dual-hop cognitive amplify-and-forward relaying networks over η − µ fading channels

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2015 1

Dual-Hop Cognitive Amplify-and-Forward RelayingNetworks over η − µ Fading Channels

Jing Yang, Member, IEEE, Lei Chen, Xianfu Lei, Member, IEEE, Kostas P. Peppas, Senior Member, IEEE, andTrung Q. Duong, Senior Member, IEEE

Abstract—This paper presents a thorough performance anal-ysis of dual-hop cognitive amplify-and-forward (AF) relayingnetworks under spectrum-sharing mechanism over independentnon-identically distributed (i.n.i.d.) η − µ fading channels. Inorder to guarantee the quality-of-service (QoS) of primarynetworks, both maximum tolerable peak interference power Q atthe primary users (PUs) and maximum allowable transmit powerP at secondary users (SUs) are considered to constrain transmitpower at the cognitive transmitters. For integer-valued fadingparameters, a closed-form lower bound for the outage probability(OP) of the considered networks is obtained. Moreover, assumingarbitrary-valued fading parameters, the lower bound in integralform for the OP is derived. In order to obtain further insights onthe OP performance, asymptotic expressions for the OP at highSNRs are derived, from which the diversity/coding gains andthe diversity-multiplexing gain tradeoff (DMT) of the secondarynetwork can be readily deduced. It is shown that the diversitygain and also the DMT are solely determined by the fadingparameters of the secondary network whereas the primarynetwork only affects the coding gain. The derived results includeseveral others available in previously published works as specialcases, such as those for Nakagami-m fading channels. In addition,performance evaluation results have been obtained by MonteCarlo computer simulations which have verified the accuracy ofthe theoretical analysis.

Index Terms—Outage probability (OP), amplify-and-forward(AF), cognitive relay network (CRN), η − µ fading, spectrumsharing.

I. INTRODUCTION

Cognitive radio with spectrum sharing is regarded as apromising technique to improve spectral efficiency and solvethe problem of spectrum scarcity in 5G wireless communica-tion networks [1]. In underlay cognitive networks, secondary

Copyright c⃝ 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Manuscript received January 22, 2015; revised July 1, 2015 and August15, 2015; accept September 12, 2015. This work of J. Yang was supportedin part by the National Natural Science Foundation of China (Grant No.61301111/61472343) and China Postdoctoral Science Foundation (Grant No.2014M56074). This work of T. Q. Duong was supported in part by the U.K.Royal Academy of Engineering Fellowship under Grant RF1415/14/22. Thereview of this paper was coordinated by Prof. N. Arumugam.

J. Yang and L. Chen are with Yangzhou University, Yangzhou, China(e-mails: [email protected], [email protected]). J. Yang is also withSoutheast University, Nanjing, China.

X. Lei is with Southwest Jiaotong University, China (e-mail:[email protected]).

K. P. Peppas is with the Department of Telecommunication Scienceand Technology, University of Peloponnese, Tripoli 22100, Greece (e-mail:[email protected]).

T. Q. Duong is with Queen’s University Belfast, UK (e-mail:[email protected]).

Digital Object Identifier xx.xxxx/TVT.Year.xxxxxx

users (SUs) can simultaneously access the licensed spectrumof the primary user (PU) without causing harmful interferenceon PU. Thus, to ensure PU’s quality of service (QoS), thetransmit power constraint at SUs must be considered [2], [3].Cooperative relaying can expand the coverage area and en-hance the communication range of wireless networks withoutrequiring additional powers at the transmitter [4]. To furtherimprove the performance of cognitive networks, cooperativerelaying has been incorporated into cognitive networks to formcognitive relay networks (CRNs).

Further research efforts have been focused on the perfor-mance analysis of CRNs employing amplify-and-forward (AF)and decode-and-forward (DF) protocols, including [5]–[11].For example, the authors in [5], [6] have investigated theoutage performance of AF CRNs with maximum interferencepower constraint of the primary network. In [7], tight lowerbounds and asymptotic expressions for the outage probability(OP) of AF CRNs have been derived, where both interferenceand maximum allowable transmit power constraints are con-sidered. In [9], an exact expression for the OP of a dual-hopDF CRN has been obtained, assuming that the transmit powersat SUs are governed by both the primary network and thesecondary network. Bao et al. proposed cognitive multi-hopDF networks and analyzed the system performance with theinterference limits in [10]. In [11], closed-form and asymptoticOP expressions are presented where the mutual interferencebetween cognitive system and primary system is taken intoaccount. Most recently, CRNs incorporating multiuser di-versity and multiple-input multiple-output technologies withboth AF and DF relaying have been considered in [12]. Theauthors in [13] considered a cognitive cooperative DF relayingnetwork and investigated adaptive transmit power-allocationpolicies for the SUs. Recently, Zhang et al. considered anunderlay cognitive DF relay network including one primaryuser receiver (PU) and a secondary system and investigatedthe performance of the considered network in [14].

In all the aforementioned works, small-scale fading is mod-elled by the Rayleigh [5], [8]–[10], [12], [13] or the Nakagami-m [6], [7], [11], [14] fading distributions. The Nakagami-mdistribution is a mathematically tractable model that well char-acterizes the wireless propagation channel in many practicalcases. However, as it was pointed out in [15], this distributioncannot match well experimental data in many practical cases,particularly at the tail portion. A versatile fading distributionwhich generalizes many of the well known models for multi-path fading is the so-called η − µ distribution [15]. Thisdistribution better models small-scale fading under non-line-

2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2015

of-sight (NLoS) conditions and includes the Rayleigh, theHoyt and the Nakagami-m distributions as special cases. Inrecent years, the η − µ fading model has gained increasedinterest in the field of performance analysis of single- andmulti-hop systems over fading environment [16]–[19]. Forexample, the authors in [16] analyzed the error performanceby using moment generating function (MGF) over η−µ fadingchannels, without investigating outage performance. Later,Peppas et al. analyzed the conventional dual-hop relayingnetwork over mixed η−µ and κ−µ fading channels in [17].More recently, a hexagonal cell layout was considered withthe base stations located at the center of each cell in [20] andanalytical evaluation of OP and capacity for κ− µ and η − µfading channel distributions has been investigated. In [21], ananalytical study of selection combining diversity under η − µmulti-path fading with integer-valued µ was presented.

Despite the wide applicability of the η − µ distribution,to the best of the authors’ knowledge, the performance ofcognitive AF relay networks in η − µ fading environmentis still unexplored in the open technical literature. Motivatedby the lack of such a generalized analytical framework, inthis paper, a thorough OP analysis for dual-hop cognitiveAF relay networks operating over independent non-identicallydistributed (i.n.i.d.) η − µ fading channels, is presented. Inorder to ensure the QoS of PU, both maximum tolerable peakinterference at PU and maximum allowable transmit powerat SUs are considered to constrain the transmit power atsecondary source and relay. The main contributions of thispaper are summarized as follows:

• For integer-valued fading parameters, a closed-form lowerbound for the OP is presented which becomes tight forhigh signal-to-noise ratios (SNRs).

• For arbitrary-valued fading parameters, a genericfrequency-domain approach is developed for the eval-uation of the OP, in which the corresponding integralis transformed into the frequency domain. Moreover,such a transformation requires both the knowledge of theMGFs of the random variables and the incomplete MGFinvolved in the computation of the OP.

• In order to provide further insights as to the factors thataffect system performance, simple asymptotic expressionsfor the OP are derived from which the diversity andcoding gains as well as the diversity-multiplexing gaintradeoff (DMT) can be readily deduced.

The derived results include several others available in theopen technical literature as special cases, namely those ofNakagami-m cases.

The remainder of this paper is organized as follows. InSection II, the considered system model is provided. In Sec-tion III, tight lower bounds as well as high-SNRs asymptoticexpressions for the OP are derived. In Section IV, the var-ious performance evaluation results and their interpretationsare presented. Finally, Section V concludes this paper. Forthe convenience of the reader, a comprehensive list of themathematical operators and functions often used in this paperis presented in Table I.

II. SYSTEM MODEL

Consider a dual-hop cognitive AF relay network includingone SU source (SU-S), one AF SU relay (SU-R), one SUdestination (SU-D), and one PU destination (PU-D). All nodesare equipped with single antenna and operate in half-duplexmode. The communication from the SU-S to the SU-D isperformed into two time slots. During the first time slot, theSU-S transmits signal x to the SU-R with transmit power PS .The received signal at the SU-R is given by

yr = g1√PSx+ nr (1)

where g1 is the channel coefficient of the SU-S → SU-R linkand nr is additive white Gaussian noise (AWGN) at the SU-R.During the second time slot, the received signal yr is amplifiedby G and then forwarded to the SU-D with transmit power PR.The received signal at the SU-D can be expressed as

yd = Gg1g2√PSPRx+Gg2

√PRnr + nd, (2)

where g2 is the channel coefficient of the link the SU-R →the SU-D and nd is AWGN at the SU-D. It is assumed thatall AWGN components have zero mean and variance N0.

In order to ensure the QoS provision at PU, i.e., totalaccumulated interference at PU cannot exceed the maximumtolerable interference power Q, and considering the maximumtransmit power at SU-S and SU-R as P , the transmit powersat SU-S and SU-R are strictly governed by

PS = min(Q/|h1|2,P

), and PR = min

(Q/|h2|2,P

),

respectively, where h1 and h2 are the channel coefficientsof the interference link SU-S → PU-D and SU-R → PU-D.Consequently, the end-to-end instantaneous SNR at SU-D canbe deduced as [7]

γend =γ1γ2

γ1 + γ2 + 1, (3)

where

γ1 = min

(γQ

|g1|2

|h1|2, γP |g1|2

),

γ2 = min

(γQ

|g2|2

|h2|2, γP |g2|2

), (4)

with γQ = Q/N0 and γP = P/N0.Throughout this analysis, it is assumed that all links are

subject to i.n.i.d. η − µ fading. Thus, |gℓ|2 and |hℓ|2 followthe η − µ distribution with parameters µgℓ , ηgℓ , and µhℓ

,ηhℓ

, respectively, where ℓ ∈ 1, 2. Let E|g1|2 = Ω1,E|g2|2 = Ω2, E|h1|2 = Ω3 and E|h2|2 = Ω4.

The PDF of X , where X ∈ |gℓ|2, |hℓ|2, can be expressedas [15]

fX(x) =2√πµµ+0.5hµxµ−0.5

Γ(µ)Hµ−0.5Xµ+0.5

× exp(− 2µhx

X

)Iµ−0.5

(2µHx

X

), (5)

where X = E(X), µ > 0, µ ∈ µgℓ , µhℓ and η ∈ ηgℓ , ηhℓ

.The parameters h and H are given by h = (2 + η−1 +

η)/4, H = (η−1−η)/4 with 0 < η < ∞, with h ∈ hgℓ , hhℓ

JING YANG et al.: DUAL-HOP COGNITIVE AMPLIFY-AND-FORWARD RELAYING NETWORKS OVER η − µ FADING CHANNELS 3

TABLE I: Mathematical Operators and Functionsı =

√−1 imaginary unit

z conjugate of the complex number z

Fg(t); t;ω Fourier transform of the function g(t)

E· expectation operator

Pr · probability operator

fX(·) probability density function (PDF) of the random variable (RV) X

FX(·) cumulative distribution function (CDF) of RV X

MX(·) moment generating function (MGF) of RV X

MX(t, s) incomplete moment generating function (MGF) of RV X

Ia (·) modified Bessel function of the first kind and order a [22, eq. (8.431)]

Γ (·) Gamma function [22, eq. (8.310.1)]

Γ (·, ·) incomplete Gamma function [22, eq. (8.350.2)]

pFq(·) generalized hypergeometric function [22, eq. (9.14.1)]

δ (·) Dirac’s delta function

and H ∈ Hgℓ ,Hhℓ [15]. Assuming integer values of µ, the

CDF of X can be obtained as follows [17],

FX(x)=1− 1

Γ(µ)

( h

H

)µ µ−1∑k=0

µ−k−1∑p=0

1

p!

[Apxpa(k) exp(−Ax)

+ (−1)µBpxpb(k) exp(−Bx)]

, (6)

where

A =2µ(h−H)

X, B =

2µ(h+H)

X,

a(k) =(−1)k(µ+ k − 1)!H−k

2µ+kk!(h−H)µ−k, b(k) =

(µ+ k − 1)!H−k

2µ+kk!(h+H)µ−k,

and a(k) ∈a(k)gℓ , a

(k)hℓ

, b(k) ∈

b(k)gℓ , b

(k)hℓ

, A ∈ Agℓ , Ahℓ

,B ∈ Bgℓ , Bhℓ

.For arbitrary values of µ, the CDF of X can be expressed

as

FX (x) = 1− Yµ

(H

h,

√2hµx

X

)(7)

where

Yµ(x, y)=

√π21.5−µ(1− x2)µ

Γ(µ)xµ−0.5

∫ ∞

y

e−t2t2µIµ−0.5(t2x)dt (8)

denotes the Yacoub integral [15, eq. (20)]. It is noted thatYµ(x, y) can be expressed in terms of tabulated functions forinteger or half-integer values of µ only. For arbitrary values ofµ, an expression of Yµ(x, y) in terms of the bivariate confluenthypergeometric functions is available in [23, eq. (2)].

The MGF of X can be deduced in closed form as [24, eq.(3)]

M(s) = [(1 + s/A)(1 + s/B)]−µ. (9)

Finally, by employing an infinite series representation forthe modified Bessel function, [22, eq. (8.447)] as well asthe definition of the incomplete gamma function [22, eq.

(8.350.2)], the incomplete MGF of X , defined as M(x, s) ,∫∞t

exp(−sx)fX(x)dx, can be deduced as

M(x, s) =2√πhµ

Γ(µ)

×∞∑k=0

H2k(µ/X)2µ+2kΓ(2µ+ 2k, 2µh t /X) + s t

k!Γ(µ+ k + 1/2)(2µh t /X + s

)2µ+2k. (10)

III. OUTAGE PERFORMANCE ANALYSIS

In this section, the OP of cognitive AF relaying system overi.n.i.d. η− µ fading will be obtained. The OP, i.e., Pout(γth),is defined as the probability that the instantaneous SNR γend atSU-D is below a specified SNR threshold γth, i.e., Pout(γth) =Prγend 6 γth.

A. The Lower Bound Analysis for OP

Theorem 1. For integer values of µgℓ and µhℓ, ∀ℓ = 1, 2,

a tight lower bound for OP is given as (11) on the top of thenext page, where F|g1|2

(γγP

)is given by (6) and∑

k1,p1k2,p2

=1

Γ(µg1)Γ(µh1)

(hg1

Hg1

)µg1(hh1

Hh1

)µh1

×µg1−1∑k1=0

µg1−k1−1∑p1=0

µh1−1∑

k2=0

µh1−k2−1∑p2=0

1

p1!p2!

(γQγP

)p2

,

∑k1,p1k2,p2

=1

Γ(µg2)Γ(µh2)

(hg2

Hg2

)µg2(hh2

Hh2

)µh2

×µg2−1∑k1=0

µg2−k1−1∑p1=0

µh2−1∑

k2=0

µh2−k2−1∑p2=0

1

p1!p2!

(γQγP

)p2

.

Proof: See Appendix A.It is noted that, for the special case of Nakagami-m fading

channels, i.e., µgl = mgl , µhl= mhl

and ηgl = ηhl=


Pout(γth) ≥1−

1− F|g1|2

(γthγP

)−∑k1,p1k2,p2

(γthγP

)p1[a(k1)g1 Am1

g1

(a(k2)h1

Ap2

h1exp

[−(Ag1

γthγP

+Ah1

γQγP

)]

+ (−1)µh1 b(k2)h1

Bp2

h1exp

[−(Ag1

γthγP

+Bh1

γQγP

)])+ (−1)µg1 b(k1)

g1 Bp1g1

×(a(k2)h1

Ap2

h1exp

[−(Bg1

γthγP

+Ah1

γQγP

)]+ (−1)µh1 b

(k2)h1

Bp2

h1exp

[−(Bg1

γthγP

+Bh1

γQγP

)])]

+∑k,p,q

(γthγQ

)p a(k)g1 Ap

g1

(µh1 + p− q − 1)!

(−1)qΓ(µh1 + p− q,Ag1

γth

γP+Ah1

γQγP

)(Ag1

γth

γQ+Ah1

)µh1+p−q

+(−1)µh1Γ

(µh1 + p− q, Ag1

γth

γP+Bh1

γQγP

)(Ag1

γth

γQ+Bh1

)µh1+p−q

+ (−1)µg1 b(k)g1 Bpg1

×

(−1)qΓ(µh1 + p− q,Bg1

γth

γP+Ah1

γQγP

)(Bg1

γth

γQ+Ah1

)µh1+p−q +

(−1)µh1Γ(µh1 + p− q,Bg1

γth

γP+Bh1

γQγP

)(Bg1

γth

γQ+Bh1

)µh1+p−q

×

1− F|g2|2

(γthγP

)−∑k1,p1k2,p2

(γthγP

)p1[a(k1)g2 Ap1

g2

(a(k2)h2

Ap2

h2exp

[−(Ag2

γthγP

+Ah2

γQγP

)]

+ (−1)µh2 b(k2)h2

Bp2

h2exp

[−(Ag2

γthγP

+Bh2

γQγP

)])+ (−1)µg2 b(k1)

g2 Bp1g2

×(a(k2)h2

Ap2

h2exp

[−(Bg2

γthγP

+Ah2

γQγP

)]+ (−1)µh2 b

(k2)h2

Bp2

h2exp

[−(Bg2

γthγP

+Bh2

γQγP

)])]

+∑k,p,q

(γthγQ

)p a(k)g2 Ap

g2

(µh2 + p− q − 1)!

(−1)qΓ(µh2

+ p− q,Ag2γth

γP+Ah2

γQγP

)(Ag2

γth

γQ+Ah2

)µh2+p−q

+(−1)µh2Γ

(µh2 + p− q, Ag2

γth

γP+Bh2

γQγP

)(Ag2

γth

γQ+Bh2

)µh2+p−q

+ (−1)µg2 b(k)g2 Bpg2

×

(−1)qΓ(µh2 + p− q,Bg2

γth

γP+Ah2

γQγP

)(Bg2

γth

γQ+Ah2

)µh2+p−q +

(−1)µh2Γ(µh2 + p− q,Bg2

γth

γP+Bh2

γQγP

)(Bg2

γth

γQ+Bh2

)µh2+p−q

. (11)

η → 0(l = 1, 2) [15], where mgl and mhldenote Nakagami

fading parameters, (11) becomes identical to a previouslyknown result, i.e. [7, eq. (13)]. This can be easily provedas follows. By letting µgl = mgl , µhl

= mhland η → 0,

we have h −H → 1/2, h +H → ∞ and h/H → 1; hence,A → m/X and B → ∞. Utilizing these results and after somemathematical manipulations yield [7, eq. (13)]. For arbitraryvalues of µgℓ and µhℓ

, a lower bound for OP can be obtainedas follows:

Theorem 2. For arbitrary values of µgℓ and µhℓ, ∀ℓ = 1, 2,

a lower bound for OP can be deduced as

Pout(γth) ≥2∑

ℓ=1

[Yµgℓ

(Hgℓ

hgℓ

,

√2hgℓµgℓγth

XγP

)

×Yµhℓ

(Hhℓ

hhℓ

,

√2hhℓ

µhℓγQ

XγP

)]

+2∑

ℓ=1

[J (µgℓ , µhℓ

, ηgℓ , ηhℓ, γth, γP , γQ)

](12)


where J (µgℓ , µhℓ, ηgℓ , ηhℓ

, γth, γP , γQ) is given as

J (µgℓ , µhℓ, ηgℓ , ηhℓ

, γth, γQ) =1

2+

F|gℓ|2(Λ)

2

+1

π

∫ ∞

0

1

ωImM|gℓ|2(Λ, ȷω)M|hℓ|2 (−ȷqω)

dω,

(13)

where Λ = γQ/γP , and q = γth/γQ.

Proof: See Appendix B.

B. The Asymptotic Analysis for OP

In order to obtain further insights on the system per-formance, high-SNRs asymptotic expressions for OP willbe derived, wherefrom the diversity and coding gains canbe deduced. Without loss of generality, it is assumed thatγP = ξγQ, where ξ is a positive constant. An asymptotic OPexpression for arbitrary-valued fading parameters is deducedin the following theorem.

Theorem 3. For arbitrary values of µgℓ and µhℓ, ∀ℓ = 1, 2,

when γQ → ∞, the asymptotic approximation for OP isobtained as

Pout(γth)γQ→∞= Θ ·

(γthγQ

)min(2µg1 ,2µg2 )

, (14)

where

Θ =

Θ1, if µg1 < µg2

Θ1 +Θ2, if µg1 = µg2

Θ2, if µg1 > µg2

(15)

and Θ1,Θ2 are given by

Θ1 =hµg1g1 h

µh1

h1

4µg1µh1Γ(2µg1)Γ(2µh1)

(2µg1

ξΩ1

)2µg1(2µh1

ξΩ3

)2µh1

+

√πµ

µh1+0.5

h1hµg1g1 h

µh1

h1

µg1Γ(2µg1)Γ(µh1)Hµh1

−0.5

h1Ω

µh1+0.5

3

×(2µg1

Ω1

)2µg1

L(µg1 , µh1 , hh1 ,Ω3, y),

and

Θ2 =hµg2g2 h

µh2

h2


(2µg2

ξΩ2

)2µg2(2µh2

ξΩ4

)2µh2

+

√πµ

µh2+0.5

h2hµg2g2 h

µh2

h2


−0.5

h2Ω

µh2+0.5

4

×(2µg2

Ω2

)2µg2

L(µg2 , µh2 , hh2 ,Ω4, y),

respectively, where L(µgℓ , µhℓ, hhℓ

,Ωi, y) is given as

L(µgℓ , µhℓ, hhℓ

,Ωi, y) =

∫ ∞

1ξ

y2µgℓ+µhℓ

−0.5

× exp

(−2µhℓ

hhℓ

Ωiy

)Iµhℓ

−0.5

(2µhℓ

Hhℓ

Ωiy

)dy

which cannot be derived in closed form.

Proof: See Appendix C.

Note that the integral in (14) can be easily evaluatednumerically by employing available in popular mathematicalsoftware packages such as Matlab, Maple or Mathematica. Anasymptotic OP expression in closed-form for integer-valuedfading parameters is deduced in the following theorem.

Theorem 4. For integer values of µgℓ and µhℓ, ∀ℓ = 1, 2,

when γQ → ∞, the asymptotic approximation for OP isobtained as

Pout(γth)γQ→∞= Θ′ ·

(γthγQ

)min(2µg1 ,2µg2 )

, (16)

where

Θ′ =

Θ1′ , if µg1 < µg2

Θ1′ +Θ2′ , if µg1 = µg2

Θ2′ , if µg1 > µg2

(17)

and Θ1′ ,Θ2′ are given by

Θ1′ =hµg1g1 h

µh1

h1


(2µg1

ξΩ1

)2µg1(2µh1

ξΩ3

)2µh1

+hµg1g1

2µg1Γ(2µg1)Γ(µh1)

(hh1

Hh1

)µh1(2µg1

Ω1

)2µg1

×µh1

−1∑k=0

(µh1 + k − 1)!

k!(µh1 − k − 1)!(4Hh1)k

(µh1

Ω3

)µh1−k

×

[(−1)k

Γ (2µg1 + µh1 − k,Ah1/ξ)

A2µg1+µh1

−k

h1

+ (−1)µh1Γ (2µg1 + µh1 − k,Bh1/ξ)

B2µg1+µh1

−k

h1

],

and

Θ2′ =hµg2g2 h

µh2

h2

4µg2µh2Γ(2µg2)Γ(2µh2

)

(2µg2

ξΩ2

)2µg2(2µh2

ξΩ4

)2µh2

+hµg2g2


(hh2

Hh2

)µh2(2µg2

Ω2

)2µg2

×µh2

−1∑k=0

(µh2+ k − 1)!

k!(µh2 − k − 1)!(4Hh2)k

(µh2

Ω3

)µh2−k

×

[(−1)k

Γ (2µg2 + µh2 − k,Ah2/ξ)

A2µg2+µh2

−k

h2

+ (−1)µh2Γ (2µg2 + µh2 − k,Bh2/ξ)

B2µg2+µh2

−k

h2

],

respectively.

Proof: See Appendix D.According to (14) and (16), the diversity gain Gd and the

coding gain Gc can be given by

Gd = min(2µg1 , 2µg2), (18)

and

Gc =1

γthΘ−1/min(2µg1 ,2µg2 ), (19)

respectively. Specially, for integer values of µgℓ and µhℓ, ∀ℓ =

1, 2, Θ in (19) can be replaced by Θ′ in (17).


As it can be observed from Theorem 3 and Theorem 4,the diversity gain only depends on the more severe fadingchannel between two hops of the secondary network, whereasthe primary network only affects its coding gain.

C. Diversity-Multiplexing Tradeoff

According to [4], the diversity-multiplexing tradeoff can beformulated as

d(r) = limγQ→∞

− logPout(γQ, r)

log γQ, (20)

where r is the normalized spectral efficiency. The outagethreshold γth can be expressed in terms of the spectralefficiency R (bit/s/Hz) as γth = 22R − 1. Furthermore, Rcan be expressed in terms of r as R = r log2(1 + γQ) [4].Consequently, γth can be deduced as

γth = (1 + γQ)2r − 1. (21)

By substituting (21) into (14) or (16), Pout(γQ, r) can bereadily obtained. Finally, plugging it into (20), d(r) can bededuced as

d(r) = min(2µg1 , 2µg2)(1− 2r). (22)

From (22), it is evident that the maximum diversity order,i.e., min(2µg1 , 2µg2), can be achieved as r → 0, while themaximum normalized spectral efficiency, i.e., 1/2, can beachieved as d → 0. In addition, the DMT only depends onthe more severe fading channel of the secondary network andis independent of the primary network.

IV. NUMERICAL AND COMPUTER SIMULATION RESULTS

In this section, various performance evaluation results ob-tained using the OP expressions presented in Sections III arepresented. In order to validate the accuracy of the proposedanalytical framework, all numerical results are accompaniedby equivalent ones obtained via Monte-Carlo. Without loss ofgenerality, for the simulations in Figs. 1 and 2, it is assumedthat the average channel powers of all links are given byΩi = γQ, i = 1, 2, 3, 4, whereas in Fig. 3, the averagechannel power is written as Ωi = 1/d4i , where di denotesthe distance between the transceivers. The outage thresholdγth is set to 3 dB for all considered analysis. Moreover, itis assumed that ξ = 1, i.e., γP = γQ. From Figs. 1-4, itcan be observed that the derived OP lower bounds are verytight and the asymptotic results predict well the diversity andcoding gains, thus validating the correctness of the proposedanalysis.

Fig. 1 depicts the OP of the considered network, assumingηh1 = ηh2 = 0.7, µg1 = 2 and µh1 = µh2 = 1, respectively. Inorder to investigate the impact of parameters µg2 , ηg1 and ηg2 ,several different cases are considered. As it can be observed,the outage performance improves as µg2 increases and/orηg1 , ηg2 increase. In addition, it is obvious that, there is asignificant increase in diversity gain when µg2 increases from1 to 3, however, the same diversity gain can be achieved whenµg2 = 3. This is because the diversity gain depends on the

0 5 10 15 20 2510

−6

10−5

10−4

10−3

10−2

10−1

100

γQ(dB)

OP

,Pou

t

µg2

=1,ηg1

=ηg2

=0.7(Anal.)

µg2

=3,ηg1

=ηg2

=0.7(Anal.)

µg2

=1.4,ηg1

=ηg2

=0.1(Anal.)

µg2

=1.7,ηg1

=ηg2

=0.1(Anal.)

µg2

=3,ηg1

=ηg2

=0.1(Anal.)

AsymptoticSimulation

Fig. 1: OP of the considered network over η − µ fadingchannels with parameters ηh1 = ηh2 = 0.7, µg1 = 2, µh1 =µh2 = 1.

0 5 10 15 20 2510

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

γQ(dB)

OP

,Pou

t

µh1

=µh2

=1,ηh1

=ηh2

=0.7(Anal.)

µh1

=µh2

=1,ηh1

=ηh2

=0.1(Anal.)

µh1

=µh2

=2.5,ηh1

=ηh2

=0.1(Anal.)

µh1

=µh2

=5,ηh1

=ηh2

=0.1(Anal.)

AsymptoticSimulation

Fig. 2: OP of the considered network over η − µ fadingchannels with parameters ηg1 = ηg2 = 0.7, µg1 = 2, µg2 = 3.

more severe fading channel between two hops of the secondarynetwork.

Fig. 2 shows the impact of the primary network on theOP performance for different values of µh1 , µh2 and ηh1 , ηh2 ,assuming ηg1 = ηg2 = 0.7, µg1 = 2 and µg2 = 3. Bykeeping the parameters of secondary network fixed, severaldifferent schemes are considered. It can be observed thatthe OP performance improves when µh1 and µh2 increasefrom µh1 = µh2 = 1 to µh1 = µh2 = 5 and/or ηh1 , ηh2

increase. Moreover, as expected, the fading parameters ofinterference links only affect the coding gain, without affectingthe diversity gain, just as our preceding analysis.

To evaluate the effect of PU’s position on the considerednetwork, Fig. 3 portrays the OP of cognitive AF relay network


−5 0 5 10 15 2010

−10

10−8

10−6

10−4

10−2

100

γQ(dB)

OP

,Pou

t

Lower BoundAsymptoticSimulation



PU(0.44,0.44)

PU(0.66,0.66)

PU(0.55,0.55)

γth

=3dB

Fig. 3: OP of the considered network over η − µ fadingchannels with parameters η = 0.7, µg1 = 2, µg2 = 3, µh1 =µh2 = 1.

0 0.1 0.2 0.3 0.4 0.50

1

2

3

4

5

6

Multiplexing Gain r

Div

ersi

ty G

ain

d(r)

(µg1

,µg2

,µh1

,µh2

)=(3,3,3,3)

(µg1

,µg2

,µh1

,µh2

)=(2,3,2,3)

(µg1

,µg2

,µh1

,µh2

)=(3,2,3,2)

Fig. 4: Diversity order d(r) in (22) versus normalized spectralefficiency r for different fading severity parameters.

for different PU’s position with η = 0.7, µg1 = 2, µg2 =3 and µh1 = µh2 = 1, respectively. It is assumed that allSUs are located in a straight line. The coordinates of SU-S, SU-R and SU-D are (0,0), (1/2,0) and (1,0), respectively.Moreover, PU-D can be located in three different positions,namely (0.44,0.44), (0.55,0.55) and (0.66,0.66). From Fig. 3, itcan be observed that the position of PU-D significantly affectsthe OP performance of the secondary network. Interestingly,when PU-D is located at (0.66,0.66), the best performance canbe obtained.

Finally, Fig. 4 depicts the diversity order d(r) versus thenormalized spectral efficiency r, for different fading severityparameters. It is obvious that the maximum diversity ordercan be achieved as r → 0, whereas the maximum normalized

spectral efficiency, i.e., 1/2, can be achieved as d → 0, thusvalidating the proposed theoretical analysis.

V. CONCLUSION

In this paper, a comprehensive analytical framework forthe performance evaluation CRN operating over η-µ fadingchannels has been presented. To ensure the QoS provisionat the primary network, both maximum tolerable interferencepower at PU and maximum allowable transmit power at SUhave been taken into account. Tight lower bounds as well asasymptotic expressions of OP for cognitive AF relay networkhave been obtained. Moreover, a concise frequency-domainapproach for evaluating the OP with arbitrary-valued fadingparameters was presented. Our findings reveal that diversitygain and the DMT of secondary networks are independentof the primary networks. More specifically, they are solelydetermined by the more severe fading hop among the twohops of the secondary network. In addition, the only impactfrom primary network that can be observed is the coding gainwhich is severely degraded when the PU is located nearbythe secondary network. The generality and computationalefficiency of these results render themselves as efficient toolsfor both theoretical analysis and practical applications.

APPENDIX APROOF OF THEOREM 1

It can be observed that γend in (3) is upper bounded byγend 6 minγ1, γ2 [25], yielding

Pout(γth) > Prmin(γ1, γ2) 6 γth= 1− (1− Fγ1(γth)) (1− Fγ2(γth))

= Fγ1(γth) + Fγ2

(γth)− Fγ1(γth)Fγ2

(γth). (A-1)

In order to obtain a lower bound for OP, the CDFs of γ1 andγ2, i.e., Fγ1(γ) and Fγ2(γ), are required. Specifically, Fγ1(γ)is given as

Fγ1(γ) = Prmin

(γQ

|g1|2

|h1|2, γP |g1|2

)6 γ

= Pr

γP |g1|2 6 γ,

γQ|h1|2

> γP

︸︷︷︸

F1

+ PrγQ

|g1|2

|h1|26 γ,

γQ|h1|2

6 γP

︸︷︷︸

F2

. (A-2)

Using [22, eq. (8.467)], the modified Bessel function Iµ−0.5(z)in (6), with µ > 0 being an integer, is expressed in closed formas

Iµ−0.5(z) =1√π

µ−1∑k=0

(µ− 1 + k)!

k!(µ− 1− k)!

×[(−1)k exp(z)− (−1)µ−1 exp(−z)

(2z)k+0.5

]. (A-3)


Since |g1|2 and |h1|2 are independent, the first term of (A-2),i.e., F1, can be expressed as

F1 =Pr|g1|2 6 γ

γP

· Pr|h1|2 6 γQ

γP

= F|g1|2

(γ

γP

)· F|h1|2

(γQγP

). (A-4)

By employing (6), F|g1|2(·) and F|h1|2(·) can be readilyobtained, then substituting the resulting expressions into (A-4),F1 can be easily deduced. As far as F2 is concerned, oneobtains:

F2 = Pr|g1|2 6 γ

γQ|h1|2, |h1|2 > γQ

γP

=

∫ ∞

γQγP

f|h1|2(y)

∫ γγQ

y

0

f|g1|2(x)dxdy

=

∫ ∞

γQγP

f|h1|2(y)F|g1|2

(γ

γQy

)dy. (A-5)

From (5) and (6), f|h1|2(·) and F|g1|2(·) can be readilydeduced, respectively. By substituting the resulting expressionsinto (A-5) and employing [22, eq. (3.351.2)], F2 can beobtained. Moreover, substituting F1 and F2 into (A-2), theCDF of γ1 can be obtained as (A-6) on the top of the nextpage.

Following a similar line of arguments, Fγ2(γ) can bedirectly derived from (A-6) by substituting the respectiveparameters by their counterparts (i.e., µg1 → µg2 , µh1 → µh2 ,hg1 → hg2 , hh1 → hh2 , Hg1 → Hg2 , Hh1 → Hh2 ,a(k1)g1 → a

(k1)g2 , a(k2)

h1→ a

(k2)h2

, b(k1)g1 → b

(k1)g2 , b(k2)

h1→ b

(k2)h2

,a(k)g1 → a

(k)g2 , b

(k)g1 → b

(k)g2 , Ag1 → Ag2 , Ah1 → Ah2 ,

Bg1 → Bg2 , Bh1→ Bh2

and Ω3 → Ω4). Finally, utilizingthe CDFs of γ1 and γ2, a tight lower bound for OP can bededuced as Pout(γth) = 1 − [1− Fγ1

(γth)] [1− Fγ2(γth)],

thus concluding the proof.

APPENDIX BPROOF OF THEOREM 2

Following a similar line of arguments as in the proof ofTheorem 1, in order to obtain the required bound, F1 and F2

defined in (A-4) and (A-5) need to be evaluated for arbitraryvalues of fading parameters. In order to deduce an analyticalexpression for (A-5), integrals of the form


, γth, γP , γQ)

=

∫ ∞

γQγP

f|h1|2(y)F|g1|2

(γ

γQy

)dy. (B-1)

need to be evaluated. For arbitrary values of the µ fadingparameters, the computation of (B-1) is very difficult. In orderto circumvent this problem, J (µgℓ , µhℓ

, ηgℓ , ηhℓ, γth, γP , γQ)

can be reformulated as


, γth, γP , γQ)

=

∫ ∞

Λ

Pr|gℓ|2 6 qy

∣∣|hℓ|2 = y

f|hℓ|(y)dy (B-2)

where q = γγQ

and Λ = γQ/γP . By invoking the Gil-Pelaez theorem [26], J (µgℓ , µhℓ

, ηgℓ , ηhℓ, γth, γP , γQ) can be

expressed as (13), thus concluding the proof.

APPENDIX CPROOF OF THEOREM 3

Using the lower bound Pout(γ) = Prmin(γ1, γ2) 6 γ,Pout(γ) can be approximated at high SNRs as Pout(γ) =Fγ1(γ) + Fγ2(γ) − Fγ1(γ)Fγ2(γ) ≃ Fγ1(γ) + Fγ2(γ). From[17, eqs. (14),(15)], for x → 0+, the asymptotic approximationfor fX(x) can be expressed as

fX(x) ≃ hµ

Γ(2µ)

(2µ

X

)2µ

x2µ−1, (C-1)

where µ ∈ µg1 , µg2 , µh1 , µh2 and h ∈ hg1 , hg2 , hh1 ,hh2. Employing (C-1), one can finally obtain the asymptoticapproximation for FX(x) as

FX(x) ≃ hµ

2µΓ(2µ)

(2µ

X

)2µ

x2µ. (C-2)

For arbitrary values of fading parameters, when γQ → ∞,by substituting (5) and (C-2) into (A-4) and (A-5), the CDFof γ1 can be approximated as

Fγ1(γ)γQ→∞=

hµg1g1 h

µh1

h1


(2µg1γ

ξΩ1γQ

)2µg1(2µh1

ξΩ3

)2µh1

+

√πµ

µh1+0.5

h1hµg1g1 h

µh1

h1


−0.5

h1Ω

µh1+0.5

3

×(2µg1γ

Ω1γQ

)2µg1

L(µg1 , µh1 , hh1 ,Ω3, y). (C-3)

Similarly, the asymptotic expression for Fγ2(γ) can be directlyobtained from (C-3) after replacing the parameters by theircounterparts. Finally, utilizing Pout(γ) ≃ Fγ1(γ) + Fγ2(γ),Theorem 3 can be readily deduced.

APPENDIX DPROOF OF THEOREM 4

For integer values of fading parameters, when γQ → ∞,substituting the modified Bessel function in closed form (A-3)into (6), and then substituting (5) and (C-2) into (A-4) and(A-5), the CDF of γ1 can be approximated as

Fγ1(γ)γQ→∞=

hµg1g1 h

µh1

h1


(2µg1γ

ξΩ1γQ

)2µg1(2µh1

ξΩ3

)2µh1

+hµg1g1


(hh1

Hh1

)µh1µh1

−1∑k=0

× (µh1 + k − 1)!

k!(µh1 − k − 1)!(4Hh1)k

(µh1

Ω3

)µh1−k (

2µg1γ

Ω1γQ

)2µg1

×

[(−1)k

Γ (2µg1 + µh1 − k,Ah1/ξ)

A2µg1

+µh1−k

h1

+ (−1)µh1Γ (2µg1 + µh1 − k,Bh1/ξ)

B2µg1+µh1

−k

h1

]. (D-1)


Fγ1(γ) = F|g1|2

(γ

γP

)+∑k1,p1k2,p2

(γ

γP

)p1a(k1)g1 Ap1

g1

(a(k2)h1

Ap2

h1exp

[−(Ag1

γ

γP+Ah1

γQγP

)]

+(−1)µh1 b(k2)h1

Bp2

h1exp

[−(Ag1

γ

γP+Bh1

γQγP

)])+ (−1)µg1 b(k1)

g1 Bp1g1

×(a(k2)h1

Ap2

h1exp

[−(Bg1

γ

γP+Ah1

γQγP

)]+ (−1)µh1 b

(k2)h1

Bp2

h1exp

[−(Bg1

γ

γP+Bh1

γQγP

)])

−∑k,p,q

(γ

γQ

)p

a(k)g1 Ap

g1

(µh1 + p− q − 1)!

(−1)qΓ(µh1

+ p− q, Ag1γγP

+Ah1

γQγP

)(Ag1

γγQ

+Ah1

)µh1+p−q

+(−1)µh1Γ

(µh1 + p− q, Ag1

γγP

+Bh1

γQγP

)(Ag1

γγQ

+Bh1

)µh1+p−q

+(−1)µg1 b

(k)g1 Bp

g1

(µh1 + p− q − 1)!

×

(−1)qΓ(µh1 + p− q,Bg1

γγP

+Ah1

γQγP

)(Bg1

γγQ

+Ah1

)µh1+p−q +

(−1)µh1Γ(µh1 + p− q,Bg1

γγP

+Bh1

γQγP

)(Bg1

γγQ

+Bh1

)µh1+p−q

. (A-6)

Similarly, the asymptotic expression for Fγ2(γ) can be directlyobtained from (D-1) after replacing the parameters by theircounterparts. Finally, utilizing Pout(γ) ≃ Fγ1(γ) + Fγ2(γ),thus concluding the proof.

REFERENCES

[1] C.-X. Wang, F. Haider, X.-Q. Gao, X.-H. You, Y. Yang, D. Yuan, H. Ag-goune, H. Haas, S. Fletcher, and E. Hepsaydir, “Cellular architectureand key technologies for 5G wireless communication networks,” IEEECommun. Mag., vol. 52, no. 2, pp. 122–130, Feb. 2014.

[2] H. A. Suraweera, P. J. Smith, and M. Shafi, “Capacity limits and perfor-mance analysis of cognitive radio with imperfect channel knowledge,”IEEE Trans. Veh. Technol., vol. 59, no. 4, pp. 1811–1822, May 2010.

[3] P. J. Smith, P. A. Dmochowski, H. A. Suraweera, and M. Shafi,“The effects of limited channel knowledge on cognitive radio systemcapacity,” IEEE Trans. Veh. Technol., vol. 62, no. 2, pp. 927–933, Feb.2013.

[4] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversityin wireless networks: Efficient protocols and outage behavior,” IEEETrans. Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.

[5] T. Q. Duong, V. N. Q. Bao, and H. J. Zepernick, “Exact outageprobability of cognitive AF relaying with underlay spectrum sharing,”Electron. Lett., vol. 47, no. 17, pp. 1001–1002, Aug. 2011.

[6] M. H. Xia and S. Aıssa, “Cooperative AF relaying in spectrum-sharing systems: Performance analysis under average interference powerconstraints and Nakagami-m fading,” IEEE Trans. Commun., vol. 60,no. 6, pp. 1523–1533, Jun. 2012.

[7] T. Q. Duong, D. B. da Costa, M. Elkashlan, and V. N. Q. Bao, “Cognitiveamplify-and-forward relay networks over Nakagami-m fading,” IEEETrans. Veh. Technol., vol. 61, no. 5, pp. 2368–2374, Jun. 2012.

[8] H. A. Suraweera, P. J. Smith, and N. A. Surobhi, “Exact outageprobability of cooperative diversity with opportunistic spectrum access,”in Proc. IEEE ICC 2008 Workshops (Cognitive and Cooperative WirelessNetworks Workshop - CoCoNet 2008), Beijing, China, May 2008, pp.79–84.

[9] W. Xu, J. Zhang, P. Zhang, and C. Tellambura, “Outage probabilityof decode-and-forward cognitive relay in presence of primary user’sinterference,” IEEE Commun. Lett., vol. 16, no. 8, pp. 1252–1255, Aug.2012.

[10] V. N. Q. Bao, T. Q. Duong, and C. Tellambura, “On the performanceof cognitive underlay multihop networks with imperfect channel stateinformation,” IEEE Trans. Commun., vol. 61, no. 12, pp. 4864–4873,Dec. 2013.

[11] J. L. Wang, Z. S. Zhang, Q. H. Wu, and Y. Z. Huang, “Outage analysisof cognitive relay networks with interference constraints in Nakagami-m channels,” IEEE Wireless Commun. Lett., vol. 2, no. 4, pp. 387–390,Aug. 2013.

[12] F. R. V. Guimaraes, D. B. da Costa, T. A. Tsiftsis, C. C. Cavalcante, andG. K. Karagiannidis, “Multiuser and multirelay cognitive radio networksunder spectrum-sharing constraints,” IEEE Trans. Veh. Technol., vol. 63,no. 1, pp. 433–439, Jan. 2014.

[13] H. Tran, H.-J. Zepernick, H. Phan, and L. Sibomana, “Performanceanalysis of a cognitive radio network with a buffered relay,” IEEE Trans.Veh. Technol., vol. 64, no. 2, pp. 566–579, Feb. 2015.

[14] X. Zhang, Y. Zhang, Z. Yan, J. Xing, and W. Wang, “Performanceanalysis of cognitive relay networks over Nakagami-m fading channels,”IEEE J. Sel. Areas Commun., vol. 33, no. 5, pp. 865–877, May 2015.

[15] M. D. Yacoub, “The κ−µ distribution and the η−µ distribution,” IEEEAnt. and Propag. Mag., vol. 49, no. 1, pp. 68–81, Feb. 2007.

[16] H. Yu, G. Wei, F. Ji, and X. Zhang, “On the error probability of cross-QAM with MRC reception over generalized η − µ fading channels,”IEEE Trans. Veh. Technol., vol. 60, no. 6, pp. 2631–2643, Jul. 2011.

[17] K. P. Peppas, G. C. Alexandropoulos, and P. T. Mathiopoulos, “Perfor-mance analysis of dual-hop AF relaying systems over mixed η−µ andκ− µ fading channels,” IEEE Trans. Veh. Technol., vol. 62, no. 7, pp.3149–3163, Sep. 2013.

