Content uploaded by Saeed Vahidian
Author content
All content in this area was uploaded by Saeed Vahidian on Dec 19, 2017
Content may be subject to copyright.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017 1299
Network-Coded Two-Way Relaying
in Spectrum-Sharing Systems With
Quality-of-Service Requirements
Sajad Hatamnia, Saeed Vahidian, Sonia Aïssa, Senior Member, IEEE,
Benoit Champagne, Senior Member, IEEE, and Mahmoud Ahmadian-Attari
Abstract—We investigate the performance of a dual-hop
two-way cognitive radio system, where the secondary users (SUs)
exchange information in an underlay mode with the assistance
of a half-duplex relay utilizing physical-layer network coding
over finite GF(2). Moreover, we consider a practical scenario of
interference from the primary users (PUs) affecting the relay and
source nodes. The analysis provides a generalization of previous
works as it considers an extended transmission system where
the channels can consist of a combination of independent and
identically distributed (i.i.d.) and independent but non-identically
distributed (i.n.i.d.) Nakagami-mfading models. In addition, un-
like prior works, this paper focuses on the performance of both
the PUs and the SUs. Closed-form expressions for the symbol
error probability (SEP) and the outage probability of the in-
tended PU are obtained. In addition, we derive exact closed-form
expressions for the SEP with consideration of special cases of
practical interest (e.g., no interference power, interference limited,
and single dominant interference cases) for the SUs. Furthermore,
an upper bound on the achievable rate of the secondary system is
provided. Subsequently, a closed-form approximating expression
for the SEP of the secondary system at high signal-to-noise ratios
(SNRs) is obtained. Simulation results are provided and attest to
the accuracy of the analytical results.
Index Terms—Cognitive radio networks (CRNs), network cod-
ing, symbol error probability (SEP), two-way relaying.
I. INTRODUCTION
IN THE design of modern wireless communication systems,
achieving higher data rates and more reliable transmissions
have become pivotal goals. While some recent studies pre-
dict multifold increase in data traffic by 2020 [1]–[3], mobile
operators must currently deal with resource congestion and
energy limitations of existing systems. In this context, coop-
erative communication has emerged as an advanced paradigm
to achieve robustness and high-data-rate transmissions [4].
Manuscript received July 29, 2015; revised February 25, 2016; accepted
April 16, 2016. Date of publication April 27, 2016; date of current version
February 10, 2017. The review of this paper was coordinated by Dr. X. Wang.
S. Hatamnia, S. Vahidian, and M. Ahmadian-Attari are with the Faculty of
Electrical and Computer Engineering, K. N. Toosi University of Technology,
Tehran 19697, Iran (e-mail: sajad.hatamnia@ee.kntu.ac.ir; saeed.vahidian@ee.
kntu.ac.ir; mahmoud@eetd.kntu.ac.ir).
S. Aïssa is with the Institut National de la Recherche Scientifique (INRS-
EMT), University of Quebec, Montréal, QC H3C 3P8, Canada (e-mail: aissa@
emt.inrs.ca).
B. Champagne is with the Department of Electrical and Computer Engi-
neering, McGill University, Montréal, QC H3A 0G4, Canada (e-mail: benoit.
champagne@mcgill.ca).
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.2016.2558600
Among the many cooperative communication schemes that
have been proposed in recent years, two-way relaying offers
many advantages in terms of capacity increase, coverage ex-
tension, and energy savings. One of the most widely embraced
protocols in two-way relaying is physical-layer network coding
(PNC) in which two sourcenodes simultaneously transmit their
information message to an intermediate relay over a multiple-
access channel (MAC) in the first stage, and the relay retrans-
mits an XOR’ed version of the received messages to the source
nodes over a broadcast channel (BC) in the second stage [5].
Despite higher complexity, the PNC relaying protocol can offer
lower bit error rates, which is a desirable attribute for future
wireless cellular networks. For this purpose, we, henceforth,
evaluate the performance of PNC relaying schemes.
Meanwhile, the spectrum resources are extremely scarce.
Cognitive radio (CR) together with dynamic spectrum access
(DSA) provide an advanced strategy for addressing the spec-
trum scarcity problem of wireless networks by allowing the
sharing of resources between different classes of users [6].
One of the most common approaches for DSA in spectrum-
sharing systems is in the form of an underlay scheme, whereby
secondary users (SUs) are allowed to coexist with primary users
(PUs) as long as the primary’s quality-of-service (QoS) is not
affected. Since the underlay approach does not necessarily rely
on the detection of spectrum white space, it is of special interest
[7]. Moreover, most wireless networks operate according to a
frequency reuse principle, which makes cochannel interference
(CCI) a dominant factor. Hence, the transmit power of the SUs
is dependent not only on the radio channel between them but
also on the interference channels from the PU to the SUs as
well as on the primary channel.
Based on these considerations, much research effort was de-
voted to the performance study of various schemes for relaying
the SU’s messages in underlay CR networks (CRNs), taking
into account interference from and to the PUs. In [8]–[17], the
purpose was to investigate the effect of primary transmissions
on the performance of traditional CRNs. For instance, in [8], a
closed-form expression for the outage probability (OP), under
a peak interference power constraint in the presence of multi-
ple unidirectional primary transceivers, was derived assuming
Rayleigh fading. The performance metrics in an amplify-and-
forward (AF) CRN with best-relay selection were studied in
[10]. Zou et al. in [11] presented a closed-form expression
for the OP of a secondary network implementing decode-and-
forward (DF) relaying. In [12], the OP of a unidirectional
0018-9545 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
1300 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017
cognitive multiple-input multiple-output (MIMO) relaying sys-
tem was analyzed. The asymptotic OP for three relay selection
strategies were obtained in [13]. Xia and Aïssa in [15] exam-
ined the outage performance of DF CRNs. The same authors
[16] studied the performance of a multirelay spectrum-sharing
system, where the diversity order was shown to be equal to 1
regardless of the number of relaying nodes. Huang et al. in
[17] investigated the impact of multiuser diversity on the outage
performance of DF CRNs.
Compared with the traditional relaying considered in the
aforementioned works, two-way relaying techniques can po-
tentially double the spectral efficiency [18]. For example, the
authors in [19]–[23] derived the OP of two-way relaying sys-
tems in the presence of CCI and additive white Gaussian noise
(AWGN) at the relay(s) and end sources. Alsharoa et al. in
[24] studied the problem of relayselection and optimal resource
allocation for two-way AF and DF relaying in spectrum-sharing
systems, and Hamdi et al., in [25], proposed a transmit beam-
forming technique for an underlay CRN, where the CR system
uses part of the primary spectrum, whereas a MIMO secondary
base station acts as a relay for the primary network. A cognitive
relay precoder based on the mean-square-errorcriterion was de-
signed in [26], where only imperfect channel state information
(CSI) was assumed available. In [27], a relay selection strategy
for two-way AF relaying was presented. The OP of incremental
AF and DF relaying in underlay spectrum-sharing systems over
Nakagami-mfading channels was derived in [28]. A MIMO
two-way relay scheme for CRN was proposed in [29], where an
AF relay is optimally selected to maximize the sum rate of the
SUs while taking into account the interference level of the PU.
While previous works enhanced the knowledge on cognitive
relaying, they did not elaborate on the performance of both the
primary network and the two-way DF relaying secondary net-
work when the interacting SUs and relay are affected by multi-
ple primary interferers. This scenario can occur, for instance, in
a cellular network where two mobile users are communicating
via a base station or another type of relay using the spectrum
holes of a nearby primary network. Motivated by these con-
siderations, we herein pursue a detailed performance analysis
of dual-hop two-way DF relaying in spectrum-sharing systems
with multiple primary interferers. The contributions of this pa-
per can be summarized as follows: 1) In the two-way dual-hop
secondary network, the source nodes and the relay are affected
by multiple interferers originating from the primary network in
a Nakagami-mfading environment. This practical but intricate
setup has scarcely been considered in the related literature.1
Assuming Nakagami-mfading channels, we consider a general
scenario in which the fading can be independent and identically
distributed (i.i.d.) or independentbut non-identically distributed
(i.n.i.d.) and obtain exact closed-form expressions for the OP
1Performance analysis of two-way spectrum-sharing systems in Nakagami-
menvironments has its own challenges, which is why many papers appeared
even with the same topics as in unidirectional networks suffering from Rayleigh
fading [30], [31]. There are also many works on bidirectional relay networks
that are only noise limited or interference limited or assuming Rayleigh fading
[32], [33]. Therefore, none of the prior works presented such practical and
comprehensive analysis of the proposed scenario.
and the average SEP of the PU. 2) The average SEP of the sec-
ondary network under binary phase-shift keying (BPSK) mod-
ulation is derived. Furthermore, the average SEP behavior is
analyzed in detail for several practical cases of interest, includ-
ing i.i.d. and i.n.i.d. fading channels, the interference-free case
and the scenario with a single dominant interferer. 3) We ex-
plore the achievable rate performance of the two-way cognitive
DF relaying, assuming availability of CSI at the receiving nodes.
Upper bounds on the achievable rate of the secondary system
are derived based on Jensen’s inequality. 4) For additional
insights into the impact of system parameters, such as fading
parameters and the number of primary interferers, we derive the
asymptotic SEP for different cases. The results indicate that an
equal number of interferers at each SU node yields better SEP
performance than the unequal case, over the whole signal-to-
noise ratio (SNR) range of interest. 5) Simulations are presented
to corroborate the analysis and to provide interesting horizons
on the impact of noise, interference, fading parameters, and
primary outage threshold on performance.
The rest of this paper is organized as follows: Section II intro-
duces the system model and fading statistics. In Section III, we
pursue the performanceanalysis of the primary networkand de-
rive an exact closed-form expression for the SEP and an upper
bound on the sum rate. The asymptotic analysis for the sec-
ondary network is developed inSection IV. Asymptotic perfor-
mance analysis is provided in Section V. Section VI presents a
set of numerical results, andSection VII concludes this paper.
II. SYSTEM MODEL
We examine the impact of multiple primary interferers on the
performance of a unidirectional primary network as well as of
a CR two-way relay network. The intended primary network
consists of a transmitter node, ˜
P, and a receiver node, P.The
CRN consists of two source nodes, S1and S2, which exchange
information via a relay Remploying PNC, as shown in Fig. 1.
We assume that the direct channel between S1and S2has a
negligibly small SNR due to severe fading. The amplitudes of
all channels undergo flat Nakagami-mfading, and the channels
are assumed to be reciprocal in the forward and backward
directions. The PNC scheme consists of two stages: During the
MAC stage, sources S1and S2simultaneously transmit to R;in
the BC stage, Rbroadcasts the XOR’ed version of the received
symbols to the sources.
