading channelrdquo AEU-international Journal of Electronics and Communicationsvol 95 pp 199ndash206 2018

[10] B C Nguyen T M Hoang and P T Tran ldquoPerformanceanalysis of full-duplex decode-and-forward relay system withenergy harvesting over nakagami-m fading channelsrdquo AEU-International Journal of Electronics and Communicationsvol 98 pp 114ndash122 2019

[11] T N Nguyen P T Tran and M Voznak ldquoPower splitting-based energy-harvesting protocol for wireless-poweredcommunication networks with a bidirectional relayrdquo In-ternational Journal of Communication Systems vol 31 no 13p e3721 2018

[12] S Mondal S Dhar Roy and S Kundu ldquoPrimary behav-iour-based energy harvesting multihop cognitive radionetworkrdquo IET Communications vol 11 no 16 pp 2466ndash2475 2017

[13] M R Camana P V Tuan and I Koo ldquoOptimised powerallocation for a power beacon-assisted swipt system witha power-splitting receiverrdquo International Journal of Elec-tronics vol 106 no 3 pp 415ndash439 2019

[14] N P Le ldquoOutage probability analysis in power-beaconassisted energy harvesting cognitive relay wireless networksrdquoWireless Communications and Mobile Computing vol 2017Article ID 2019404 15 pages 2017

[15] S-L Wang and T-M Wu ldquoStochastic geometric perfor-mance analyses for the cooperative noma with the full-duplexenergy harvesting relayingrdquo IEEE Transactions on VehicularTechnology vol 68 no 5 pp 4894ndash4905 2019

[16] C Guo L Zhao C Feng Z Ding and H-H Chen ldquoEnergyharvesting enabled noma systems with full-duplex relayingrdquoIEEE Transactions on Vehicular Technology vol 68 no 7pp 7179ndash7183 2019

[17] X Zhang and F Wang ldquoResource allocation for wirelesspower transmission over full-duplex ofdmanoma mobilewireless networksrdquo IEEE Journal on Selected Areas in Com-munications vol 37 no 2 pp 327ndash344 2019

10 Wireless Communications and Mobile Computing

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[18] A H Gazestani S A Ghorashi B Mousavinasab andM Shikh-Bahaei ldquoA survey on implementation and appli-cations of full duplex wireless communicationsrdquo PhysicalCommunication vol 34 pp 121ndash134 2019

[19] X Lu P Wang D Niyato D I Kim and Z Han ldquoWirelessnetworks with rf energy harvesting a contemporary surveyrdquoIEEE Communications Surveys and Tutorials vol 17 no 2pp 757ndash789 2015

[20] C Zhong H A Suraweera G Zheng I Krikidis andZ Zhang ldquoWireless information and power transfer with fullduplex relayingrdquo IEEE Transactions on Communicationsvol 62 no 10 pp 3447ndash3461 2014

[21] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11pp 4754ndash4767 2013

[22] B C Nguyen X N Tran and D T Tran ldquoPerformanceanalysis of in-band full-duplex amplify-and-forward relaysystem with direct linkrdquo in Proceedings of the 2018 2nd In-ternational Conference on Recent Advances in Signal Pro-cessing Telecommunications amp Computing (SigTelCom)pp 192ndash197 IEEE Ho Chi Minh Vietnam January 2018

[23] A Sabharwal P Schniter D Guo D W Bliss S Rangarajanand R Wichman ldquoIn-band full-duplex wireless challengesand opportunitiesrdquo IEEE Journal on Selected Areas in Com-munications vol 32 no 9 pp 1637ndash1652 2014

[24] K Yang H Cui L Song and Y Li ldquoEfficient full-duplexrelaying with joint antenna-relay selection and self-in-terference suppressionrdquo IEEE Transactions on WirelessCommunications vol 14 no 7 pp 3991ndash4005 2015

[25] X Li C Tepedelenlioglu and H Senol ldquoChannel estimationfor residual self-interference in full duplex amplify-and-for-ward two-way relaysrdquo IEEE Transactions on Wireless Com-munications vol 16 no 8 pp 4970ndash4983 2017

[26] B C Nguyen and X N Tran ldquoPerformance analysis of full-duplex amplify-and-forward relay system with hardwareimpairments and imperfect self-interference cancellationrdquoWireless Communications and Mobile Computing vol 2019Article ID 4946298 10 pages 2019

[27] X-X Nguyen D-T Do T M Hoang et al ldquoSystem per-formance of cooperative NOMA with full-duplex relay overnakagami-m fading channelsrdquo Mobile Information Systemsvol 2019 pp 1ndash12 2019

[28] X N Tran B C Nguyen andD T Tran ldquoOutage probability oftwo-way full-duplex relay system with hardware impairmentsrdquoin Proceedings of the 2019 3rd International Conference onRecent Advances in Signal Processing Telecommunications ampComputing (SigTelCom) pp 135ndash139 IEEE HaNoi VietnamMarch 2019

[29] A Goldsmith Wireless Communications Cambridge Uni-versity Press Cambridge UK 2005

[30] A Jeffrey and D Zwillinger Table of Integrals Series andProducts Academic Press Cambridge MA USA 2007

[31] A Leon-Garcia and A Leon-Garcia Probability Statisticsand Random Processes for Electrical Engineering PearsonPrentice Hall Upper Saddle River NJ USA 3rd edition 2008

[32] M Abramowitz and I A Stegun Handbook of MathematicalFunctions with Formulas Graphs and Mathematical TablesVol 9 Dover New York NY USA 1972

Wireless Communications and Mobile Computing 11

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom