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2656 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60,NO. 6, JULY2011
End-to-End Performance of Cooperative Relaying in
Spectrum-Sharing Systems With Quality of
Service Requirements
Vahid Asghari, Student Member, IEEE, and Sonia Aïssa, Senior Member, IEEE
Abstract—We propose adopting a cooperative relaying tech-
nique in spectrum-sharing cognitive radio (CR) systems to more
effectively and efficiently utilize available transmission resources,
such as power, rate, and bandwidth, while adhering to the quality
of service (QoS) requirements of the licensed (primary) users of
the shared spectrum band. In particular, we first consider that
the cognitive (secondary) user’s communication is assisted by an
intermediate relay that implements the decode-and-forward (DF)
technique onto the secondary user’s relayed signal to help with
communication between the corresponding source and the des-
tination nodes. In this context, we obtain first-order statistics
pertaining to the first- and second-hop transmission channels,
and then, we investigate the end-to-end performance of the pro-
posed spectrum-sharing cooperative relaying system under re-
source constraints defined to assure that the primary QoS is
unaffected. Specifically, we investigate the overall average bit
error rate (BER), ergodic capacity, and outage probability of the
secondary’s communication subject to appropriate constraints on
the interference power at the primary receivers. We then consider
a general scenario where a cluster of relays is available between the
secondary source and destination nodes. In this case, making use of
the partial relay selection method, we generalize our results for the
single-relay scheme and obtain the end-to-end performance of the
cooperative spectrum-sharing system with a cluster of Lavailable
relays. Finally, we examine our theoretical results through simu-
lations and comparisons, illustrating the overall performance of
the proposed spectrum-sharing cooperative system and quantify
its advantages for different operating scenarios and conditions.
Index Terms—Clustered setting, cognitive radio (CR), coopera-
tive relaying, relay selection, spectrum sharing.
I. INTRODUCTION
ELECTROMAGNETIC spectrum shortage is one of the
main challenges in wireless communication systems [1].
Based on the frontier technology of cognitive radio (CR), the
concept of spectrum sharing was proposed as a solution to the
Manuscript received May 3, 2010; revised September 22, 2010 and
January 25, 2011; accepted March 3, 2011. Date of publication April 5, 2011;
date of current version July 18, 2011. This work was supported by a Discovery
Grant from the Natural Sciences and Engineering Research Council (NSERC)
of Canada under grant number RGPIN/222907. This paper was presented
in part at the IEEE International Communications Conference, Cape Town,
South Africa, May 23–27, 2010. The review of this paper was coordinated by
Prof. B. Hamdaoui.
V. Asghari is with Institut National de la Recherche Scientifique (INRS),
University of Quebec, Montreal, QC, Canada (e-mail: vahid@emt.inrs.ca).
S. Aïssa is with INRS, University of Quebec, Montreal, QC, Canada, and
with KAUST, Thuwal, KSA (e-mail: sonia.aissa@ieee.org).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2011.2136391
inefficient utilization of the spectrum. Spectrum-sharing CR
offers tremendous potential to improve spectral efficiency by
allowing unlicensed (secondary) users to share the spectrum
band originally allocated to the licensed (primary) users, as
long as the generated interference aggregated at the primary
receivers is below acceptable levels.
Generally, in spectrum-sharing systems, the secondary user’s
transmission is limited according to the maximum interference
power inflicted onto the primary receiver in terms of average or
peak values [2]. In this context, capacity of a spectrum-sharing
system was investigated in [3] considering either peak or aver-
age interference constraint at the primary receiver. Later, in [4],
the ergodic capacity and optimal power allocation policy of fad-
ing spectrum-sharing channels was studied, considering joint
constraints on the peak and average interference powers at the
primary receiver. In addition to the primary users having privi-
leged access to the spectrum in spectrum-sharing systems, any
transmission by the secondary party should not affect their qual-
ity of service (QoS), which necessitates proper management of
the resources at the secondary users’s transmitters. For instance,
appropriate constraints on the secondary transmit power need
to be imposed so that the primary user’s rate is guaranteed to
remain higher than a target value for a given percentage of time.
Resource management is indeed of fundamental importance
in spectrum-sharing systems [4], [5]. However, when the avail-
able spectrum resources are not sufficient enough to guaran-
tee reliable transmission at the secondary party, the resource
allocation policy may not be able to fulfill the secondary
users’ requirements. In such cases, the secondary system has
to implement sophisticated techniques to meet its performance
requirements. One notable technique is cooperative communi-
cation, which exploits the natural spatial diversity of multiuser
systems. Indeed, cooperative transmission (communication us-
ing relay nodes) is a promising way to combat signal fading
due to multipath radio propagation and improve the system
performance and coverage area [6].
A basic cooperative relay communication model consists
of three terminals, i.e., a source, a relay, and a destination.
Relaying protocols mainly include decode-and-forward (DF)
[6], [7], where the relay decodes the received signal and then re-
encodes it before forwarding it to the destination, and amplify-
and-forward (AF) [8], where the relay sends a scaled version
of its received signal to the destination. Recently, different
cooperative transmission models were analyzed in terms of
outage and error probability performance. For instance, the
0018-9545/$26.00 © 2011 IEEE
ASGHARI AND AÏSSA: END-TO-END PERFORMANCE OF COOPERATIVE RELAYING IN SPECTRUM-SHARING SYSTEM 2657
bit error rate (BER) performance of dual-hop cooperative
transmissions was analyzed in [6] and [9], considering DF
and AF relaying over Rayleigh and Nakagami fading channels,
respectively. The effects of the interference generated by the
relays in cooperative networks has also been addressed, e.g.,
in [10]. On the other hand, achievable capacities and power
allocation for cooperative and relay channels were investigated
in [11]. The concept of relaying has also been applied in
CR context to assist the transmission of secondary users and
improve spectrum efficiency [12]–[16].
Using cooperative transmission in spectrum-sharing CR sys-
tems can indeed yield higher efficiency in utilizing the spectrum
resources. In this context, we herein adopt the cooperative re-
laying technique for the secondary transmission in a spectrum-
sharing system to more effectively use the available spectrum
resources and decrease the generated interference at the primary
receivers. Specifically, we consider a dual-hop cooperative
spectrum-sharing relaying system and investigate its end-to-end
performance when transmissions are limited by constraints on
the tolerable interference by the primary user such that its trans-
mission is supported with a constant rate for a certain period of
time. DF relays are employed in the communication between
the secondary source (transmitter) and destination (receiver)
nodes, and we obtain the average BER and ergodic capacity
of the cooperative spectrum-sharing relaying system with an
intermediate relay between the source and destination to help
the secondary communication process. We further consider
the scenario when a cluster of relays is available between the
secondary source and destination nodes. In this case, using
partial relay selection (PRS) [17], we generalize the results
presented here for the single-relay scenario and obtain the
average BER and the ergodic capacity of the cooperative system
with a cluster of Lavailable relays. Finally, we investigate the
outage probability performance of the cooperative spectrum-
sharing system under consideration for both the single-relay
and multiple-relay schemes.
In detailing these contributions, the remainder of this paper is
organized as follows: Section II describes the system and chan-
nel models. In Section III, we determine the power constraints
that need to be satisfied by the secondary users to guarantee the
QoS requirement at the primary-user side is always met. Several
relevant statistics corresponding to the instantaneous signal-to-
noise ratio (SNR) of the first- and second-hop transmission
channels are derived in Section IV. In Section V, we obtain
the average BER and the ergodic capacity of the spectrum-
sharing cooperative systems under the aforementioned power
constraints. Thereafter, the system with PRS strategy is con-
sidered in Section VI. Section VII presents numerical results
and comparisons illustrating the performance of the secondary
communication in terms of average BER, ergodic capacity, and
outage probability for the cases with and without relay selec-
tion. At the end, concluding remarks are drawn in Section VIII.
II. SYSTEM AND CHANNEL MODELS
Consider a spectrum-sharing CR system where DF relays
are employed to help in the secondary user’s communication
process. More specifically, our system consists of a pair of sec-
Fig. 1. Dual-hop cooperative spectrum-sharing system.
ondary source and destination nodes (SS and SD) located in the
vicinity of the primary receiver (PR) and a DF relay node (Rs),1
as shown in Fig. 1. There is no direct link between the source
and destination nodes, and the communication is established
only via the relay in a dual-hop fashion. In this way, during
the first hop, the SS communicates with the relay node Rs.
As the primary and secondary users share the same frequency
band, the cognitive (secondary) user is allowed to operate in
the licensee’s spectrum, as long as the primary QoS remains
satisfied. For this, based on the interference channel state g1,
the SS adjusts its transmit power under predefined resource
constraints to assure that the primary QoS is unaffected. Similar
to the first-hop transmission, in the second-hop one, the Rsnode
uses the same spectrum band originally assigned to the primary
signals to communicate with SD. In the second hop, Rsmakes
use of the interference channel state g2to adhere to the primary
requirements. It is assumed that the first and second hops’ trans-
missions are independent. It is also conjectured that SS and Rs
have perfect knowledge of their respective interference channel
gains. This can be obtained through a spectrum-band manager
that mediates between the licensed and unlicensed users [18].
However, it is worth noting that, for certain scenarios, obtaining
the interference channel power gains at the secondary network
may be challenging. For these cases, our results serve as upper
bounds for the performance of the considered spectrum-sharing
relay channels and represent efficient system design tools.
We assume that all nodes transmit over discrete-time
Rayleigh fading channels. The channel power gain between SS
and Rsis given by βwith mean τf, and the one between Rs
and SD is given by αwith mean τs. The interference channel
gains g1and g2are mutually independent and exponentially
distributed with unit mean. Perfect channel state information
(CSI) is available at terminals SS, Rs, and SD. Finally, we con-
sider that the interference generated by the primary transmitter
(PT) operating in the secondary transmission area is modeled
as additive zero-mean Gaussian noise at Rsand SD, with noise
variance σ2
1and σ2
2, respectively.2
III. SPECTRUM-SHARING CONSTRAINTS
The aim of this section is to define the QoS requirements
pertaining to the primary users of the shared spectrum band and
1The scheme with multiple relays and partial relay selection is considered in
Section VI.
2Validity of this assumption is sustained by the fact of considering the “low-
interference regime,” as studied in [19].
2658 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60,NO. 6, JULY2011
present them in terms of resource constraints on the secondary
transmission policy, which are considered throughout this pa-
per. As briefly mentioned, to control the interference power
inflicted on the primary receivers, the secondary transmitters
must adjust their transmit powers so that the QoS requirements
associated with the primary communication is maintained at a
predefined required level. Herein, the primary user’s QoS is
defined in terms of a minimum service rate r0that should be
satisfied with a certain outage probability Pout
p, according to
PrEβ,g1
log21+ Sph1
Ssr(β, g1)g1+δ2
1<r0
≤Pout
p,(1a)
PrEα,g2
log21+ Sph2
Srd(α, g2)g2+δ2
2<r0
≤Pout
p,(1b)
where Pr{·}stands for probability; EX[·]denotes statistical av-
erage with respect to X,h1and h2are the channel power gains
pertaining to the links PT-PR1and PT-PR2, respectively3; and
Ssr(β, g1)and Srd(α, g2)denote the secondary source–relay
and relay–destination transmit powers,4respectively, written
as a function of (β,g1)and (α, g2). Furthermore, Spdenotes
the average transmit power of the primary user, and δ2
1and
δ2
2designate the variances of the additive Gaussian noise at
nodes PR1and PR2, respectively. In the following theory, we
translate the primary QoS requirements into average interfer-
ence constraints that should be accounted for in the secondary
transmission policy.
Theorem 1: (Average Interference Constraints): Inapri-
mary/secondary cooperative spectrum-sharing system, where
the secondary user’s communication is performed through dual-
hop relaying (cf. Fig. 1) and the primary QoS is defined by (1),
the secondary user has to adhere to the following average inter-
ference constraints for the first and second hops, respectively:
Eβ,g1[Ssr(β,g1)g1]≤W1,(2a)
Eα,g2[Srd(α, g2)g2]≤W2,(2b)
where the power limits W1and W2are expressed in terms of the
primary user’s minimum required rate r0and outage probability
Pout
pas
W1=ln 1−Pout
p
η−δ2
1,W
2=ln 1−Pout
p
η−δ2
2,
(3)
with η=(1−2r0/Sp).
Proof: See Appendix A.
Furthermore, given that the primary receiver does not tolerate
an interference higher than a certain threshold, in addition to the
constraints in (2), we consider limitations on the peak-received
power at the primary receivers, as follows:
Ssr(β, g1)g1≤Q1,(4a)
Srd(α, g2)g2≤Q2,(4b)
3We consider that h1and h2are independent and exponentially distributed
with unit mean.
4Subscripts “sr” and “rd” denote the source–relay and relay–destination
links, respectively.
where Q1and Q2are the peak received-power limits pertaining
to the first and second hops, respectively.
IV. MAIN STATIS T I C S
In this section, based on the average and peak received power
constraints at the primary receivers, we derive the probability
distribution function (PDF) and cumulative distribution func-
tion (CDF) of the instantaneous SNR pertaining to each hop
on the secondary link. As well known, these statistics are two
important metrics that can be used to study the performance
of cooperative communication systems in general. In our case,
such statistics will be crucial in the analysis of the proposed
spectrum-sharing cooperative relaying system (see Fig. 1),
where the relay Rsis utilized by the secondary user to enable
communication between SS and SD.5
From the interference constraints given in (2a) and (4a), the
optimal power transmission policy that maximizes the ergodic
capacity of the secondary’s first-hop link can be obtained as [4]
Ssr(β, g1)=⎧
⎪
⎪
⎨
⎪
⎪
⎩
Q1
g1,β
g1>σ2
1
μf
λf
g1−σ2
1
β,σ2
1
λf≤β
g1≤σ2
1
μf
0,β
g1<σ2
1
λf
(5)
where μf=λf−Q1, and the first-hop optimization parameters
λfand μfare found by setting the power constraints in (2a) and
(4a) at equality. These optimization parameters can be obtained
using
λf=Q1
1−exp(X)−σ2
1
τf,(6)
μf=Q1
exp(X)−1−σ2
1
τf,(7)
where X=(W1−Q1)τf/σ2
1. Details pertaining to the deriva-
tions of (6) and (7) are provided in Appendix B.
Accordingly, the instantaneous received SNR at the sec-
ondary relay (Rs)can be expressed as
γsr β
g1=Ssr(β, g1)β
σ2
1
=⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
Q1
σ2
1β
g1,β
g1>σ2
1
μf
λf
σ2
1β
g1−1,σ2
1
λf≤β
g1≤σ2
1
μf
0.β
g1<σ2
1
λf
(8)
Now, since βand g1are independent exponential random
variables, it is easy to show that the PDF of Z=β/g1
is given by fZ(z)=τf/(τf+z)2[20]. In addition, from
Fig. 2, we observe two different slopes when sketching γsr in
terms of Z. Hence, to find the required first-order statistics
(PDF and CDF) of γsr, we have to take into account two
ranges: 0≤γsr ≤(Q1/μf), and γsr >(Q1/μf).For0≤γsr ≤
(Q1/μf),γsr increases by the order of λf/σ2
1; hence, its PDF is
given by
fγsr (γ)= σ2
1
λffZ(z)z=σ2
1
λf(γ+1)
.(9)
5Hereafter, for clarity, this relay is referred to as secondary relay.
ASGHARI AND AÏSSA: END-TO-END PERFORMANCE OF COOPERATIVE RELAYING IN SPECTRUM-SHARING SYSTEM 2659
Fig. 2. Schematic variation of the total received SNR at the secondary
destination SD.
For the second range, i.e., when γsr >(Q1/μf), the PDF of γsr
can be obtained according to
fγsr (γ)= σ2
1
Q1
fZ(z)z=σ2
1
Q1γ
.(10)
Thus, combining (9) and (10) and after some mathematical
manipulations,6it follows that
fγsr (γ)=⎧
⎪
⎨
⎪
⎩
σ2
1λfτf
(λfτf+σ2
1γ)2,0≤γsr ≤λf
μf,
σ2
1Q1τf
(Q1τf+σ2
1(γ−1))2,γ
sr >λf
μf.(11)
Subsequently, using Fγsr(γ)=γ
0fγsr (γ)dγ,theCDFofγsr
can be expressed as
Fγsr (γ)=⎧
⎨
⎩
σ2
1γ
λfτf+σ2
1γ,0≤γsr ≤λf
μf,
σ2
1(γ−1)
(Q1τf+σ2
1(γ−1)),γ
sr >λf
μf.(12)
Using the same rationale previously described, the PDF of
the instantaneous SNR associated with the second-hop trans-
mission can be obtained as
fγrd (γ)=⎧
⎪
⎨
⎪
⎩
σ2
2λsτs
(λsτs+σ2
2γ)2,0≤γrd ≤λs
μs,
σ2
2Q2τs
(Q2τs+σ2
2(γ−1))2,γ
rd >λs
μs,(13)
where λsand μsdenote the second-hop optimization para-
meters, which can be obtained from (6) and (7) with the
appropriate substitutions. Then, performing the integration of
(13) with respect to γ,theCDFofγrd can be expressed as
shown in
Fγrd (γ)=⎧
⎨
⎩
σ2
2γ
λsτs+σ2
2γ,0≤γrd ≤λs
μs,
σ2
2(γ−1)
(Q2τs+σ2
2(γ−1)),γ
rd >λs
μs.(14)
In the next section, using the derived statistics and focusing
on the secondary communication through a single relay, we
investigate the end-to-end performance of the spectrum-sharing
6Note that λf=μf+Q1.
cooperative system with DF relaying. More specifically, closed-
form expressions for the average BER and ergodic capacity are
provided under the resource constraints given in (2) and (4).
V. E ND-TO-END PERFORMANCE ANALYSIS
A. Average BER
We now investigate the average BER of the spectrum-sharing
cooperative system described in Section IV. Considering DF
as the relaying technique implemented at node Rs, the average
end-to-end (e2e) BER of the system under study is given by [6]
Pe2e =Pγsr +Pγrd −2Pγsr Pγrd ,(15)
where Pγsr and Pγrd correspond to the average BER of the
first and second hops, respectively, which can be calculated
according to [21]
Pγτ=1
√2π
∞
0
Fγτξ2
Cexp −ξ2
2dξ, (16)
where τ∈{sr,rd}, and Cis a constant related to the modu-
lation scheme, e.g., C=2for phase-shift keying modulation.
Substituting (12) in (16), the average BER for the first-hop
transmission is given by
Pγsr =1
√2π×⎡
⎢
⎢
⎢
⎢
⎣
λfC
μf
0σ2
1ξ2
λfτfC+σ2
1ξ2exp−ξ2
2dξ
+
∞
λfC
μf
σ2
1(ξ2−C)
(Q1Cτf+σ2
1(ξ2−C))exp−ξ2
2dξ⎤
⎥
⎥
⎥
⎥
⎦
,(17)
which, after simple manipulations, can be rewritten as
Pγsr =σ2
1
√2π(I1+I2),(18)
where
I1
Δ
=λfC
μf
0ξ2
λfτfC+σ2
1ξ2exp −ξ2
2dξ, (19a)
I2
Δ
=
∞
λfC
μf
(ξ2−C)
(Q1Cτf+σ2
1(ξ2−C))exp −ξ2
2dξ.
(19b)
In the sequel, we provide closed-form expressions for the
integrals I1and I2. For the first integral form (19a), we perform
2660 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60,NO. 6, JULY2011
the change of variable t=(μf/λfC)ξ2, thus leading to
I1=⎛
⎝1
μfτfλfC
4μf⎞
⎠
1
0
exp−λfC
2μftt1
21+ σ2
1
μfτft
−1
dt
(20)
which can further be derived according to the following closed-
form expression:
I1=⎛
⎝1
3μfτfλfC
μf⎞
⎠Φ13
2,−1; 5
2;−σ2
1
μfτf,−λfC
2μf,(21)
where Φ1(a, b1,b
2;z;x1,x
2,y)is the first-kind confluent hy-
pergeometric function [22] defined by
Φ1(a, b1,...,b
L;z;x1,...,x
L,y)= Γ(z)
Γ(a)Γ(z−a)
×
1
0
exp(yt)ta−1(1 −t)z−a−1
L
i=1
(1 −xit)−bidt (22)
with Γ(·)denoting the Gamma function [23].
Then, carrying out the change of variable t=(μf/λfC)ξ2in
the integral of (19b) and after further algebraic manipulations,
we obtain
I2=√λfC
2 μf(σ2
1−Q1τf)
∞
1
exp −λfC
2μftt−1
21−λf
μft
×1−σ2
1λf
μf(σ2
1−Q1τf)t−1
dt. (23)
By considering the integral complementary characteristic, (23)
can be reexpressed as given in
I2=√λfC
2 μf(σ2
1−Q1τf)
×⎛
⎝
∞
0
exp−λfC
2μftt−1
21−λf
μft
×1−σ2
1λf
μf(σ2
1−Q1τf)t−1
dt
−
1
0
exp −λfC
2μftt−1
21−λf
μft
×1−σ2
1λf
μf(σ2
1−Q1τf)t−1
dt⎞
⎠.(24)
To solve (24), we first present an integral representation for the
second-kind confluent hypergeometric function given by [24]
Φ2(a, b1,...,b
K;z;x1,...,x
K,y)= 1
Γ(a)
×
∞
0
exp(−yt)ta−1(1 + t)z−a−1
K
i=1
(1 + xit)−bidt. (25)
Then, after careful observation, one can recognize that (24) can
be expressed in terms of confluent hypergeometric functions of
the first and second kind as follows:
I2=√λfC
2 μf(σ2
1−Q1τf)
×√πΦ21
2,−1,1; 3
2;−λf
μf,−σ2
1λf
μf(σ2
1−Q1τf),λfC
2μf
−2Φ1
1
2,−1,1; 3
2;λf
μf,σ2
1λf
μf(σ2
1−Q1τf),−λfC
2μf.
(26)
Finally, incorporating the expressions in (21) and (26) into (18)
yields a closed-form expression for the average BER of the first-
hop link according to
Pγsr =σ2
1√λfC
3μfτf 2πμf
×Φ1
3
2,−1; 5
2;−σ2
1
μfτf,−λfC
2μf+σ2
1√λfC
8μf(σ2
1−Q1τf)
×Φ2
1
2,−1,1; 3
2;−λf
μf,−σ2
1λf
μf(σ2
1−Q1τf),λfC
2μf
−σ2
1√λfC
2πμf(σ2
1−Q1τf)
×Φ1
1
2,−1,1; 3
2;λf
μf,σ2
1λf
μf(σ2
1−Q1τf),−λfC
2μf.
(27)
It is worth noting that applying the same approach for the
second-hop transmission, Pγrd can be easily obtained by appro-
priate substitutions of the respective second-hop transmission
parameters (Q1,λ
f,μ
f,τf,σ
2
1)→(Q2,λ
s,μ
s,τs,σ
2
2). Finally,
by substituting Pγsr and Pγrd into (15), a closed-form expres-
sion for the average BER is attained.
B. Ergodic Capacity
Ergodic capacity is an important performance index for the
system under study. In theory, ergodic capacity corresponds
to the maximum long-term achievable rate over all channel
states of the time-varying fading channel. Herein, we obtain a
closed-form expression for the ergodic capacity of the dual-hop
cooperative spectrum-sharing relaying system under average
and peak received-power constraints defined in Section III.
In dual-hop DF cooperative relaying transmission, based
on the min-cut max-flow theorem presented in [25], the total
system capacity cannot be larger than the capacity achieved
by each individual relaying link. Mathematically speaking,
the overall system capacity is the minimum of the individual
capacity that can be achieved over the first and second hops
[26]. Therefore, the ergodic capacity of dual-hop DF relaying
channels is given by
C=1
2min{Cγsr ,C
γrd },(28)
where Cγsr and Cγrd denote the capacity of the first and second
hops, respectively, with Cγ(γ∈{γsr,γ
rd})calculated accord-
ing to Cγ=Eγ[log2(1 + γ)]. By substituting the obtained
ASGHARI AND AÏSSA: END-TO-END PERFORMANCE OF COOPERATIVE RELAYING IN SPECTRUM-SHARING SYSTEM 2661
PDFs pertaining to the first- and second-hop transmissions
expressed in (11) and (13), these terms can be expressed as
Cγsr =
λf
μf
0
log2(1 + γ)fγsr (γ)dγ +
∞
λf
μf
log2(1 + γ)fγsr (γ)dγ,
(29)
and
Cγrd =
λs
μs
0
log2(1 + γ)fγrd (γ)dγ +
∞
λs
μs
log2(1 + γ)fγrd (γ)dγ.
(30)
Then, evaluating the integrals in the preceding expressions
and using some mathematical manipulation [27], the first- and
second-hop capacity expressions are obtained as given in
Cγsr =Q1τf
2σ2
1−Q1τflog2σ2
1
Q1−λfτf
σ2
1−λfτflog2(τf)
+σ2
1τf(Q1−2λf)
(2σ2
1−Q1τf)(σ2
1−λfτf)log2λf+μf
σ2
1−μfτf,
(31)
and
Cγrd =Q2τs
2σ2
2−Q2τslog2σ2
2
Q2−λsτs
σ2
2−λsτslog2(τs)
+σ2
2τs(Q2−2λs)
(2σ2
2−Q2τs)(σ2
2−λsτs)log2λs+μs
σ2
2−μsτs,
(32)
respectively. Having obtained closed-form expressions for Cγsr
and Cγrd , we can evaluate the ergodic capacity of the system
under consideration according to (28).
VI. END-TO-END PERFORMANCE WITH
PARTIAL RELAY SELECTION
In this section, we extend our cooperative system model
by considering a cluster of relays between SS and SD nodes,
which consists of Lrelays Rsl,l=1,...,L (Fig. 3). We
assume that the relays are located close to each other (optimal
clustering [28]), which implies the same average received SNR
at relays within a cluster.7However, it is worth noting that the
instantaneous SNR values vary from relay to relay in a cluster.
We define the channel power gain between SS and the lth relay
by βland the interference channel from the SS to the PR by
g1, as shown in Fig. 3. We assume that the channel power gains
{βl}L
l=1 are exponentially distributed with the same mean τf.
7Note that an important factor for the performance of cooperative relaying
systems is the selection of appropriate relay stations out of a set of po-
tential candidates [28], which might be either fixed relay part of a certain
network infrastructure or simply other neighboring users in case of cooperative
communication.
Fig. 3. Dual-hop cooperative spectrum-sharing system with PRS.
Furthermore, it is assumed that the channel gains are mutually
independent and that perfect CSI is available at the SS and the
relays through appropriate feedback. Using this information,
the SS selects the best relay that provides the maximum instan-
taneous SNR during the first-hop transmission. Hence, denoting
the instantaneous SNR of each link as γsr(Zl)=Ssr (Zl)βl/σ2
1,
where Zl=βl/g1, the maximum instantaneous SNR of the
first-hop transmission is given by γsr = maxl=1,...,L{γsr(Zl)}.
The chosen relay detects and forwards the received signal to
the destination node SD. For more details about the previously
described selection strategy, which is called PRS, see [17]
and [29].
As the PRS strategy is employed in the first hop, from the
order statistics theory [30], the CDF of the first hop can be
expressed as
Fprs
γsr (γ)=[Fγsr (γ)]L,(33)
where Fγsr (γ)is given by (12). Accordingly, we can obtain the
PDF of the first-hop transmission by performing the derivative
of the CDF expression in (33) with respect to γsr, i.e.,
fprs
γsr (γ)Δ
=dF prs
γsr (γ)
dγ =L(Fγsr (γ))L−1fγsr (γ),(34)
which, after appropriate substitutions and some mathematical
manipulations, can be expressed as
fprs
γsr (γ)=⎧
⎪
⎪
⎨
⎪
⎪
⎩
Lλfτf(σ2
1)LγL−1
(λfτf+σ2
1γ)L+1 ,0≤γsr ≤λf
μf,
LQ1τf(σ2
1)L(γ−1)L−1
(Q1τf+σ2
1(γ−1))L+1 ,γ
sr <λf
μf.
(35)
Note that the PDF and CDF of the second hop, i.e., fγrd (γ)
and Fγrd (γ), remain the same, as presented in (13) and (14),
respectively. In what follows, considering the PRS strategy,
we obtain closed-form expressions for the average BER and
the achievable ergodic capacity of the dual-hop cooperative
spectrum-sharing system under the constraints on the average
and peak received interference at the primary receivers.
A. Average BER
Considering the aforementioned relay selection strategy,
the end-to-end average BER of the cooperative DF relaying
2662 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60,NO. 6, JULY2011
spectrum-sharing communication system is calculated accord-
ing to
Pprs
e2e =Pprs
γsr +Pγrd −2Pprs
γsr Pγrd ,(36)
where Pprs
γsr and Pγrd are the average SERs corresponding to
the first and second hops, respectively. Note that Pγrd is calcu-
lated similar to (18) by making the necessary substitutions, as
explained in Section V. Furthermore, substituting the CDF (33)
into (16) yields the expression for the average BER of the first
hop, i.e., Pprs
γsr , according to
Pprs
γsr =σ2
1L
√2π(Iprs
1+Iprs
2),(37)
where
Iprs
1=λfC
μf
0ξ2
λfτfC+σ2
1ξ2L
exp −ξ2
2dξ, (38)
Iprs
2=
∞
λfC
μf
(ξ2−C)
C(Q1τf−σ2
1)+σ2
1ξ2L
exp −ξ2
2dξ.
(39)
To calculate Iprs
1and Iprs
2, changing the variable to t=
(μf/λfC)ξ2and following the approach adopted in Section V,
we get
Iprs
1=(μfτf)−L√λfC
(2L+1) μfΦ1L+1
2,L;L+3
2;−σ2
1
μfτf,−λfC
2μf,
(40)
and
Iprs
2=√λfC
2 μf(σ2
1−Q1τf)L
×√πΦ2
1
2,−L, L;3
2;−λf
μf,−σ2
1λf
(σ2
1−Q1τf)μf,λfC
2μf
−2Φ1
1
2,−L, L;3
2;λf
μf,σ2
1λf
(σ2
1−Q1τf)μf,−λfC
2μf.
(41)
Then, substituting the expressions in (40) and (41) into (37),
the average BER of the first-hop link Pprs
γsr can be obtained as
given by
Pprs
γsr =σ2
1L(μfτf)−L√λfC
(2L+1)
2πμfΦ1
×L+1
2,L;L+3
2;−σ2
1
μfτf,−λfC
2μf
+σ2
1L√λfC
8μf(σ2
1−Q1τf)LΦ2
×1
2,−L, L;3
2;−λf
μf,−σ2
1λf
(σ2
1−Q1τf)μf,λfC
2μf
−σ2
1L√λfC
2πμf(σ2
1−Q1τf)LΦ1
×1
2,−L, L;3
2;λf
μf,σ2
1λf
(σ2
1−Q1τf)μf,−λfC
2μf.(42)
Finally, incorporating Pprs
γsr and Pγrd (given in Section V) into
(36) yields the average BER expression of the spectrum-sharing
cooperative system when using the PRS strategy.
B. Ergodic Capacity
Herein, we investigate the ergodic capacity of the cooperative
transmission system under consideration when the PRS strategy
is used in the first-hop transmission, which is mathematically
given by
Cprs =1
2min !Cγprs
sr ,C
γrd ",(43)
where Cγrd is calculated according to (32), and Cγprs
sr is
obtained using the expectation of log2(1 + γprs
sr ), which is
given by
Cprs
sr =Eγprs
sr [log2(1 + γprs
sr )] .(44)
Then, considering the PDF of the received SNR for the Lrelays
participating in PRS over the first transmission link, as given in
(35), we can express (44) as
Cprs
sr =Lσ2
1Lτf
ln(2) (λfJ1+Q1J2),(45)
where
J1=
λf
μf
0
γL−1ln(1 + γ)
(λfτf+σ2
1γ)L+1 dγ, (46)
J2=
∞
λf
μf
(γ−1)L−1ln(1 + γ)
(Q1τf+σ2
1(γ−1))L+1 dγ. (47)
In the following, we derive the approximated closed-form
expressions for the integrals J1and J2. For the first integral,
we use the following expansion series given by [27, eq. 1.11]:
1
(a+z)p=
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
1
(a)p
N
#
n=0 −1
anP+n−1
nzn,z
a≤1
+εz
a
N
#
n=0
(−a)nP+n−1
nz−n−p,z
a>1
+εz
a(48)
where a
b:= (a!/(a−b)!b!) represents the binomial coeffi-
cients [27], and ε(z/a)is the truncation error.8Now, for the
8In numerical results, the parameter Nis considered such that the truncation
error always satisfies |ε(z/a)|<3×10−3.
ASGHARI AND AÏSSA: END-TO-END PERFORMANCE OF COOPERATIVE RELAYING IN SPECTRUM-SHARING SYSTEM 2663
sake of accuracy in using these series in (46) and since the
integral limit λf/μfis always larger than unity, owing to the fact
that μf=λf−Q1, we split the integration interval [0,λ
f/μf]
into two intervals. Thus, considering (48) and after expressing
the logarithm function in terms of Meijer’s G-function [22],
namely, using ln(1 + γ)=G1,2
2,2(γ|1,1
1,0),J1can be expressed as
J1=1
(λfτf)L+1
N
$
n=0 −σ2
1
λfτfnL+n
n
×
λfτf
σ2
1
0
γL+n−1G1,2
2,2γ
1,1
1,0dγ
+1
(σ2
1)L+1
N
$
n=0 −λfτf
σ2
1nL+n
n
×
λf
μf
λfτf
σ2
1
γ−n−2G1,2
2,2γ
1,1
1,0dγ. (49)
Then, knowing that the integral of the Meijer’s G-functions is
also a Meijer’s G-function [31], i.e.,
zα−1G1,2
2,2z
a1,a2
b1,b2dz =G1,3
3,3z
1,α+a1,α+a2
α+b1,0,α+b2(50)
and after some mathematical manipulations, (49) can be ex-
pressed as [27, eq. 9.31.2]
J1=1
(λfτf)L+1
N
$
n=0 −σ2
1
λfτfnL+n
n
×G1,3
3,3λfτf
σ2
1
1,L+n+1,L+n+1
L+n+1,0,L+n
+1
(σ2
1)L+1
N
$
n=0 −λfτf
σ2
1nL+n
n
×G3,1
3,3μf
λf
1+n,1,n+2
0,n+1,n+1 −G3,1
3,3σ2
1
λfτf
1+n,1,n+2
0,n+1,n+1 .
(51)
It is worth noting that the Meijer’s G-functions are implemented
in most popular computing softwares such as Matlab and
Mathematica.
As for the integral J2, by considering the integral comple-
mentary characteristic, (47) can be rewritten as
J2=
∞
0
(γ−1)L−1ln (1 + γ)
(Q1τf+σ2
1(γ−1))L+1 dγ
%&' (
Ja
2
−
λf
μf
0
(γ−1)L−1ln(1 + γ)
(Q1τf+σ2
1(γ−1))L+1 dγ
%&' (
Jb
2
.(52)
To solve the integral Ja
2in (52), using the change of variable
x=γ−1and substituting the logarithm function representa-
tion in terms of Meijer’s G-function [22], followed by some
mathematical manipulations, Ja
2can be simplified as follows
[27, eq. 9.31.5]:
Ja
2=
∞
−1
G1,2
2,2x+1
L,L
L,L−1
(Q1τf+σ2
1x)L+1 dx. (53)
Now, representing the denominator of the fraction in (53) in
terms of Meijer’s G-function as [27, eq. 9.31.2]
1
(Q1τf+σ2
1x)L+1 =(Q1τf)−L−1
Γ(L+1) G1,1
1,1σ2
1x
Q1τf−L
0(54)
and substituting (54) into (53), we obtain
Ja
2=(Q1τf)−L−1
Γ(L+1)
×
∞
−1
G1,1
1,1σ2
1x
Q1τf−L
0G1,2
2,2x+1
L,L
L,L−1dx. (55)
Then, after some further manipulations, Ja
2can be derived as
follows:
Ja
2=HL
L(Q1τfσ2
1)(σ2
1)L−1
L(σ2
1)L+1
×2F(1,0,0,0)
11,L+1;L+1;2−Q1τf
σ2
1
+2F(0,0,1,0)
11,L+1;L+1;2−Q1τf
σ2
1,(56)
where HL:= #L
l=1 1/l denotes the Lth harmonic num-
ber [23]. Furthermore, in (56), 2F(1,0,0,0)
1(a, b;c;z)and
2F(0,0,1,0)
1(a, b;c;z)represent the first-order symbolic differen-
tiation of the Gauss hypergeometric function [24] with respect
to parameters aand c, respectively, and are defined as [24]
2F(1,0,0,0)
1(a, b;c;z)= ∞
$
k=0
(b)k
(c)kk!
∂(a)k
∂a zk(57)
2F(0,0,1,0)
1(a, b;c;z)=; ∞
$
k=0
(a)k(b)k
(c)kk!
∂1/(c)k
∂c zk(58)
with (a)i
Δ
=(Γ(a+i)/Γ(a)) denoting the Pochammer symbol
|z|<1. It is worth noting that the symbolic differentiation
of the Gauss hypergeometric function used in (56) can be
easily implemented in most popular numerical softwares such
as Mathematica.
For the integral Jb
2in (52), making the change of variable
x=γ−1,Jb
2can be simplified to
Jb
2=
Q1
μf
−1
xL−1ln(2 + x)
(Q1τf+σ2
1x)L+1 dx. (59)
2664 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60,NO. 6, JULY2011
Then, making use of the expansion series given in (48) and
using the same approach applied for the derivation of J1, (59)
can be rewritten as
Jb
2=1
(σ2
1)L+1
N
$
n=0 −Q1τf
σ2
1nL+n
n
×
−Q1τf
σ2
1
−1
x−n−2G1,2
2,2x+1
1,1
1,0dx
+1
(Q1τf)L+1
N
$
n=0 −σ2
1
Q1τfnL+n
n
×
Q1τf
σ2
1
−Q1τf
σ2
1
xL+n−1G1,2
2,2x+1
1,1
1,0dx
+1
(σ2
1)L+1
N
$
n=0 −Q1τf
σ2
1nL+n
n
×
Q1
μf
Q1τf
σ2
1
x−n−2G1,2
2,2x+1
1,1
1,0dx, (60)
which, after some mathematical manipulations [27, eq. 9.31.2],
yields
Jb
2=1
(Q1τf)L+1
N
$
n=0 L+n
n−σ2
1
Q1τfn
×G1,3
3,3σ2
1+Q1τf
σ2
1
1,L+n+1,L+n+1
L+n+1,0,L+n
−G1,3
3,3σ2
1−Q1τf
σ2
1
1,L+n+1,L+n+1
L+n+1,0,L+n
+1
(σ2
1)L+1
N
$
n=0 L+n
n−Q1τf
σ2
1n
×G3,1
3,3μf
λf
1+n,1,n+2
0,1+n,1+n
+G3,1
3,3σ2
1
σ2
1−Q1τf
1+n,1,n+2
0,1+n,1+n
−G3,1
3,3σ2
1
Q1τf+σ2
1
1+n,1,n+2
0,1+n,1+n.(61)
Finally, incorporating the expressions in (51) and (52) into
(45) gives the ergodic capacity expression for the first-hop
transmission when the PRS strategy is used in the first-hop
transmission. Then, the overall achievable capacity of the dual-
hop DF cooperative spectrum-sharing system is calculated ac-
cording to the expression in (43).
VII. NUMERICAL RESULTS AND DISCUSSIONS
Using the analysis in the previous sections, we now investi-
gate the performance and benefits of the proposed cooperative
spectrum-sharing system when using the PRS strategy. Simu-
Fig. 4. Interference limit Wversus Pout
pfor r0=0.1, 0.3, 0.6 bit/s/Hz and
different values for Sp.
lation results are also provided, and as will be seen, a good
agreement is achieved between the analytical and simulated
curves.9In our simulations, the fading channels pertaining
to the first- and second-hop links are modeled according to
Rayleigh PDFs with E[βl]=τfand E[α]=τs, respectively.
We consider exponential distribution for the associated inter-
ference channels g1and g2with expected values of unity. It is
also assumed that σ2
1=σ2
2=1.
At first, we start by investigating the range of interference
limit tolerable at the PRs for different primary QoS require-
ments defined in terms of the minimum required rate r0with a
certain outage probability Pout
p. Fig. 4 shows the upper bounds
for the average interference limit (W=W1=W2)versus the
outage probability in percentage for r0=0.1, 0.3, 0.6 bit/s/Hz
and different values for Sp(9 and 10 dB). In this figure, we
set δ2
1=δ2
2=1. The figure shows that, after certain values for
Pout
p, the interference limit Wrapidly decreases as the outage
probability Pout
pdecreases or as the minimum required rate r0
increases. For comparison purposes, the exact calculated values
of the interference limit are shown for the case considering
Q=1.5W, where Q=Q1=Q2. It is worth noting that, when
W<0, no feasible power allocation satisfying the constraints
in (2) exists. The arrows indicate the regions for which W<0
holds true.
A. Error Probability Performance
Figs. 5–7 plot the end-to-end average BER as a function of
the peak transmit power limits for each hop and considering
different numbers for the relays participating in the selection. In
Fig. 5, we set Q1=Q2=Qand W1=W2=W, and vary the
interference limit as W= 50%Qor W= 95%Qfor the num-
ber of relays L=1,2,4, considering τf=0dB and τs=2dB.
The figure shows that, as Wincreases, the system performance
improves, but for higher values of Q, it converges toward that of
the system with no peak transmit-power constraints. Analysis
9Note that, for clarity of presentation, simulation data have been omitted in
some of the curves.
ASGHARI AND AÏSSA: END-TO-END PERFORMANCE OF COOPERATIVE RELAYING IN SPECTRUM-SHARING SYSTEM 2665
Fig. 5. Average BER for the BPSK spectrum-sharing cooperative relaying
system with L=1,2,or 4relays and balanced resource limits, i.e., Q1=Q2,
and W1=W2.
Fig. 6. Average BER for the BPSK spectrum-sharing cooperative relaying
system with L=1,2,or 3relays and imbalanced resource limits.
of the number of relays shows substantial improvements in
performance as Lincreases.
Fig. 6 investigates the effect of imbalanced resource limits,
which are defined by parameters Qiand Wifor i=1,2, corre-
sponding to the first- and second-hop transmission constraints.
In this figure, we observe the significant effect of the imbalance
between the resource limits on the dual-hop spectrum-sharing
system. Fig. 6 also shows that, for a fixed value of Q1=Q2,as
the average interference limit increases, e.g., as W2increases
(or W2/Q2increases), the system performance increases and
converges toward that of the system with no average received-
interference constraints. In fact, this means that a higher Wican
be considered as an advantage for the system performance and
decreases the average BER, but after a certain value of Wi,for
instance, when W2>Q
2, the average BER is only limited by
the peak received-interference constraints and does not increase
as Wiincreases.
In Fig. 7, we analyze the advantages of implementing the
PRS strategy in the dual-hop cooperative spectrum-sharing
system. In this figure, setting W1= 50%Q1and W2= 70%Q2,
Fig. 7. Average BER for the BPSK spectrum-sharing cooperative relaying
system with L=1or 3 relays and imbalanced resource limits for different
τf’s, and τs=2dB.
the variation of τfis investigated when τs=2 dB. We ob-
serve the significant improvement in the overall performance
of the cooperative system when the first transmission link is in
weak propagation conditions, i.e., with lower values of τf,by
increasing the number of relays participating in the selection
over the first-hop transmission. It is worth noting that, although
we consider a system with binary phase-shift keying (BPSK)
modulation, which implies C=2in the derived average BER
expressions, the obtained expressions can easily be evaluated
for other modulation schemes.
B. Ergodic Capacity Performance
The ergodic capacity of the dual-hop cooperative spectrum-
sharing system is investigated in Figs. 8 and 9 for different
values of the average interference limit W=W1=W2and
number of relays L.InFig.8,wesetτf=−1dB and τs=
2dB. As observed, the overall achievable capacity of the dual-
hop cooperative system increases as Q1or the number of relays
increases. On the other hand, in Fig. 9, we set Q1=1.1W
and Q2=1.5W. From the plots, we observe a capacity gain
achievement by increasing the number of relays available for
the PRS strategy, particularly when the transmission of the first
link is more restricted than the second link, i.e., Q1<Q
2,or
τf<τ
s.
C. Outage Probability Performance
Outage probability is the most commonly used performance
measures in wireless systems and defined as the probability
that the received SNR falls below a predetermined threshold
γth. Particularly, in spectrum-sharing systems, given that the
first- and second-hop transmissions are limited by constraints
on the average and peak interference at the primary receivers,
it is obvious that some percentage of outage is unavoidable
[32]. The outage probability may mathematically be defined as
Pout =Pr(γsr&γrd <γ
th), where γth is a predefined thresh-
old. Indeed, the received signal power or, specifically, the
received SNR has to be kept above a certain threshold at
2666 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 6, JULY 2011
Fig. 8. Ergodic capacity of the spectrum-sharing cooperative relaying system
with DF relays versus W=W1=W2, with L=1,2,3,or 6relays and
imbalanced resource limits.
Fig. 9. Ergodic capacity of the spectrum-sharing cooperative relaying system
with DF relays versus W=W1=W2with L=1or 2relays and imbalanced
resource limits for different τf’s and τs=2dB.
the secondary receivers to assure that the secondary QoS is
guaranteed. In this regard, the outage probability of the dual-
hop cooperative spectrum-sharing system in terms of channel
CDFs is given by
Pout =Fγsr (γth)+Fγrd (γth )−Fγsr (γth)Fγrd (γth ).(62)
Accordingly, the outage probability of the system under consid-
eration when implementing the PRS strategy can be obtained by
Pprs
out =Fprs
γsr (γth)+Fγrd (γth )−Fprs
γsr (γth)Fγrd (γth ),(63)
which, after substituting the results obtained in (33), can be
rewritten as
Pprs
out =[Fγsr (γth)]L+Fγrd (γth )−[Fγsr (γth)]LFγrd (γth ).
(64)
Fig. 10. Outage probability of the cooperative spectrum-sharing system with
L=1or 3relays and γth =−2dB or −5 dB, for different τf’s an d τs=
2dB.
Note that the CDFs involved in (62) and (64) are obtained in
Section IV, and that Lin (64) denotes the number of relays
participating in the PRS strategy.
Numerical results corresponding to the preceding expres-
sions are shown in Fig. 10. In this figure, we plot the outage
probability performance of the dual-hop cooperative spectrum-
sharing system in terms of the effective noise power (ENP) per-
taining to the first and second hops defined by 1/σ2
1and 1/σ2
2,
respectively. For illustration purposes, it is assumed that σ2
1=
σ2
2. In these figures, we keep the peak and average interference
limits at Q1=Q2=3dB and W1=W2=−1dB and vary
the outage threshold γth or τfwhile considering various values
for the number of relays L. As observed, for γth =−2dB,
when the first link condition gets stronger, i.e., τfincreases,
the outage probability decreases, and for higher values of
ENP, i.e., lower values of σ2
1or σ2
2, it converges toward that
of the system with better channel condition. On the other hand,
as γth decreases, the outage probability decreases as well. As
expected, analysis of the number of relays shows a significant
improvement in the outage performance as Lincreases.
VIII. CONCLUSION
In this paper, we have studied a spectrum-sharing system
that implements cooperative relaying to more efficiently use
the available transmission resources such as power and rate
in the shared spectrum while adhering to predefined interfer-
ence constraints to guarantee that the QoS over the primary
user is always satisfied. Specifically, we have considered that
the secondary source–destination communication relies on an
intermediate relay node in the transmission process. In this
context, we have obtained the first-order statistics (PDF and
CDF) pertaining to the first and second transmission chan-
nels. Then, making use of these statistics, we have investi-
gated the end-to-end performance of the proposed cooperative
spectrum-sharing system under interference power constraints
satisfying the QoS requirements at the primary-user side. More
specifically, we have obtained closed-form expressions for the
ASGHARI AND AÏSSA: END-TO-END PERFORMANCE OF COOPERATIVE RELAYING IN SPECTRUM-SHARING SYSTEM 2667
average BER, ergodic capacity, and outage probability of the
secondary communication, whereas the primary user’s QoS
requirements are specified in terms of appropriate resource
constraints on the average and peak received interference power
at the primary receiver. We have further generalized our results
for the case when multiple relays are available between the
secondary source and destination nodes. In this case, consid-
ering the PRS technique for the first-hop transmission, the
performance of the cooperative spectrum-sharing system has
been studied under the underlying resource constraints. Our
theoretical analysis has been sustained by numerical and sim-
ulation results illustrating the performance and benefits of the
proposed spectrum-sharing cooperative relaying system.
APPENDIX A
From (1a), due to the independence of h1,β, and g1, and
the convexity of the function f(x) = log2(1 + (a/x +b)) for
a,b, and x≥0, the minimum rate inequality in (1a) can be
simplified by using Jensen’s inequality10 as follows:
Eβ,g1log21+ Sph1
ssr(β, g1)g1+δ2
1
Jens
≥log21+ Sph1
Eβ,g1[ssr(β,g1)g1]+δ2
1
≥log21+ Sph1
W1+δ2
1,(65)
where the second inequality results from the fact that the aver-
age received interference power is assumed to be constrained:
Eβ,g1[ssr(β,g1)g1]≤W1. Now, substituting the upper bound
presented in (65) into (1a), we obtain
Pr log21+ Sph1
W1+δ2
1<r
0≤Pout
p.(66)
Reorganizing (66) according to the primary channel h1and
after some manipulations, the constraint is simplified to
Pout
p≥Pr !h1<ˆηW1+δ2
1"
=
ˆη(W1+δ2
1)
0
fh1(h1)dh1
=Fh1ˆηW1+δ2
1,(67)
where ˆη=(2
r0−1/Sp). Now, since we consider that the
primary channel is exponentially distributed, then Fh1(x)=
1−exp(−x), and the preceding expression can be sim-
plified to
Pout
p≥1−exp −ˆηW1+δ2
1.(68)
For achieving a target Pout
pvalue, the preceding inequality
can be used to adjust the transmission power Ssr(β, g1). Thus,
after simple manipulations of (68), for a given outage target
Pout
p, the constraint limit W1is as expressed in (3). Further-
10i.e., E[f(X)] ≥f(E[X]).
more, applying the same approach in (1b) for the second hop
yields the constraint limit W2provided in (3).
APPENDIX B
Substituting the optimal power allocation policy shown in (5)
into the average received power constraint given by (2a) with
equality, we obtain
σ2
1
μf
σ2
1
λf
λf−σ2
1
zfZ(z)dz +
∞
σ2
1
μf
Q1fZ(z)dz =W1,(69)
where ZΔ
=β/g1with PDF given by fZ(z)=τf/(τf+z)2
[20]. After evaluating the integrations in (69), the latter equation
can be simplified according to
W1=Q1+σ2
1
τfln σ2
1+(λf−Q1)τf
σ2
1+λfτf,(70)
which, after further manipulation, yields (6). Then, substituting
(6) into μf=λf−Q1results in the expression shown in (7).
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Vahid Asghari (S’07) received the B.S. degree in
electrical engineering from Azad University and the
M.S. degree in telecommunication systems from
K. N. Toosi University of Technology, Tehran,
Iran, in 2002 and 2005, respectively. From 2005 to
2007, he was a Researcher with the Department of
Electrical Engineering, K. N. Toosi University of
Technology, where he worked on the analysis and
design of Turbo codes. He is currently pursuing the
Ph.D. degree with the National Institute of Scien-
tific Research-Energy, Materials, and Telecommuni-
cations (INRS-EMT), University of Quebec, Montreal, QC, Canada.
His research interests include resource scheduling and management, cooper-
ative communications and performance evaluation of wireless communication
systems, with a focus on cognitive radio and ad hoc networks.
Mr. Asghari was co-recipient of Best Paper Award from the 2010 IEEE
Wireless Communications and Networking Conference.
Sonia Aïssa (S’93–M’00–SM’03) received the
Ph.D. degree in electrical and computer engineer-
ing from McGill University, Montreal, QC, Canada,
in 1998. Since then, she has been with the National
Institute of Scientific Research-Energy, Materials,
and Telecommunications (INRS-EMT), University
of Quebec, Montreal, QC, Canada, where she is a
Full Professor.
From 1996 to 1997, she was a Researcher with the
Department of Electronics and Communications of
Kyoto University, Kyoto, Japan, and with the Wire-
less Systems Laboratories of NTT, Kanagawa, Japan. From 1998 to 2000, she
was a Research Associate at INRS-EMT, Montreal. From 2000 to 2002, while
she was an Assistant Professor, she was a Principal Investigator in the major
program of personal and mobile communications of the Canadian Institute
for Telecommunications Research (CITR), leading research in radio resource
management for code division multiple access systems. From 2004 to 2007,
she was an Adjunct Professor with Concordia University, Montreal. In 2006,
she was Visiting Invited Professor with the Graduate School of Informatics,
Kyoto University, Japan. Her research interests lie in the area of wireless and
mobile communications, and include radio resource management, cross-layer
design and optimization, design and analysis of multiple antenna (MIMO)
systems, cognitive and cooperative transmission techniques, and performance
evaluation, with a focus on Cellular, Ad Hoc, and Cognitive Radio (CR)
networks.
Dr. Aïssa was the Founding Chair of the Montreal Chapter IEEE Women
in Engineering Society in 2004–2007, acted or is currently acting as Technical
Program Leading Chair or Cochair for the Wireless Communications Sympo-
sium of the IEEE International Conference on Communications (ICC) in 2006,
2009, 2011, and 2012, and as PHY/MAC Program Chair for the 2007 IEEE
Wireless Communications and Networking Conference (WCNC). She has
served as a Guest Editor of the EURASIP Journal on Wireless Communications
and Networking in 2006, and as Associate Editor of the IEEE Wireless Com-
munications Magazine in 2006–2010. She is currently an Editor of the IEEE
TRANSACTIONS ON WIRELESS COMMUNICATIONS, the IEEE TRANSAC-
TIONS ON COMMUNICATIONS,andtheIEEE Communications Magazine,
and Associate Editor of the Wiley Security and Communication Networks
Journal. Awards and distinctions to her credit include the Quebec Government
Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT)
Strategic Fellowship for Professors-Researchers in 2001–2006; the INRS-EMT
Performance Award in 2004 for outstanding achievements in research, teaching
and service; the IEEE Communications Society Certificate of Appreciation in
2006, 2009, and 2010; and the Technical Community Service Award from the
FQRNT Center for Advanced Systems and Technologies in Communications
(SYTACom) in 2007. She is also co-recipient of Best Paper Awards from IEEE
ISCC 2009, WPMC 2010, IEEE WCNC 2010, and IEEE ICCIT 2011; and
recipient of Natural Sciences and Engineering Research Council of Canada
(NSERC) Discovery Accelerator Supplement Award.