In our formulation, h,g,andhPdenote the random channel
coefficients from S1to R, from S2to R, and from the intended
PU, ˜
P, to its receiver P, respectively. Moreover, fR,j ,fS1,j,
and fS2,j represent the channel coefficients from the jth inter-
ferer to R,S1,andS2, respectively. Additionally, fP,S1,fP,S2,
fP,R,andfP,j are the flat-fading coefficients from S1to P,
from S2to P, from Rto P, and from the jth primary interferer
to P, respectively.
The amplitudes of all the links have Nakagami-mdistribu-
tions, where m≥0.5 represents the fading severity parameter.
Therefore, the corresponding SNRs are random variables (RVs)
following Gamma distributions with shape parameter mand
mean Ω, which is denoted as G(m, Ω). The distributions of the
various channel squaredmagnitudes can be expressed, via their
HATAMNIA et al.: TWO-WAY RELAYING IN SPECTRUM-SHARING SYSTEMS WITH QoS REQUIREMENTS 1301
Fig. 1. Two-way cognitive cooperative network in the presence of multiple
primary interferers.
corresponding parameters, as |h|2d
∼G(mh,Ωh),|g|2d
∼G(mg,
Ωg),|fR,j |2d
∼G(mR,j ,ΩR,j ),|fS1,j |2d
∼G(mS1,j,ΩS1,j ),
|fS2,j|2d
∼G(mS2,j ,ΩS2,j ),|hP|2d
∼G(mP,ΩP),|fP,S1|2d
∼
G(mP,S1,ΩP,S1),|fP,S2|2d
∼G(mP,S2,ΩP,S2),|fP,j|2d
∼
G(mP,j,ΩP,j ),and|fP,R|2d
∼G(mP,R,ΩP,R), where symbol
d
∼denotes “distributed as.” Furthermore, we define the scale
parameter βx=mx/Ωx,x∈{(S1,j),(S2,j),(R, j),(P, j ),
(P, R),(P, S1),(P, S2),h,g,P}. In the MAC stage, S1and
S2send their respective messages x1and x2to R. During this
stage, LPPUs out of the existing ones that exchange messages
with their respective receivers interfere with node P.Insuch
a case, there is no need for state feedback to synchronize the
primary and secondary networks. The sources and the relay are
affected by LSi,i∈{1,2},andLRinterferers, respectively.
The interferers, which are the PUs in the proximity of the
secondary network, may be i.i.d. or i.n.i.d. Under this scenario,
the signal received by Rin the MAC stage is given by
yR=EShx1+ESgx2+
LR
j=1 ER,j fR,jdR,j +nR(1)
where ESis the transmit energy at S1and S2,andER,j is
the transmit energy at the jth interferer in the vicinity of R.
x1,x2,anddR,j represent the unit-energy symbols transmitted
from S1,S2,andthejth interferer, respectively, and nR∼
CN(0,N
0)represents the AWGN at R. The signal received by
the intended primary receiver Pcan be expressed as
yP,S =EPhPxP+
LP
j=1 EP,jfP,j dP,j
+ESfP,S1x1+ESfP,S2x2+nP(2)
where EPdenotes the transmit energy at the intended primary
transmitter; EP,j is the transmit energy at the jth primary
interferer in the proximity of primary node P;xPand dP,j rep-
resent the modulated symbols with unit energy emitted by the
intended primary transmitter and the jth interferer in the vicin-
ity of P, respectively; and nP∼CN(0,N
0)is the AWGN at P.
By employing the minimum Euclidean distance rule, the
relay proceeds for joint detection of the received signal yR,as
expressed by [34]
[¯x1,¯x2]= argmin
[s1,s2]:s1,s2∈A yR−EShs1+ESgs2(3)
where ¯x1and ¯x2are the estimates of x1and x2, respectively, and
|A| =Q denotes the cardinality of the Q-ary constellation. The
relaying node Rselects the best map out of a well-designed fi-
nite mapping book according to the channel condition. Then, ¯x1
and ¯x2are decoded, and ¯
X1and ¯
X2are obtained. Next, using
the PNC protocol over the finite GF(2), the relay encodes the
XOR’ed version of the decoded binary symbols and produces
ˆyR=¯
X1⊕¯
X2(4)
where ⊕is the bitwise XOR operation. Then, Rencodes ˆyR
and produces xR, which is broadcast to S1and S2in the BC
stage. Then, the received signals at the two sources and node P
will be
yS1=ERhxR+
LS1
j=1 ES1,j fS1,jdS1,j +nS1(5)
yS2=ERgxR+
LS2
j=1 ES2,j fS2,j dS2,j +nS2(6)
yR,P =EPhPxP+
LP
j=1 EP,jfP,j dP,j
+ERfP,RxR+nP(7)
where ES1,j and ES2,j denote the transmit power of the jth
interferer affecting S1and S2;dS1,j and dS2,j are the jth
interference unit-power symbols affecting S1and S2;nS1∼
CN(0,N
0)and nS2∼CN(0,N
0)are AWGN at nodes S1and
S2, respectively; and ERis the transmit power of the relay.
Based on (5) and (6), the received signal-to-interference-
plus-noise ratio (SINR) at S1and S2can be expressed by
γR,S1=ER|h|2
LS1
j=1 ES1,j |fS1,j |2+N0
(8)
γR,S2=ER|g|2
LS2
j=1 ES2,j |fS2,j |2+N0
.(9)
Next, the performance analysis with respect to (w.r.t.) the PU is
presented.
