wireless energy harvesting in a cognitive relay network

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2015.2504520, IEEETransactions on Wireless Communications

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Wireless Energy Harvesting in a Cognitive RelayNetwork

Yuanwei Liu, Student Member, IEEE, S. Ali Mousavifar, Student Member, IEEE, Yansha Deng, StudentMember, IEEE, Cyril Leung, Member, IEEE, Maged Elkashlan, Member, IEEE,

Abstract—Wireless energy harvesting is regarded as a promis-ing energy supply alternative for energy-constrained wirelessnetworks. In this paper, a new wireless energy harvesting protocolis proposed for an underlay cognitive relay network with multipleprimary user (PU) transceivers. In this protocol, the secondarynodes can harvest energy from the primary network (PN) whilesharing the licensed spectrum of the PN. In order to assessthe impact of different system parameters on the proposednetwork, we first derive an exact expression for the outageprobability for the secondary network (SN) subject to threeimportant power constraints: 1) the maximum transmit powerat the secondary source (SS) and at the secondary relay (SR), 2)the peak interference power permitted at each PU receiver, and3) the interference power from each PU transmitter to the SRand to the secondary destination (SD). To obtain practical designinsights into the impact of different parameters on successful datatransmission of the SN, we derive throughput expressions for boththe delay-sensitive and the delay-tolerant transmission modes.We also derive asymptotic closed-form expressions for the outageprobability and the delay-sensitive throughput and an asymptoticanalytical expression for the delay-tolerant throughput as thenumber of PU transceivers goes to infinity. The results showthat the outage probability improves when PU transmitters arelocated near SS and sufficiently far from SR and SD. Our resultsalso show that when the number of PU transmitters is large, thedetrimental effect of interference from PU transmitters outweighsthe benefits of energy harvested from the PU transmitters.

Index Terms—Cognitive relay network, energy harvesting,multiple primary user transceivers.

I. INTRODUCTION

Energy harvesting (EH), i.e., the process of extractingenergy from the surrounding environment, has been proposedas an alternative method to supply energy and to prolongthe lifetime of energy-constrained communication networks.A variety of harvestable energy sources such as heat, light,wave, and wind have been considered for EH in wirelessnetworks [1–3]. Recently, harvesting energy from ambientradio frequency (RF) signals has received increasing attentiondue to its convenience in providing energy self-sufficiency to alow power communication system [4]. With recent advances inthe technology of low power devices both in industry [5] andacademia [6, 7], it is expected that harvesting energy from RF

The review of this paper was coordinated by Dr. Mehmet Can Vuran.Y. Liu, Y. Deng, and M. Elkashlan are with the School of

Electronic Engineering and Computer Science, Queen Mary Universi-ty of London, London E1 4NS, UK (email: {yuanwei.liu, yansha.deng,maged.elkashlan}@qmul.ac.uk).

S. Ali Mousavifar and Cyril Leung are with the Department of Electricaland Computer Engineering, The University of British Columbia, VancouverV6T 1Z4, Canada (email: {seyedm, cleung}@ece.ubc.ca).

This work was supported in part by the Natural Sciences and EngineeringResearch Council (NSERC) of Canada under Grant RGPIN 1731-2013.

signals will provide a practically realizable solution for futureapplications, especially for networks with low power devicessuch as wireless sensor network (WSN) nodes [8, 9].

Wireless EH has been proposed in non-relay assisted as wellas relay assisted networks [10–14]. Two commonly used EHreceiver architectures, namely power splitting (PS) receiverand time switching (TS) receiver, are proposed and studiedin [10]. In a PS receiver, a fraction of the received signalpower is used to harvest energy and the remainder is usedto retrieve information. A TS receiver harvests energy fromthe received signal for a fraction of the time and retrievesthe information from the received signal the rest of the time[10]. The fundamental tradeoff between harvesting energy andtransmitting information in a non-relay assisted network overa variety of channel models is investigated in [11, 12]. Twopractical receivers based on PS are proposed and the rate ofinformation transfer and the harvested energy are studied in[13]. Inspired by the TS and PS receiver architectures, twoEH relaying protocols, namely time switching relay (TSR)protocol and power splitting relay (PSR) protocol, are pro-posed for an amplify-and-forward dual-hop network in [14],where the energy constrained relay node harvests energy fromRF signals of the source and uses the harvested energy toforward the information from the source to the destination. Thedelay-tolerant and delay-limited throughputs for EH relayingprotocols are analyzed in [14].

Cognitive radio (CR) is a promising technology which aimsto achieve better spectrum utilization [15]. Since point-to-pointcommunications in CR networks is well established in theexisting literature, recent research on CR mainly focused oncooperative relaying. In [16], a scenario with a single source-destination pair, assisted by a group of cognitive relay nodes,is considered. In [17], considering a relay selection criterion,the outage probability of cognitive relay networks is evaluated.It is also shown in [17] that the diversity order of selection incognitive relay networks is the same as in conventional relaynetworks. Note that the aforementioned works mainly considersingle primary transmitter and receiver. For the multiple pri-mary transmitters and receivers case, the outage performanceof cognitive relay networks with single antenna and multiple-input multiple-output (MIMO) is investigated in [18] and [19],respectively.

Recently, based on the advantages of the aforementionedtwo concepts, energy harvesting has been introduced to CRnetworks in [20–27]. In [20], EH and opportunistic spectrumaccess (OSA) are jointly studied, where OSA refers to aparadigm in which secondary users (SUs) utilize unused PUspectrum for transmissions. The throughput in a non-relay



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assisted CR with EH and overlay spectrum access is studiedin [21]. An optimal spectrum sensing policy which aimsto maximize the throughput subject to an energy constraintand a collision constraint is investigated in [22]. In [23], anoptimal mode selection policy is proposed to maximize totalthroughput in the cognitive radio network (CRN), where theSU switches between EH mode and OSA mode. In [24], thethroughput in an amplify-and-forward (AF) cognitive relaynetwork is maximized subject to transmission time and energyconstraints at the CRN. In [25], the sum of harvested powers atmultiple energy harvesting SU receivers in a MIMO underlayCR is maximized, subject to satisfying two constraints (i.e.,a target minimum-square-error at multiple CR informationreceivers and the peak interference power constraint at theprimary network receivers). In [26], the outage probabilityis analyzed for a non-relay assisted secondary network (SN)which shares the spectrum and harvests energy while assistinga primary transmission. The results in [26] show that the SNcan harvest sufficient energy from RF signals to relay theinformation for the primary network (PN) as well as transmitits own information. In [27], an EH protocol for a non-relayassisted SN in underlay CR with a single SU transmitter andmultiple energy-constrained SU receivers is studied.

A. Motivation and Contributions

The motivation behind adopting wireless energy harvestingin underlay spectrum sharing networks with multiple PUtransceivers can be described as follows: 1) From the perspec-tive of SU, the RF signal from the PUs can be regarded asa constant energy source due to the concurrent transmissionbetween the PN and the SN; 2) The transmit power at SUmust remain below a predetermined threshold due to theinterference power constraint from PN. This well matches thenotion of wireless energy harvesting as a promising techniquefor low-power devices due to the limitation of power transferefficiency; and 3) It is realistic to consider multiple PUtransceivers to operate simultaneously in a large scale CRnetwork. Increasing the number of PU transmitters increase theenergy harvested by the SU. However, as the number of PUtransmitters increases, the interference from PU transmitterson the SU also increases. Therefore, it is important to studythe tradeoff between the benefits of energy harvesting and theharmful effects of interference.

In this paper, we propose a wireless EH protocol for adecode-and-forward (DF) cognitive relay network with mul-tiple PU transceivers. With this protocol, both the energyconstrained SS and secondary relay (SR) nodes can harvestenergy from the RF signals of multiple PU transmitters tosupport information transmission. The impact of EH and PUinterference on the outage probability and the throughput inthe SN are studied.

The main contributions of this paper are summarized asfollows:

• We derive an exact expression for the system outageprobability in the cognitive relay network subject tothree power constraints: 1) the maximum transmit powerat SS and SR based on the harvested energy; 2) the

peak interference power at each PU receiver; and 3) theinterference power from multiple PU transmitters at SRand SD.

• We derive analytical expressions for the throughput bothin the delay-sensitive and the delay-tolerant transmissionmodes.

• We derive asymptotic closed-form expressions for theoutage probability and delay-sensitive throughput and anasymptotic expression for the delay-tolerant throughputas the number of PU transmitters and receivers goes toinfinity.

• We show that there exists an optimal number of PUtransceivers that achieves the minimum outage probabilityand the maximum throughput for the SN.

• We show that when the number of PU transmitters islarge, the negative impact caused by the interference fromthe PU transmitters outweighs the positive impact broughtby the EH from the PU transmitters at the SN.

B. Notation and Organization

The remainder of the paper is organized as follows. InSection II, we present the system model and assumptionsfor the EH relaying protocol. In Section III, we derive exactexpressions for the outage probability and the delay-tolerantand delay-sensitive throughputs. In Section IV, we deriveexact asymptotic expressions for the outage probability and thedelay-tolerant and delay-sensitive throughputs as the numberof PU transceivers goes to infinity. Illustrative results andconclusions are provided in Sections V and VI, respectively.

II. NETWORK MODEL

As shown in Fig. 1, we consider an underlay cognitiverelay network where an energy constrained SS transmits to anenergy sufficient SD through an energy constrained SR usingthe licensed PU spectrum. The primary network consists of Mprimary transmitters (PUtx) and N primary receivers (PUrx) 1.We assume that all PU transmitters are closely located in onecenter point and all PU receivers are closely located in anothercenter point [18, 19, 29]. We assume that there is no directlink between SS and SD due to deep fading [30, 31] and thecommunication between SS and SD can only be completedwith the help of SR [14]. Both of the SS and SR only usethe energy harvested from RF signals of PU transmitters. Weconsider a communication system with rechargeable storage a-bility at SS and SR. All the energy harvested during the energyharvesting time slot is used for information transmission [14,32]. From the implementation point of view, this rechargeablestorage unit can be a supercapacitor or a short-term/high-efficiency battery to support the switching between energyharvesting and information transmission [33]. Note that theSN shares the spectrum with the PN in an underlay paradigm,which means that secondary users can perform concurrenttransmission as long as the interference at PU does not exceeda peak permissible threshold, denoted by PI . Since thereis no sensing in an underlay paradigm, we assume that the

1We assume that PU receivers apply multi-user detectors to cancelinterference from different PU transmitters [28].



3

SRh1 h2

f1, j

g1, i

f2 , j f3, j

g2, i

PUrx

SS SD

SN

PUtx

PN

TX1

TX2

TXN RX

2

RX1 RX

M

Fig. 1. System model of the energy harvesting cognitive radio system. TheEH links, interference links, and information links are illustrated with thedashed, dotted, and solid lines, respectively.

energy required to receive/process information is negligiblecompared to the energy required for information transmission[14, 34, 35]. We consider interference-limited case where theinterference power caused by PU transmitters at SR and SDis dominant relative to the noise power [18]. All channels areassumed to be quasi-static Rayleigh fading channels where thechannel coefficients are constant for each transmission blockbut vary independently between different blocks.

As shown in Fig. 1, we denote the channel gain coefficientsfrom SS and SR to the ith PUrx by g1,i and g2,i fori = 1, 2, . . . ,M , respectively. We denote the channel gaincoefficients from SS to SR and from SR to SD by h1 andh2, respectively. And the channel gain coefficients from thejth PUtx to SS, SR, and SD, are denoted by f1,j , f2,j , andf3,j for j = 1, 2, , . . . , N , respectively. We denote the distancebetween the jth PUtx and SS, SR, and SD as d1,j , d2,j , andd3,j , respectively. The distance between SS and SR and theith PUrx are denoted as d4,i and d5,i, respectively. And thedistances between SS and SR and between SR to SD aredenoted as d6 and d7, respectively. The link gain realizations|h1|2, |h2|2, |g1,i|2, |g2,i|2, |f1,j |2, |f2,j |2, and |f3,j |2 areexponentially distributed with parameters λ1, λ2, ω1,i, ω2,i,ν1,j , ν2,j , and ν3,j , respectively; for example, λ1 = d−m

6 ,where m is the path loss factor. The link gains from the PUtransmitters to the SS are assumed to be identically distributedas well as those to the SR and SD [18], i.e., ν1,j = ν1,ν2,j = ν2, and ν3,j = ν3 for j = 1, 2, . . . , N . Similarly,the link gains from SS to the PU receivers are assumed tobe identically distributed as well as those from SR to PUreceivers, i.e., ω1,i = ω1, ω2,i = ω2 for i = 1, 2, . . . ,M .2

As shown in Fig. 2, the SS and SR harvest energy fromRF signals of PU transmitters for a duration of αT at thebeginning of each energy harvesting-information transmission(EH-IT) time slot, where T is the duration of one EH-IT timeslot and 0 < α < 1. We assume that regardless of how muchenergy is harvested at SS and SR in the EH time slot, they canstore it in a storage device (e.g., a supercapacitor or a short-

2To keep the analysis tractable, shadow fading is not considered in thispaper.

term/high-efficiency battery). Subsequent to the harvesting pe-riod, SS transmits information to SR for a duration β(1−α)T ,where 0 < β < 1. Then, SR forwards the information to SDfor a duration of (1− β)(1−α)T . For simplicity, we assumeβ = 1

2 in this network.

SR Harvests energy

SR Receives theInformation from SS

SR Transmits theInformation to SD

(a)

(b)

Tα 2/)1( Tα−2/)1( Tα−

SS Harvests energy

SS transmits theInformation to SR

Fig. 2. (a) illustrates the protocol at SS in one EH-IT time slot and (b)illustrates the protocol at SR in one EH-IT time slot.

The energy harvested using the TS receiver architecture atSS and SR are given by 3

Ehs = ηPPUtx

N∑j=1

|f1,j |2αT, (1)

and

Ehr = ηPPUtx

N∑j=1

|f2,j |2αT, (2)

respectively, where 0 < η < 1 is the energy conversionefficiency [35], and PPUtx is the transmit power of all PUtransmitters). We consider constant transmit power of SSand SR during the IT time slot, therefore, the maximumpowers that SS and SR can transmit at based on the harvestedenergy are Ehs

(1−α)T/2 and Ehr

(1−α)T/2 , respectively. Therefore,the transmit power at SS and SR are given by

Ps = min(Ehs

(1− α)T/2,

PI

max |g1,i|2), (3)

andPr = min(

Ehr

(1− α)T/2,

PI

max |g2,i|2), (4)

respectively.As the SS and SR share the same spectrum with the PUs,

the transmitted signals from SS and SR cause interference toeach PUrx. Constraints on the transmit power of SS and SRare imposed in order that the interference power to the PUdoes not exceed PI .

Then signal to interference ratio (SIR) at SR and SD areobtained as

ΓR = min(ρZ1,PI

Y1)X1

Z2, (5)

and

ΓD = min(ρZ2,PI

Y2)X2

Z3, (6)

3In this work, we assume that the power that can be transferred to SS andSR is greater than the activation threshold and the energy harvesting circuitsat SS and SR are always activated.



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respectively, where ρ = 2ηα(1−α) , X1 = |h1|2, X2 =

|h2|2, Z1 =∑N

j=1 PPUtx |f1,j |2, Z2 =∑N

j=1 PPUtx |f2,j |2,Z3 =

∑Nj=1 PPUtx |f3,j |2, Y1 = max

i=1,...,M|g1,k|2, and Y2 =

maxi=1,...,M

|g2,k|2. Note that ΓR and ΓD are dependent random

variables because they both are functions of Z2.

III. EXACT PERFORMANCE ANALYSIS

In this section, we derive expressions for the outage proba-bility and throughput for the secondary network with the pro-posed energy harvesting protocol. These expressions providepractical design insights into the impact of various parameterson the performance of the secondary network.

A. Outage Probability

The outage probability Pout, is defined as the probabilitythat the equivalent SIR at each hop is below a threshold value,γth. In our paper, the DF relay assisted spectrum sharingnetwork is considered to be in outage if only one of the linksis suffering from an outage, i.e.,

Pout(γth) = 1− Pr{ΓR ≥ γth,ΓD ≥ γth}, (7)

where ΓR and ΓD denote the SIR RVs at SR and SD, and aregiven in (5) and (6), respectively.

To facilitate the outage probability, we first derive thecumulative distribution function (CDF) and the probabili-ty distribution function (PDF) of Zp, p ∈ {1, 2, 3} and Yq ,q ∈ {1, 2}. Note that each Zp is the sum of N independentexponential RVs and its distribution is chi-square distribution.The PDF and CDF of Zp are expressed as

fZp(zp) =zN−1p e

− zpPPUtx

νp

Γ(N)(PPUtxνp)N, (8)

and

FZp(zp) =Γ(N,

zpPPUtxνp

)

Γ(N), (9)

respectively, where Γ(.) and Γ(.,.) denote the gamma andincomplete gamma functions, respectively. The PDF and CDFof Yq are expressed as

fYq (yq) =M

ωq

M−1∑k

(M − 1

k

)(−1)ke

−( k+1ωq

)yq , (10)

and

FYq (yq) = (1− e− yq

ωq )M , (11)

respectively. We assume that the distances between the PUtransmitters are relatively smaller than the distances betweenthe PU transmitters and SS, SR, and SD. The same assumptionis used for PU receivers with respect to SS, SR, and SD.

The exact expression for the outage probability is given inthe following theorem.

Theorem 1. The outage probability of the SN with theproposed energy harvesting protocol is given by

Pout(γth) =1−∫ ∞

0

(JR,I + JR,II)

× (JD,I + JD,II)zN−12 e

− z2PPUtx

ν2

Γ(N)(PPUtxν2)Ndz2, (12)

where JR,I , JR,II , JD,I , and JD,II are defined in Ap-pendix A.

Proof: See Appendix A.

B. Throughput

In this section, we evaluate the throughput in two transmis-sion modes: delay-sensitive mode and delay-tolerant mode.The evaluation of throughput provides insight into practicalimplementations and challenges of EH cognitive relay net-work.

1) Delay-sensitive Transmission: In this mode, SS trans-mits information to SR at a fixed rate, denoted by Rds, whereRds , log2(1+ γth). The throughput in delay-sensitive modeis expressed as [14]

τds =(1−α)T

2

TRds(1− Pout(γth))

=(1− α)

2Rds(1− Pout(γth)), (13)

where τds is equal to the rate of the successful transmissionsduring the transmission time, (1−α)T

2 , when SIR requirement(γth) is satisfied at SR and SD. Note, the system outageprobability is obtained from (12).

2) Delay-Tolerant Transmission: In this mode, users cantransmit messages reliably while the transmission rate is lessthan or equal to the ergodic capacity Cerg, which is definedas [36]

Cerg = E{log2(1 + Γth)},

where E{.} denotes the expected value of an argument andΓth is a random variable defined as γth = min(γR, γD). Weobtain delay-tolerant throughput, denoted by τdt, as

τdt =(1−α)T

2

TCerg =

(1− α)

2ln2

∫ ∞

0

1− FΓth(x)

(1 + x)dx, (14)

where FΓth(γth) denotes the CDF of γth and it can be

evaluated by (12), i.e., FΓth(γth) = Pout(γth). In contrast

to delay-sensitive mode, where SS is expected to transmit ata fixed rate to satisfy a certain outage probability, in delay-tolerant transmission mode, SS can transmit at any rate equalor less than the evaluated ergodic capacity.

IV. LARGE SYSTEM ANALYSIS

In this section, we analyze the outage probability, the delay-sensitive throughput, and the delay-tolerant throughput as thenumber of PU transceivers grows to infinity. As N increases,more interference imposed on SR and SD may cause outages.On the other hand, as N increases, SS and SR can poten-tially harvest more energy from multiple PU transmitters. In



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addition, as M increases, SS and SR can impose interferenceat more number of the PU receivers. The tradeoff betweenthe positive impact brought by the energy harvesting frommultiple PU transmitters and the negative influence brought bythe interference of the multiple PU transmitters on SR and SDcan result in optimal values for M and N which correspond tothe minimum outage probability and the maximum throughput.

To do so, we will first look at the distribution of Z1, Z2,and Z3 as N → ∞. Since Z1 is independent and non-identically distributed exponential RVs, the distribution of Z1

is asymptotically normal as Z1 → ∞. Using law of largenumbers, we have

Z1d→NPPUtxν1, (15)

where Ad→B denotes convergence in distribution of a rv A

to a rv B. Similarly, we have

Z2d→NPPUtxν2 (16)

and

Z3d→NPPUtxν3. (17)

In the same manner, we obtain the distribution of Y1 and Y2

as M → ∞. Since Y1 is the maximum of M independent andnon-identically distributed exponential RVs, the distributionof Y1 is asymptotically normal, as Y1 → ∞. From [37,Proposition 1], we have

Y1d→ω1 + ω1 lnM + Y 1, (18)

where Y 1 is the normal distribution with N (0, 2ω12). Simi-

larly, we obtain

Y2d→ω2 + ω2 lnM + Y 2, (19)

where Y 2 is the normal distribution with N (0, 2ω22). Having

the distribution of Y1, Y2, Z1, Z2, and Z3 for large numberof PU transceivers, we rewrite SIR in (5) and (6) at SR andat SD as

Γ∞R

d∼min(ρNPPUtxν1,PI

ω1 + ω1 lnM + Y 1

)X1

PPUtxNν2(20)

and

Γ∞D

d∼min(ρNPPUtxν2,PI

ω2 + ω2 lnM + Y 2

)X2

PPUtxNν3,

(21)

respectively. We use the SIR in (20) and (21) to obtain theoutage probability for large number of PU tranceivers in thenext section.

A. Outage probability

The asymptotic outage probability of the SN is given by

P∞out(γth) = 1− Pr{Γ∞

R ≥ γth,Γ∞D ≥ γth}. (22)

In contrast to (7), Γ∞R and Γ∞

D in (22) are independent andtherefore, we can write the second term in (22) as the productof two terms.

Theorem 2. As the number of transceivers goes to infinity, theoutage probability of the proposed cognitive relay network isgiven by in closed form

P∞out(γth) = 1−ΘRΘD, (23)

where ΘR = Pr{Γ∞R ≥ γth} and ΘD = Pr{Γ∞

D ≥ γth},respectively.

Proof: The term ΘR is obtained in (26) at the top of nextpage. The terms in (25) can be obtained using the CDF andPDF expressions for X1 and Y 1. Applying [38, Eq 3.322.1],we can further simplify ΘR obtained in (26) as

ΘR =eω1

2γR2−γRω1(1+lnM)

2

(1− Φ

(γRω1 +

uR

2ω1

))+

1

2e−

ν2γthλ1ρν1

[Φ

(uR

2ω1

)− Φ

(uR∗

2ω1

)], (27)

where γR =PPUtxNν2γth

λ1PI, Φ(x) = 2√

π

∫ x

0e−t2dt, uR =

PI

ρNPPUtxν1− ω1 − ω1 lnM , and uR∗ = −ω1 − ω1 lnM .

Similarly, we obtain ΘD by substituting the parameters of (27)with ν1 → ν2, ω1 → ω2, λ1 → λ2, and ν2 → ν3. Then wehave

ΘD =eω2

2γD2−γDω2(1+lnM)

2

(1− Φ

(γDω2 +

uD

2ω2

))+

1

2e−

ν3γthλ2ρν2

[Φ

(uD

2ω2

)− Φ

(uD∗

2ω2

)], (28)

where uD = PI

ρPPUtxNν2− ω2 − ω2 lnM,uD∗ = −ω2 −

ω2 lnM , and γD =PPUtxNν3γth

λ2PI. Substituting (27) and (28)

into (23), we obtain a closed-form expression for the outageprobability.

B. Throughput

We derive the delay-sensitive throughput and delay-tolerantthroughput in this section. We use the expression derived in(23) to evaluate τ∞ds and τ∞dt , respectively, as

τ∞ds =(1− α)

2Rds(1− P∞

out(γth)), (29)

and

τ∞dt =(1− α)

2ln2

∫ ∞

0

1− FΓth(x)

(1 + x)dx, (30)

where FΓth(γth) can be evaluated using (23), i.e., FΓth

(γth) =P∞out(γth).

V. NUMERICAL RESULTS

In this section, we present numerical results to examinethe outage probability and the throughput for the proposedcognitive relay networks with wireless EH. We show theoutage probability and the throughput as functions of PI ,PPUtx , and the position of PUtx. To gain more insights, weexamine the asymptotic behavior of the outage probabilityand the throughput as the number of PU transceivers goes toinfinity. In this work, we assume that all the distances betweeneach nodes are not smaller than one. Without loss of generality,SS, SR, and SD are located at (0,0), (1,0), and (2,0) on the X-Y



6

ΘR =Pr{Γ∞R ≥ γth}

=Pr

{X1 ≥

PPUtxNν2γth(ω1 + ω1 lnM + Y 1

)PI

, Y 1 ≥ PI

ρNPPUtxν1− ω1 − ω1 lnM

}

+ Pr

{X1 ≥ ν2γth

ρν1

}Pr

{−ω1 − ω1 lnM ≤ Y 1 ≤ PI

ρNPPUtxν1− ω1 − ω1 lnM

}(24)

=

∫ ∞

uR

(1− FX1

((ω1 + ω1 lnM + Y 1

)PPUtxNν2γth

PI

))f (y1) dy1

+ e−ν2γthλ1ρν1

(1

2

[Φ

(uR

2ω1

)− Φ

(uR∗

2ω1

)])(25)

=e−

PPUtxNν2γthω1(1+lnM)

λ1PI

2ω1√π

∫ ∞

uR

e− Y 1

2

4ω12 −

PPUtxNν2γthY 1λ1PI dY 1

+1

2e−

ν2γthλ1ρν1

[Φ

(uR

2ω1

)− Φ

(uR∗

2ω1

)]. (26)

−20 −15 −10 −5 0 5 10 15 20

Outa

ge P

robabil

ity

P (dBW) I

γ

th = 0 dB

-5 dB

-10 dB

Exact Analysis

Simulation

10−2

10−1

100

Fig. 3. Outage probability as a function of PI , with M = 3, PPUtx =0 dBW.

plane, respectively and the center of PU receivers is located at(2, 1). We specify the location of the center of PU transmittersin the description of each figure. We assume that α = 0.5(Figs. 3-9), η = 0.8, and M = N for all the figures. In eachfigure, we see excellent agreement between the Monte Carlosimulation points marked as “•” and the analytical curves,which validates our derivation.

Fig. 3 shows the outage probability as a function of PI forvarious threshold γth values. We assume that the center ofPUtx is located at (0, 1). The solid curves, representing theexact analysis, are obtained from (12). Several observationscan be drawn as follows: 1) For a given value of PI , theoutage probability decreases as threshold value γth decreases;2) As the interference power constraint, PI , increases, theoutage probability decreases. This is due to the fact that SS andSR can transmit at higher powers without causing interferencebeyond PI ; and 3) The outage probability reaches error floorswhen PI is in the high power regime. This is because whenPI goes to infinity, the power constraints at SS and SR are

−10 −5 0 5 10 15 20 25 300

0.05

0.15

0.25

0.35

0.45

PPUtx = 0 dBW

10 dBW

Delay-sensitive

Simulation

Delay-tolerant

PPUtx = 0 dBW

10 dBW

P (dBW) I

0.1

0.2

0.3

0.4T

hro

ughput

(bit

s/s/

Hz)

Fig. 4. Throughput as a function of PI , with M = 3, and γth = 0 dB.

relaxed. The maximum transmit powers at SS and SR are onlydependent on the harvested energies.

Fig. 4 shows the throughput in delay-sensitive and delay-tolerant modes as a function of PI for various transmit powerfrom PU transmitters. The center of PUtx is located at (0, 1).The solid curves, representing the exact analysis of delay-sensitive mode, are obtained from (13). The dashed curves,representing the exact analysis of delay-tolerant mode, areobtained from (14). The results show that: 1) the throughputincreases as PI increases. This is because SS and SR cantransmit at higher transmission power without causing inter-ference beyond PI as it increases; 2) for different value ofPPUtx , the throughput can reach the same asymptotic valueswhen PI is in high power regime. The reason is that as PIgoes to infinity, the power constraints at SS and SR are relaxed.The SIR expressions at SR and SD become independent of thevalue PPUtx ; and 3) The throughput results for delay-sensitivemode is lower than those in delay-tolerant. The reason is thatin delay-sensitive, the information is transmitted at a fixed rate.If the rate is above the channel rate, the outage occurs and the



7

−10 −5 0 5 10 15 20 25 30

Exact Analysis

Simulation

PUtx (1,1)

(0.75,1)

(0.5,1)

(0,1)

Outa

ge P

robabil

ity

10−2

10−1

100

PPUtx (dBW)

Fig. 5. Outage probability as a function of PPUtx , with M = 3, γth = −10dB, and PI = 10 dBW.

throughput suffers. While in delay-tolerant transmission mode,the transmission rate is flexible due to the fact that the data atSS can tolerate delays.

Fig. 5 illustrates the outage probability as a function ofPPUtx for various locations of the PU transmitter center.We observe that: 1) The outage performance degrades withincreasing PPUtx . This can be explained as follows. On the onehand, as PPUtx increases, SS and SR can harvest more energyfrom PU transmitters, which can improve the performance ofSN. On the other hand, as PPUtx increases, the interferenceat SR and SD also increases. There exists a tradeoff betweenthe transmit power and performance. The observed simulationresults indicate that the detrimental effect of interference fromPU transmitters outweighs the benefits of increased energyharvested from the PU transmitters; 2) The outage probabilitydecreases as the center point of PUtx moves towards SS andaway from SR and SD. This is because less interference isimposed on SR and SD while more energy is being harvestedat SS, as PUtx moves towards SS and away from SR and SD.As a result, SS and SR can transmit information successfully athigh power levels and hence, the outage probability for a givenPPUtx decreases; 3) There exists error floors when PPUtx isin the low power regime, since in this case, the energy thatcan be harvested at SS and SR is the power constraint whichlimits the performance; and 4) There exists error ceilings whenPPUtx is in the high power regime, since in this case, the fixedinterference power constraint PI limits the transmit power ofSS and SR to affect the outage probability. Therefore, if PPUtx

goes to infinity, the interference will go to infinity and theoutage probability will approach one.

Fig. 6 shows the outage probability as a function of PPUtx

for various PI . We assume PUtx is located at (0, 1). Weobserve that there exists floors and ceilings of the outageprobability similar to those observed in Fig. 5. In addition, weobserve that the outage probability decreases as PI increases.This is expected since higher interference power constraintPI allows higher transmit power at the SS and SR, whichresults in a lower outage probability. The outage probability

−10 −5 0 5 10 15 20 25 30

P = 0 dBW

10 dBW

20 dBW

I

Exact Analysis

Simulation

PPUtx (dBW)

Outa

ge P

robabil

ity

10−2

10−1

100

Fig. 6. Outage probability as a function of PPUtx , with M = 3 andγth = −10 dB.

−10 −5 0 5 10 15 20 25 30

P = 0 dBW

10 dBW

20 dBW

I

P = 0 dBW

10 dBW

20 dBW

I

0

0.05

0.15

0.25

0.35

0.45

0.1

0.2

0.3

0.4

Thro

ughput

(bit

s/s/

Hz)

PPUtx (dBW)

Delay-sensitive

Delay-tolerant

Simulation

Fig. 7. Throughput as a function of PPUtx , with M = 3 and γth = 0 dB.

curves shift to the right as PI increases. This behavior canbe explained as follows: 1) as PPUtx increases, SS and SRcan use higher transmit power to offset the interference fromPU transmitters at SR and SD, respectively, and 2) as PIincreases, the transmit power constraints at SS and SR arerelaxed, thereby, allowing SS and SR to transmit at higherpower levels without exceeding the PI interference powerconstraint.

In Fig. 7, we plot the throughput for delay-sensitive anddelay-tolerant transmission modes as a function of PPUtx ,where we assume PUtx is located at (0, 1). It is shownthat the throughput ceilings and floors exit for PPUtx . Weobserve that the detrimental effect of the interference fromPUtx dominates the throughput performance, such that thethroughput decreases as PPUtx increases. We also observe thatthe throughput curves moves to the right as PI increases. Thisis due to the fact that when PI is relaxed (i.e., increased),SS and SR can transmit at higher power levels to offset theinterference from PU transmitters at SR and SD, respectively,as PPUtx increases. Note that similar to our discussion inFig. 4, the throughput in delay-tolerant mode is higher than



8

Exact Analysis

Large Analysis

Simulation

PUtx (1,1)

PU (0,1)

tx

Outa

ge P

robabil

ity

10−2

10−1

100

10 310 210 110 0

M

Fig. 8. Outage probability as a function of M , with γth = −10 dB,PI = 10 dBW, and PPUtx = 0 dBW.

that in delay-sensitive mode.Fig. 8 shows the exact outage probability and asymptotic

outage probability as a function of M for various PUtx

positions. We plot the exact outage probability and asymptoticoutage probability curves using (12) and (23), respectively.The results from the large analysis converge to those from theexact analysis as the number of PU transceivers approachesinfinity. There exists an optimal M which can minimize theoutage probability. It is shown that the outage probabilitydecreases and then increases as the number of PU transceiversgrows large. Since SS and SR can harvest energy from all PUtransmitters, it is natural to assume that the opportunity toharvest energy from the PU network increases as the numberof PU transmitters increases. In order to improve the systemoutage probability given by (12), SS and SR can forwardinformation at higher transmit power as the harvested energyimprove. However, the harmful impact of the interference im-posed on the secondary network from the PN counterbalancesthe benefits gained from the energy harvesting as the numberof PU transmitters increases. Similar to the observation in Fig.5, a lower outage probability can be achieved when PUtx isfar from SD and SR, and close to SS for the each M value.It is also shown that increasing the number of PUs can notguarantee lower outage probability.

In Fig. 9, we plot the throughput for delay-sensitive anddelay-tolerant transmission modes as a function of M . Weassume PI = 10 dB, PPUtx = 0 dB, and PUtx is locatedat (0, 1). It can be seen that the throughput increases andthen decreases as a function of M . We observe that thethroughput approaches zero as M grows large (M ∼ 100)due to excessive interference power from PU transmitters atSR and SD. The large interference power disables SS and SRfrom communicating the information to SD. The throughputresults from the large analysis converges to those from theexact analysis as M increases.

In Fig. 10, we plot the throughput for delay-sensitive anddelay-tolerant transmission modes versus α for various valuesof M . We assume that the PU transmitters are loceted at

10 310 210 110 0

M

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

Th

rou

gh

pu

t (b

its/

s/H

z)

Delay-sensitive

Delay-tolerant

Exact Analysis

Simulation

Large Analysis

Fig. 9. Throughput as a function of M , with γth = 0 dB, PI = 10 dBW,and PPUtx = 0 dBW.

(0, 1). The results show that the throughout increases and thendecreases as a function of α. For small values of α (∼ 0),the SS and SR harvest insufficient energy for a reliable in-formation transmission due to short energy harvesting periodsand therefore, the throughput is low. For large values of α(∼ 1), the SS and SR are unable to transmit reliably due toshort information transmitting periods. As α increases fromsmall values to large values, the throughput is influenced bythe tradeoff between the energy harvesting and informationtransmission periods. We observe that the delay-sensitive anddelay-tolerant throughput improve when the number of PUtransceivers increase from 3 to 15. This is due to the factthat the negative effects brought by the interference from PUtransmitters on SR and SD offsets the positive effects broughtby harvesting energy from PU transmitters on SS and SR. Theresults also show that the optimal α value is not necessarily thesame for the delay-sensitive and delay-tolerant transmissionmodes.

Remark 1: The value chosen for α greatly impacts theoutage probability and the throughput of the secondary net-work. As the value of α increases from 0 to 1, the durationof EH at SS and SR in each time slot increases and naturally,the remaining duration of the time slot to transmit informationdecreases. In other words, more energy may be available at SSand SR but less time is available to transmit the information.It is desired to find a value for α which can maximizethe throughput. The optimal value of α can be evaluatednumerically (and off-line) using search methods for (13) and(14). Note that the closed form expression for the optimalα is not tractable due to the complexity of the throughputexpressions.

Remark 2: It is desired to deploy SS, SR, and SD (withrespect to the PN) where the outage probability is minimizedand the throughput is maximized. For example, the SN canbe deployed so that PU transmitters are located near SS andSR for EH and away from SR and SD to reduce interferencepower at SR and SD. In order to reduce the interference fromSS and SR at the PN, it is desired that SS and SR are far



9

α0 0.2 0.4 0.6 0.8 1

0

0.05

0.15

0.25

0.35

0.45

0.1

0.2

0.3

0.4

Thro

ughput

(bit

s/s/

Hz)

0.5

Delay-sensitive

Simulation

Delay-tolerant

M=15

3

M=15

3

Fig. 10. Throughput as a function of α, with γth = 0 dB, PPUtx = 0 dBW,and PI = 10 dBW.

from PU receivers. This can be observed in Fig. 5, at thelocation where the outage probabilities as a function of PPUtx

for four PUtx locations are illustrated. If the system engineercan deploy the SN network at a desired location and PUtx

and PUrx are immobile, the optimal location of SS, SR, andSD with respect to PUtx and PUrx can be obtained. Althougha closed-form solution for the optimal location of SS, SR,and SD from (12) is intractable, the solution can be obtainedoffline by numerical searching methods.

VI. CONCLUSIONS

A wireless energy harvesting protocol for an underlay cogni-tive relay network with multiple primary users (PUs) was pro-posed. We performed the exact analysis as well as asymptoticanalysis as the number of PUs goes to infinity. Expressionsfor the exact outage probability and the exact throughput fortwo transmission modes, namely delay-sensitive and delay-tolerant, were derived. For a sufficiently large number of PUs,we derived closed-form asymptotic expressions for the outageprobability and the delay-sensitive throughput and an analyt-ical expression for the delay-tolerant throughput. Our resultsshow that the detrimental effect caused by the interferencefrom the multiple PU transmitters at the secondary user (SU)outweighs the benefits brought by harvesting energy when thenumber of PUs is large. The results also show that as PUtransmitters move closer to SS and farther away from SR andSD, more energy is harvested at SS and less interference isimposed on SR and SD so that the outage probability of the SUdecreases. In our future work, we will use stochastic geometryto model the locations of PUs and investigate the relationshipbetween density of PUs and performance of SUs.

APPENDIX A

In this Appendix, we provide a proof of Theorem 1. Recallthat ΓR and ΓD are two random variables which are dependenton Z2. In order to express (7) in terms of the product oftwo independent random variables, we condition the term

Pr{ΓR ≥ γth,ΓD ≥ γth} on Z2. Thus,

Pr{ΓR ≥ γth,ΓD ≥ γth|Z2} = Pr{ΓR ≥ γth|Z2} ×Pr{ΓD ≥ γth|Z2},(31)

where Pr{ΓR ≥ γth|Z2 = z2} and Pr{ΓD ≥ γth|Z2 = z2}are two independent probabilities for a given z2. We deriveand simplify the expressions for Pr{ΓR ≥ γth|Z2 = z2} andPr{ΓD ≥ γth|Z2 = z2}. The term Pr{ΓR ≥ γth|Z2 = z2}can be obtained as

Pr{ΓR ≥ γth|Z2}

= Pr

{min

(ρZ1,

PI

Y1

)X1

Z2≥ γth

}(32)

= Pr

{X1 ≥ Z2γth

Z1ρ, Y1 ≤ PI

Z1ρ

}︸︷︷︸

JR,I

+ Pr

{X1 ≥ Y1Z2γth

PI,PI

Y1ρ≤ Z1

}︸︷︷︸

JR,II

, (33)

where (32) presents the probability that SIR is greater than γthbased on the three important power constraints. We present(32) in terms of the addition of JR,I and JR,II based on twopossibilities: ρZ1 < PI

Y1and ρZ1 > PI

Y1. Conditioning JR,I in

(33) on Z1 and taking the expected value of the results overthe distribution of Z1, we have

JR,I =

∫ ∞

0

e−Z2γthz1ρλ1 (1− e−

PIz1ρω1 )MfZ1(z1)dz1

=

∫ ∞

0

e−Z2γthz1ρλ1 (1− e−

PIz1ρω1 )M

× zN−11 e

− z1PPUtx

ν1

Γ(N)(PPUtxν1)Ndz1. (34)

Note that by conditioning JR,I on Z1, the two terms inJR,I become independent with respect to one another andtherefore, JR,I can be presented as the product of the twoterms. Similarly, by conditioning JR,II in (33) on Y1 and bytaking the expected value of the result over the distribution ofY1, we have

JR,II =

∫ ∞

0

e− y1Z2γth

PIλ1

(1− FZ1(

PI

y1ρ))fY1(y1)dy1

=

∫ ∞

0

e− y1Z2γth

PIλ1

(1−

Γ(N, PIPPUtxν1y1ρ

)

Γ(N)

)×M

ω1

M−1∑k

(M − 1

k

)(−1)ke−( k+1

ω1)y1dy1.

(35)

In the same manner, the term Pr{ΓD ≥ γth|Z2} in (12) can



10

be obtained as

Pr{ΓD ≥ γth|Z2}

= Pr

{min

(ρZ2,

PI

Y2

)X2

Z3≥ γth

}= Pr

{X2 ≥ γthZ3

Z2ρ, Y2 ≤ PI

Z2ρ

}︸︷︷︸

JD,I

+ Pr

{X2 ≥ γthY2Z3

PI, Y2 ≥ PI

Z2ρ

}︸︷︷︸

JD,II

. (36)

Since JD,I is conditioned on Z2, the joint probability can bewritten as the product of two marginal probabilities, i.e.,

JD,I = Pr{X2 ≥ γthZ3

ρZ2}︸︷︷︸

I1

Pr{Y2 ≤ PI

ρZ2}︸︷︷︸

I2

,

=

(1− e−

PIZ2ρω2

)M(1 +

PPUtxν3γth

ρZ2λ2

)N , (37)

where I1 is obtained by applying [38, Eq 3.326.2]

I1 =

∫ ∞

0

e−γthz3ρZ2λ2 fZ3(z3)dz3

=

(1 +

PPUtxν3γthρZ2λ2

)−N

, (38)

andI2 = (1− e−

PIZ2ρω2 )M . (39)

We condition JD,II on Z3

JD,II |Z3 = Pr{X2 ≥ Y2Z3γthPI

, Y2 ≥ PI

ρZ2}

=

∫ ∞

PIρZ2

e− y2Z3γth

PIλ2M

ω2

M−1∑k

(M − 1

k

)(−1)ke−( k+1

ω2)y2dy2

(40)

Averaging JD,II over the PDF of Z3 we have,

JD,II =

∫ ∞

0

JD,II |Z3fZ3(z3)dz3

=

∫ ∞

PIρZ2

M

ω2

M−1∑k

(M − 1

k

)(−1)ke−( k+1

ω2)y2

× 1(1 + y2

γthPPUtxν3

PIλ2

)N dy2. (41)

The outage probability can be evaluated using the resultsobtained from (34), (35), (37), and (41) in (12).

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Yuanwei Liu (S’13) is currently working towardthe Ph.D. degree in Electronic Engineering at QueenMary University of London. Before that, he receivedhis M.S. degree and B.S. degree from the BeijingUniversity of Posts and Telecommunications in 2014and 2011, respectively.

His research interests include wireless energyharvesting, non-orthogonal multiple access, cogni-tive radio, physical layer security, multiple-antennasystems and cooperative networks.

S. Ali Mousavifar (M’08) received his BASc,MASc, Ph.D (2006, 2009, 2015) from the Depart-ment of ECE at the University of British Columbia(UBC), Canada. He has also worked as an RFEngineer and CDMA System Engineer at Researchin Motion (RIM) in 2007-2008. He has held anadjunct professorship position at the Department ofECE at UBC. He currently works as a SystemsDeveloper at Broadridge Financial Solutions. Hisresearch interests include trust and reputation man-agement systems in cognitive radio and RF energy

harvesting applications in wireless communication systems.

Yansha Deng (S’13) received the Ph.D. degree inElectrical Engineering from Queen Mary Universityof London, UK, 2015. She is currently with Centrefor Telecommunications Research at King’s CollegeLondon. Her research interests include multiple-antenna systems, cognitive radio, cooperative net-works, massive MIMO, molecular communication,and physical layer security.

Cyril Leung received the B.Sc. (First class hon-ours) degree from Imperial College, University ofLondon, UK, and the M.S. and Ph.D. degrees inelectrical engineering from Stanford University. Hehas been an Assistant Professor in the Departmentof Electrical Engineering and Computer Science,Massachusetts Institute of Technology and the De-partment of Systems Engineering and ComputingScience, Carleton University. Since July 1980, hehas been with the Department of Electrical andComputer Engineering, The University of British

Columbia, Vancouver, Canada, where he is a Professor and currently holdsthe PMC-Sierra Professorship in Networking and Communications. He servedas Associate Dean, Research and Graduate Studies, in the Faculty of AppliedScience at UBC from 2008 to 2011.

His research interests include wireless communication systems, and tech-nologies to support active aging for the elderly. He is a member of theAssociation of Professional Engineers and Geoscientists of British Columbia,Canada.

Maged Elkashlan (M’06) received the Ph.D. de-gree in Electrical Engineering from the Universityof British Columbia, Canada, 2006. From 2006 to2007, he was with the Laboratory for AdvancedNetworking at University of British Columbia. From2007 to 2011, he was with the Wireless and Net-working Technologies Laboratory at CommonwealthScientific and Industrial Research Organization (C-SIRO), Australia. During this time, he held anadjunct appointment at University of TechnologySydney, Australia. In 2011, he joined the School

of Electronic Engineering and Computer Science at Queen Mary Universityof London, UK, as an Assistant Professor. He also holds visiting facultyappointments at the University of New South Wales, Australia, and BeijingUniversity of Posts and Telecommunications, China. His research interests fallinto the broad areas of communication theory, wireless communications, andstatistical signal processing for distributed data processing and heterogeneousnetworks.

Dr. Elkashlan currently serves as an Editor of IEEE TRANSACTIONSON WIRELESS COMMUNICATIONS, IEEE TRANSACTIONS ON VEHICULARTECHNOLOGY, and IEEE COMMUNICATIONS LETTERS. He also serves asLead Guest Editor for the special issue on “Green Media: The Future ofWireless Multimedia Networks” of the IEEE WIRELESS COMMUNICATIONSMAGAZINE, Lead Guest Editor for the special issue on “Millimeter WaveCommunications for 5G” of the IEEE COMMUNICATIONS MAGAZINE, GuestEditor for the special issue on “Energy Harvesting Communications” of theIEEE COMMUNICATIONS MAGAZINE, and Guest Editor for the special issueon “Location Awareness for Radios and Networks” of the IEEE JOURNAL ONSELECTED AREAS IN COMMUNICATIONS. He received the Best Paper Awardat the IEEE International Conference on Communications (ICC) in 2014,the International Conference on Communications and Networking in China(CHINACOM) in 2014, and the IEEE Vehicular Technology Conference(VTC-Spring) in 2013. He received the Exemplary Reviewer Certificate ofthe IEEE Communications Letters in 2012.

wireless energy harvesting in a cognitive relay network

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