[18] K. Peppas, F. Lazarakis, A. Alexandridis, and K. Dangakis, “Error per-formance of digital modulation schemes with MRC diversity receptionover η-µ fading channels,” IEEE Trans. Wireless Commun., vol. 8,no. 10, pp. 4974–4980, Oct. 2009.

[19] K. Peppas, “Dual-hop relaying communications with cochannel interfer-ence over η − µ fading channels,” IEEE Trans. Veh. Technol., vol. 62,no. 8, pp. 4110–4116, Oct. 2013.

[20] S. Kumar, G. Chandrasekaran, and S. Kalyani, “Analysis of outageprobability and capacity for κ−µ/η−µ faded channel,” IEEE Commun.Lett., vol. 19, no. 2, pp. 211–214, Feb. 2015.

[21] J. P. Pena-Martın, J. M. Romero-Jerez, and C. Tellez-Labao, “Perfor-mance of selection combining diversity in η − µ fading channels withinteger values of µ,” IEEE Trans. Veh. Technol., vol. 64, no. 2, pp.834–839, Feb. 2015.

[22] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, andProducts, 6th ed. New York: Academic Press, 2000.

[23] D. Morales-Jimenez and J. F. Paris, “Outage probability analysis for η-µ fading channels,” IEEE Commun. Lett., vol. 14, no. 6, pp. 521–523,Jun. 2010.

[24] K. P. Peppas, F. Lazarakis, T. Zervos, A. Alexandridis, and K. Dangakis,“Sum of non-identical independent squared η-µ variates and applicationsin the performance analysis of DS-CDMA systems,” IEEE Trans.Wireless Commun., vol. 9, no. 9, pp. 2718–2723, Sep. 2010.


[25] H. A. Suraweera, R. H. Y. Louie, Y. Li, G. K. Karagiannidis, andB. Vucetic, “Two hop amplify-and-forward transmission in mixedRayleigh and Rician fading channels,” IEEE Commun. Lett., vol. 13,no. 4, pp. 227–229, Apr. 2009.

[26] J. Gil-Pelaez, “Note on the inversion theorem,” Biometrika, vol. 38, pp.481–482, 1951.

Jing Yang was born in Tai’an, China, in 1982.She received her Ph. D. degree in communicationsand information systems from Southwest JiaotongUniversity, Chengdu, in 2013. She is currently withthe School of Information Engineering, Yangzhou U-niversity. Her research interests include cooperativecommunications, cognitive radio networks, physicallayer security, massive MIMO.

Lei Chen was born in Jiangsu, China, in 1991. Shereceived the B.S. degree in communication engi-neering from Yangzhou University, Jiangsu, in 2009.She is currently working towards her M.S. degree inthe School of Information Engineering, YangzhouUniversity. Her research interests are in cooperativerelaying communications, cognitive radio networks,physical layer security.

Xianfu Lei (S’09-M’13) was born in December1981. He received the B.E. and Ph.D. degreesin Communication and Information Systems fromSouthwest Jiaotong University, Chengdu, China, in2003 and 2012, respectively. Since 2015, he has beenan Associate Professor with the School of Infor-mation Science and Technology, Southwest JiaotongUniversity. From 2012 to 2014, he was a ResearchFellow with the Department of Electrical and Com-puter Engineering, Utah State University, Logan,UT, USA. He has published nearly 60 journal and

conference papers in his areas of interest. His current research interests includefifth-generation wireless communications, cooperative communications, cog-nitive radio, physical-layer security, and energy harvesting. Dr. Lei currentlyserves on the Editorial Board of the IEEE COMMUNICATIONS LETTERS,Telecommunication Systems (Springer), and Security and CommunicationNetworks (Wiley). He served as the Lead Guest Editor of the Special Issueon Energy Harvesting Wireless Communications of the EURASIP Journalon Wireless Communications and Networking (2014). He has also servedas a Technical Program Committee Member for several major internationalconferences, such as the IEEE International Conference on Communications;the IEEE Global Communications Conference; the IEEE Wireless Com-munications and Networking Conference; the IEEE Vehicular TechnologyConference Spring/Fall; and the IEEE International Symposium on Personal,Indoor, and Mobile Radio Communications. He received an ExemplaryReviewer Certificate from the IEEE COMMUNICATIONS LETTERS andthe IEEE WIRELESS COMMUNICATIONS LETTERS in 2013.

Kostas P. Peppas (M’09-SM’14) was born in A-thens, Greece in 1975. He obtained his diplomain electrical and computer engineering from theNational Technical University of Athens in 1997and the Ph.D. degree in wireless communicationsfrom the same department in 2004. From 2004 to2007 he was with the University of Peloponnese,Department of Computer Science, Tripoli, Greeceand from 2008 to 2014 with the National Centrefor Scientific Research-“Demokritos,” Institute ofInformatics and Telecommunications as a researcher.

In 2014, he joined the Department of Telecommunication Science and Tech-nology, University of Peloponnese, where he is currently a lecturer. His currentresearch interests include digital communications, MIMO systems,cooperativecommunications, wireless and personal communication networks, cognitiveradio, digital signal processing, system level analysis, and design. Dr. K. P.Peppas has authored more than 70 journal and conference papers.

Trung Q. Duong (S’05, M’12, SM’13) received hisPh.D. degree in Telecommunications Systems fromBlekinge Institute of Technology (BTH), Sweden in2012. Since 2013, he has joined Queen’s UniversityBelfast, UK as a Lecturer (Assistant Professor).His current research interests include cooperativecommunications, cognitive radio networks, physicallayer security, massive MIMO, cross-layer design,mm-waves communications, and localization for ra-dios and networks. He is the author or co-author of170 technical papers published in scientific journals

and presented at international conferences.Dr. Duong currently serves as an Editor for the IEEE COMMUNICATIONS

LETTERS, IET COMMUNICATIONS, WILEY TRANSACTIONS ON EMERGINGTELECOMMUNICATIONS TECHNOLOGIES. He has also served as the GuestEditor of the special issue on some major journals including IEEE JOURNALIN SELECTED AREAS ON COMMUNICATIONS, IET COMMUNICATIONS,IEEE WIRELESS COMMUNICATIONS MAGAZINE, IEEE COMMUNICATION-S MAGAZINE, EURASIP JOURNAL ON WIRELESS COMMUNICATIONS ANDNETWORKING, EURASIP JOURNAL ON ADVANCES SIGNAL PROCESSING.He was awarded the Best Paper Award at the IEEE Vehicular TechnologyConference (VTC-Spring) in 2013, IEEE International Conference on Com-munications (ICC) 2014.

dual-hop cognitive amplify-and-forward relaying networks over η − µ fading channels

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