III. PERFORMANCE ANALYSIS OF
THE PRIMARY NETWORK
A. OP and Power Allocation
We aim at obtaining the OP of the intended PU, based on
which the power allocation of the SUs is investigated. One of the
1302 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017
major challenges of spectrum-sharing systems is that the SUs
should satisfy the QoS requirements of the primary network.
In our case, the reliability requirements of the PUs shall be
ensured. Specifically, the OP of primary transmissions shall be
guaranteed to be below a predefined threshold λ[35], as in
(10),2shown at the bottom of the page, where RPis the primary
transmission rate. In the sequel, we refer to λas the primary
OP threshold. It is noteworthy that we assume that some of the
channels can be i.i.d. whereas others are i.n.i.d., which provides
a generalization of the channel models used in some earlier
works, e.g., [23]. The following proposition states the OP of the
SINR of the PU and power constraint of the secondary sources.
Proposition 1: According to the preceding equation, the OP
of the PU can be obtained as
FP,S(γth )=1−
LFP
j=1
MP,j
k=1
LFSP
t=1
MP,St
w=1
mP−1
n=0
n
r=0
r
q=0
ׯγn
PΓ(n+k−r)Γ(w+q)θtwαjk
Γ(n+1)Γ(w)Γ(k)n
rr
q
×γn
th exp(−¯γPγth)
(¯γPγth +¯γP,j)n+k−r(¯γPγth +¯γP,St)w+q≤λ
(11)
where γth =2RP−1, ¯γP=βPN0E−1
P,αjk =(Γ(MP,j −
k+1))−1ψ(MP,j−k)
j(−¯γP,j),ψj(s)=¯γMP,j
P,j ×LFP
l=1
l=j
(s/
¯γP,l+1)−MP,l ,¯γP,St=βP,StN0E−1
S,θtw =(Γ(MP,St−w+
1))−1σ(MP,St−w)
j(−¯γP,St),andσj(s)=¯γMP,Sj
P,SjLFSP
l=1
l=j
(s/
¯γP,Sl+1)MP,Sl. In addition, LFSP is the number of secondary
interferers affecting P, which have different values of ¯γP,St,
and LFP is the number of primary interferers at node P,which
may have different values of ¯γP,j =βP,jN0E−1
P,j.MP,S1,M
P,S2
and MP,j are, respectively, the sum of the shape parameters of
the interferers’ channels at S1,S2,andP, with equal values
of ¯γP,S1,¯γP,S2,and¯γP,j . Moreover, throughout this paper,
f(i)(x)represents the ith derivative of f(x)w.r.t. x.
2The power allocation of the SUs in many prior works, e.g., [10] and
[36], is obtained based on the instantaneous interference threshold at the pri-
mary receiver, i.e., PS1=IP/|hP−S1|2,PS2=IP/|hP−S2|2,andPR=
IP/|hP−R|2,whereIPis the threshold. This requires knowledge of the
instantaneous CSI of the link between the secondary nodes and the primary
nodes. In practical setups a with high mobility, the channel experiences fast
fading. In such cases, it is difficult to estimate the instantaneous CSI, and
importantly, additional channel resources are required to implement the state
feedback of the channel estimates. In our proposed OP-based power allocation,
we only need to assume that a SU (S1,S2,andR) has knowledge of the average
channel gains of the link from itself to the PU. In contrast to the fast variations
of instantaneous channel gains, the average channel gains of the PU, which
relate to the nominal system parameters only, such as the transmission distance,
transmit/receive antenna gain, wavelength of electromagnetic wave, etc., are
relatively stable and can be estimated within the CRN.
Proof: See Appendix A.
In the adopted power control scheme, we employ a static
method to control the transmit power of the SUs. As such, the
SUs utilize the maximum average admissible power for trans-
mission. Finally, for a given value of the primary OP threshold
λ, the power of the secondary sources is derived by solving (11)
w.r.t. ESusing popular computing softwares, such as MATLAB
and Mathematica.
Note that the allowed values of ERare obtained by applying
the same strategy as in evaluating the power constraint of
the two sources. According to (7) and similar to the proof of
Proposition 1, it can be shown that the OP of the PU’s SINR in
the BC phase is given by (12), based on which the power
constraint of the relay is achieved. Thus
FP,R(γth
)=1−
LFP
j=1
MP,j
k=1
mP−1
n=0
n
r=0
r
q=0 n
rr
q
ׯγn
P¯γmP,R
P,R Γ(n+k−r)Γ(mP,R +q)αjk
Γ(n+1)Γ(mR,P )Γ(k)
×γn
th exp(−¯γPγth )
(¯γPγth +¯γP,j)n+k−r(¯γPγth +¯γP,R)mP,R+q≤λ
(12)
where ¯γP,R =βP,RN0E−1
R. By solving (12) w.r.t. ER,the
admissible power values for the relay can be obtained. We note
that the outage performance of the PU is investigated for two
reasons. First, the OP is a key performance measure for CRN
operating under time-varying and slow flat fading conditions,
and second, it can be used to solve the power allocationproblem
for the SUs, as considered in this work.
B. Symbol Error Probability (SEP)
The error rates of several modulation schemes employed in
practice represented in terms of the Q-function as aQ(√2bγ),
where aand bare modulation-specific constants [37]; for in-
stance, a=1andb=1 for BPSK. One method to evaluate the
SEP in fading environments is to make use of the cumulative
distribution function (cdf)-based approach, which allows us
to write the average SEP of the two-way relaying system,
assuming BPSK modulation, as
Pe=EaQ(2bγ)=a√b
2√π
∞
0
e−bγ
√γFγ(γ)dγ (13)
where E[.]represents expectation over the SINR distribution.
To compute the SEP, we need to perform partial fraction
Pout
Pri =Pr⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
log2⎛
⎜
⎜
⎜
⎝
1+EP|hP|2
LP
j=1
EP,j|fP,j |2+ES|fP,S1|2+ES|fP,S2|2+N0
⎞
⎟
⎟
⎟
⎠≤RP⎫
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎭
≤λ(10)
HATAMNIA et al.: TWO-WAY RELAYING IN SPECTRUM-SHARING SYSTEMS WITH QoS REQUIREMENTS 1303
expansion on (11), which results in
F(γ)=1−
LFP
j=1
MP,j
k=1
mp−1
n=0
n
p=0
p
q=0 n
pp
qγn
ׯγmRP
R,P Γ(n+k−p)Γ(mR,P +q)αjk
Γ(n+1)Γ(mR,P )Γ(k)γmR,P +k+q−p
P
exp(−¯γPγ)
×n+k−p
l=1
lγ+¯γP,j
¯γP−l
+
mR,P +q
m=1
ϑmγ+¯γR,P
¯γP−m(14)
where l=(Γ(n+k−p−l+1))1ς(n+k−p−l)(−(¯γP,j/¯γP)),
ς(γ)=(¯γPγ+¯γR,P )−mR,P −q,ϑm=(Γ(mR,P +q−m+
1))−1ε(mR,P +q−m)(−(¯γR,P /¯γP)),andε(γ)=(¯γPγ+
¯γP,j)p−k−n. Then, substituting (14) into (13) and utilizing [38],
the SEP of the PU can be found in a closed-form expression as
in (15), shown at the bottom of the page, where Gx,y =Φ(n+
1/2,n−x+3/2;y),andΦ(x;y;z)is the confluent hypergeo-
metric function of the second kind[38, eq. (9.211.4)].
IV. PERFORMANCE ANALYSIS OF
THE SECONDARY NETWORK
Here, we investigate the SEP and achievable rate of the
secondary two-way PNC relaying system. An exact SEP result
at S1is obtained, followed by an upper bound on the achievable
rate of the system. Since BPSK is easy to implement, is fairly
resistant to noise, and is the most robust of all PSK modulations,
particularly for low-data-rate applications, it has been adopted
in various third-generation standards, such as the European
Telecommunications Standards Institute (ETSI) in Europe, the
Association of Radio Industries and Business (ARIB) in Japan,
and various wireless local area network (LAN) standards, IEEE
802.11b, radio frequency identification (RFID), and Bluetooth.
BPSK modulation is therefore considered in this work for the
performance analysis of the secondary network.
A. SEP
The average SEP of the two-way relay system for BPSK
modulation can be obtained from (13). To begin, notice that
errors at the relay occur when the S1−Rmessage is correctly
decoded but the S2−Rmessage is not, or vice versa.In
addition, an error at S1occurs when the information sent from
R−S1is erroneous but correctly detected by S1or when the
information sent from R−S1is correct but decoded with error
at S1. The following proposition summarizes the SEP at S1for
the asymmetric two-way relay channel.3
Proposition 2: Denote the instantaneous SEP at Rw.r.t. links
S1−Rand S2−Rby Pb(γS1,R)and Pb(γS2,R ), respectively,
and that at S1w.r.t. link R−S1by Pb(γR,S1).Moreover,let
Pb(γR)be the probability that ˆyRis in error. Furthermore,
let eγi,j and ¯eγi,j symbolize, respectively, that the received
signal at node jw.r.t. link i−jis detected incorrectly and
correctly. Then, the SEP of the asymmetric two-way network-
coded relaying system at S1is given by
Pe
S1=Pb(γR)¯
Pb(γR,S1)+Pb(γR,S1)¯
Pb(γR)(16)
where ¯
Pb(.)=1−Pb(.),and
Pb(γR)=PbγS1,R|¯eγS2,R ¯
Pb(γS2,R)
+PbγS2,R|¯eγS1,R ¯
Pb(γS1,R)(17)
Pb(γR,S1)=JS1,h,S,λjk (18)
PbγS1,R|¯eγS2,R =JR,h,R,μjk (19)
PbγS1,R|eγS2,R =Hh,g (20)
where JS1,h,S,λjk and Hh,g are defined in (21)and (22), shown
at the bottom of the next page, whereas ¯γh,R =βhN0E−1
S,
¯γg,R =βgN0E−1
S,¯γS1,j =βS1,jN0E−1
S1,j ,¯γR,j =βR,jN0E−1
R,j ,
λjk =(Γ(MS1,j −k+1))−1ρ(MS1,j −k)
j(−¯γS1,j),ρj(s)=
¯γMS1,j
S1,j LFS
1
l=1
l=j
(s/¯γS1,l +1)−MS1,l ,μjk =(Γ(MR,j −k+
1)) −1ϕ(MR,j −k)
j(−¯γR,j),ϕj(s)= ¯γMR,j
R,j LFR
l=1
l=j
(s/¯γR,l +1)−MR,l ,
η0k=(Γ(mg−k+1))−1ω(mg−k)
0(−¯γg,R/2),ω0(s)=(¯γg,R/
2)mgLFR
l=1 (s/¯γR,l +1)−MR,l ,ηjk =(Γ(MR,j −k+
1))−1Ψ(MR,j−k)
j(−¯γR,j),andΨj(s)=(2s/¯γg,R +
1)−mg¯γMR,j
R,j LFR
l=1
l=j
(s/¯γR,l +1)−MR,l . The quantity LFx de-
notes the number of primary interferers at node x,whichmay
have different values of ¯γx,j . In addition, Mx,j ,x∈{S1,R},is
the sum of the shape parameters of interferer channels affecting
node xwith equal values of ¯γx,j . Notice that ¯
Pb(γS2,R),
Pb(γS2,R|¯eγS1,R )and their corresponding cdfs as well as the
related equations can be obtained by replacing the subscript
g↔hand s2to S1in that of S1. It is worth mentioning
that since the relay simultaneously decodes the message
3Obtaining the end-to-end performance metrics renders the analysis a very
challenging mathematical problem. Therefore, it will be impossible to obtain
any engineering insights. In addition, we recall that obtaining the performance
metrics at S1is a standard approach adopted in the majority of works reported
in the literature of two-way relaying, which enables the otherwise tedious
analytical study of these configurations [20].
Pe
Pri =a⎡
⎣1−!b
π
LFP
j=1
MP,j
k=1
mp−1
n=0
n
p=0
p
q=0
¯γmRP
R,P Γ(n+k−p)Γ(mR,P +q)αjk
Γ(n+1)Γ(mR,P )Γ(k)¯γmR,P +k+q−p
Pn
pp
q
×"n+k−p
l=1
l¯γP,j
¯γPn−l+1
2
Gl, ¯γP,j (b+¯γP)
¯γP
+
mR,P +q
m=1
ϑm¯γR,P
¯γPn−m+1
2
Gm, ¯γR,P (b+¯γP)
¯γP# (15)
1304 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017
information as in (3), the decoding processes are dependent on
each other, and we therefore used the conditional probability in
obtaining Pe
S1[39], [40].
Proof: See Appendix B.
For the symmetrical case when ¯γh,R =¯γg,R, by substituting
Pb(γS1,R|¯eγS2,R )=Pb(γS2,R|¯eγS1,R )and Pb(γS1,R |eγS2,R )=
Pb(γS2,R|eγS1,R )in (91) and (92) and then substituting the
results in (17), Pb(γR)is simplified as
Pb(γR)=2PbγS1,R|¯eγS2,R $1−PbγS2,R |eγS1,R %
PbγS1,R|¯eγS2,R +$1−PbγS2,R|eγS1,R %.
(23)
Next, we consider three special cases of interest where further
simplifications are obtained.
1) Interference-Free Case:
Corollary 1: Here, we present our main results on the error
probability performance of the CR dual-hop relaying system,
when none of the nodes is impaired by interference (ES1,j =
ES2,j =ER,j =EI=0∀j). As a consequence, the equations
obtained in Proposition 2 are simplified as
Pb(γR,S1)=Ih,S (24)
PbγS1,R|¯eγS2,R =Ih,R (25)
PbγS1,R|eγS2,R =Uh,g (26)
where
Ih,S =a1−!b
π
mh−1
n=0
Γn+1
2¯γn
h,S
Γ(n+1)(b+¯γh,S )n+1
2(27)
Uh,g =a1−!b
π
mg−1
n=0
n
i=0
Γ(mh+i)Γ n+1
2
√¯γg,RΓ(mh)Γ(n+1)
×n
i¯γh,R
2n−i+1
2Gmh+i, ¯γh
2&.(28)
2) Single-Interferer Case:
Corollary 2: If only one dominant source of interference
affects each node of the secondary network, the cdfs can be
written as
FγR,S1(γ)=AS1,h,S (29)
FγS1,R|¯eS2,R (γ)=AR,h,R (30)
FγS1,R|eS2,R (γ)=Bh,g (31)
where
AS1,h,S =1−
mh−1
n=0
n
i=0
¯γn
h,S ¯γmS1,1
S1,1Γ(mS1,1+i)
Γ(n+1)Γ (mS1,1)
×n
iγnexp(−¯γh,Sγ)
(¯γh,S γ+¯γS1,1)mS1,1+i(32)
Bh,g =1−
mh−1
n=0
n
i=0
mg
k=1
¯γn
h,Rη0kΓ(k+i)
Γ(n+1)Γ(k)
×n
iγnexp(−¯γh,R )
¯γh,Rγ+¯γg,R
2k+i
−
mh−1
n=0
n
i=0
mR,1
k=1
¯γn
h,Rη1kΓ(k+i)
Γ(n+1)Γ(k)
×n
iγnexp (−¯γh,R)
(¯γh,R γ+¯γR,1)k+i.(33)
Moreover, the error probability is simplified as
Pb(γR,S1)=CS1,h,S (34)
PbγS1,R|¯eγS2,R =CR,h,R (35)
PbγS1,R|eγS2,R =Dh,g (36)
where CS1,h,S and Dh,g are defined in (37) and (38), shown at
the bottom of the next page.
3) I.I.D. Channel Case:
Corollary 3: The interferers’ channels can be assumed to
be complex circularly symmetric i.i.d. Gaussian distributed.
This assumption is very generic and has been employed in the
literature for performance analysis and resource allocation [41].
Then, the cdfs can be further simplified as
FγR,S1(γ)=LS1,h,S (39)
FγS1,R|¯eS2,R (γ)=LR,h,R (40)
FγS1,R|eS2,R (γ)=Vh,g (41)
where
LS1,h,S =1−
mh−1
n=0
n
i=0
¯γn
h,S ¯γMS1
S1Γ(MS1+i)
Γ(n+1)Γ (MS1)
×n
iγn
(¯γh,S γ+¯γS1)MS1+iexp(−¯γh,S γ)(42)
JS1,h,S,λjk =a⎡
⎣1−!b
π
LFS
1
j=1
MS1,j
k=1
mh−1
n=0
n
i=0
¯γn
h,S λjkΓ(k+i)Γ n+1
2
Γ(n+1)Γ(k)¯γk+i
S1,j n
i¯γS1,j
¯γh,S n+1
2
G
k+i, ¯γS1,j (b+¯γh,S )
¯γh,S ⎤
⎦(21)
Hh,g =a1−!b
π"mh−1
n=0
mg
k=1
n
i=0
¯γn
h,Rη0kΓ(k+i)Γ n+1
2
Γ(n+1)Γ(k)n
i 2
¯γg,R k+i¯γg,R
2¯γh,R n+1
2
×G
k+i, ¯γg,R (b+¯γh,R )
(2¯γh,R )
+
LFR
j=1
MR,j
k=1
mh−1
n=0
n
i=0
¯γn
h,Rηjk Γ(k+i)Γ n+1
2
Γ(n+1)Γ(k)
×n
i 1
¯γR,j k+i¯γR,j
¯γh,R n+1
2
G
k+i, ¯γR,j(b+¯γh,R)
¯γh,R # (22)
HATAMNIA et al.: TWO-WAY RELAYING IN SPECTRUM-SHARING SYSTEMS WITH QoS REQUIREMENTS 1305
Vh,g =1−
mh−1
n=0
n
i=0
mg
k=1
¯γn
h,Rη0kΓ(k+i)
Γ(n+1)Γ(k)
×n
iγn
¯γh,Rγ+¯γg,R
2k+iexp(−¯γh,R)
−
mh−1
n=0
n
i=0
MR
k=1
¯γn
h,Rη1kΓ(k+i)
Γ(n+1)Γ(k)
×n
iγn
(¯γh,R γ+¯γR)k+iexp(−¯γh,R)(43)
whereas MS1=LS1mS1,j ,¯γS1=βS1N0E−1
IS1,MR=LRmR,j,
and ¯γR=βRN0E−1
IR. Moreover, the error probability is simpli-
fied as
Pb(γR,S1)=QS1,h,S (44)
PbγS1,R|¯eγS2,R =QR,h,R (45)
PbγS1,R|eγS2,R =Ph,g (46)
where
QS1,h,S =a1−!b
π
mh−1
n=0
n
i=0
¯γn
h,S Γ(MS1+i)Γn+1
2
Γ(n+1)Γ (MS1)¯γi
S1
×n
i¯γS1
¯γh,S n+1
2
G
MS1+i,¯γS1(b+¯γh,S )
¯γh,S
(47)
Ph,g =a1−!b
π"mh−1
n=0
n
i=0
mg
k=1
¯γn
h,Rη0kΓ(k+i)Γ n+1
2
Γ(n+1)Γ(k)
×n
i 2
¯γg,Rk+i¯γg,R
2¯γh,Rn+1
2
G
k+i, ¯γg,R(b+¯γh,R )
(2¯γh,R )
+
mh−1
n=0
n
i=0
MR
k=1 n
iΓ(k+i)Γ n+1
2
Γ(n+1)Γ(k)
ׯγn
h,Rη1k
¯γk+i
R,1¯γR
¯γh,R n+1
2
G
k+i, ¯γR(b+¯γh,R)
¯γh,R #.(48)
B. Achievable Rate
Achievablerate in the Shannon sense is another metric that is
presented in this paper. Rate is a suitable performance measure
for applications that are delay insensitive. Based on the cut-set
bound, we can compute the outer bound of the capacity region
for the two-way PNC relaying system. Assuming perfect CSI
at the receiving nodes, the outer bound of the capacity region is
expressed as [42], [43]
R1≤min {CR,S2,C
S1,R}(49)
R2≤min {CR,S1,C
S2,R}(50)
where CS1,R,CR,S2,CS2,R ,andCR,S1are the capacity of links
S1−R,R−S2,S2−R,andR−S1, respectively. Finding
closed-form expressions for CS1,R,CR,S2,CS2,R ,andCR,S1
requires the evaluation of Cγ=0.5E{log(1+γ)}, which be-
comes intractable or computationally impractical. To circum-
vent this difficulty, we use an alternative approach based on
Jensen’s inequality, which leads to much simpler expressions.
Specifically, we can show that we can obtain the following
expressions:
CR,S2=FS2,g,S,¯
λjk (51)
CR,S1=FS1,h,S,λjk (52)
CS1,R =FR,h,R,μjk (53)
CS2,R =FR,g,R,μjk (54)
where
FS2,g,S,¯
λjk =
LFS
2
j=1
MS2,j
k=1
mg−1
n=0
n
i=0
¯γn
g,S ¯
λjkΓ(k+i)
Γ(k)¯γk+i
S2,j
×n
i¯γS2,j
¯γg,S n+1
Φ(n+1,n−k−i+2,¯γS2,j )(55)
whereas ¯γS2,j =βS2,jN0E−1
S2,j ,¯
λjk =(Γ(MS2,j −k+
1))−1ν(MS2,j−k)
j(−¯γS2,j),andνj(s)=¯γMS2,j
S2,j LFS
2
l=1
l=j
(s/
¯γS2,l +1)−MS2,l. Here, LFS
2is the number of primary in-
terferers affecting S2, which have different values of ¯γS2,j ,
and MS2,j is the summation of the shape parameters of the
interferer channels at S2with equal values of ¯γS2,j . A rate pair
(R1,R
2)is achievable only if the expressions in (49) and (50)
are satisfied with equality.
V. A SYMPTOTIC ANALYSIS
A. Lower Bound Analysis
The performance of the two-way PNC relay system can
further be quantified by analyzing the error performance based
on (8) in the high-SNR regime. Under this condition, which
CS1,h,S =a1−!b
π
mh−1
n=0
n
i=0
¯γn
h,S Γ(mS1,1+i)Γn+1
2
Γ(n+1)Γ (mS1,1)¯γi
S1,1n
i¯γS1,1
¯γh,S n+1
2
G
mS1,1+i, ¯γS1,1(b+¯γh,S )
¯γh,S (37)
Dh,g =a1−!b
π"mh−1
n=0
n
i=0
mg
k=1
¯γn
h,Rη0kΓ(k+i)Γ n+1
2
Γ(n+1)Γ(k)n
i 2
¯γg,R k+i¯γg,R
2¯γh,R n+1
2
×G
k+i, ¯γg,R (b+¯γh,R )
(2¯γh,R )
+
mh−1
n=0
n
i=0
mR,1
k=1 n
iΓ(k+i)Γ n+1
2
Γ(n+1)Γ(k)
ׯγn
h,Rη1k
¯γk+i
R,1¯γR,1
¯γh,R n+1
2
G
k+i, ¯γR,1(b+¯γh,R)
¯γh,R # (38)
1306 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017
occurs when EIS1,j N0and EIR,j N0, (8) and (93) in
Appendix B can be upper bounded as
γR,S1<γup
R,S1=ER|h|2
LS1
j=1 ES1,j |fS1,j |2(56)
γS1,R|¯eS2,R <γup
S1,R|¯eS2,R =ES|h|2
LR
j=1 ER,j |fR,j|2.(57)
Accordingly, the cdfs of the received SINR at node S1can be
expressed as
Fγup
R,S1(γ)=Ξ
S1,h,R,λjk (58)
Fγup
S1,R|¯eS2,R
(γ)=Ξ
R,h,S,μjk (59)
where
ΞS1,h,R,λjk =1−
LFS
1
j=1
MS1,j
k=1
mh−1
n=0
βn
hλjkΓ(n+k)
En
RΓ(n+1)Γ(k)γn
×βh
ER
γ+βS1,j
ES1,j −(n+k)
.(60)
With the aim of highlighting the impact of the fading parame-
ters on the error performance, specific asymptotic regimes are
considered as follows.
1) Case 1: In this case, we characterize the impact of the
amount of received interferencepower on the error performance
of the two-way PNC relay system. To begin, consider the case
when the power of the interferers is negligible compared with
the useful signal power, i.e., EIES. As such, we have the
following simplification:
γS1,R|eS2,R <γ
up
S1,R|eS2,R =ES|h|2
2ES|g|2.(61)
Then, Fγup
S1,R|eS2,R
(γ)can be obtained as
Fγup
S1,R|eS2,R
(γ)=ξh,g (62)
where
ξh,g =1−
mh−1
n=0
βn
hΓ(mg+n)
Γ(n+1)Γ(mg)βg
2mg
γn
×βhγ+βg
2−(mg+n)
.(63)
For this case, a lower bound expression for the SEP is formu-
lated in the following proposition.
Proposition 3: The lower bound on the SEP performance of
the system in the asymptotically high SNR regime for Case 1 is
given by (16), where
Pb(γR,S1)=WS1,h,R,λjk (64)
PbγS1,R|¯eγS2,R =WR,h,S,μjk (65)
PbγS1,R|eγS2,R =ℵg,h (66)
with WS1,h,R,λjk and ℵg,h defined in (67) and (68), shown at
the bottom of the page.
Proof: The proof is similar to that of Proposition 2.
2) Case 2: Consider the case where the power of the useful
signal is much smaller than that of the interferers, i.e., ES
EI. For this case, γS1,R|eS2,R can be approximated as
γS1,R|eS2,R <γ
up
S1,R|eS2,R =ES|h|2
LR
j=1 ER,j |fR,j |2.(69)
Here, γup
S1,R|eS2,R =γup
S1,R|¯eS2,R , which implies that Fγup
S1,R|eS2,R
(γ)=Fγup
S1,R|¯eS2,R
(γ).
One may conclude that, in this case, increasing the SNR has
no impact on the average SEP. In fact, since ESEI,the
quality of the secondary links is much worse than that of the
primary-to-secondary links. Therefore, the performance of
the secondary relay network does not improve by increasing
the SNR. The diversity order in this case is equal to 0.
B. Simplified Analysis
Since the derived expressions are complex, herein, we
present simplified closed-form formulas for the SEP based on
a linearization approach as in [44]. Using Taylor series, the
behavior of the probability density function (pdf) of the SINR
around the origin can be expanded as follows:
FγR,S1(γ)≈Z
S1,h,S,λjk (70)
FγS1,R|¯eS2,R (γ)≈Z
R,h,R,μjk (71)
FγS1,R|eS2,R (γ)≈T
h,g (72)
where
ZS1,h,S,λjk =¯γmh
h,S γmh
Γ(mh+1)
LFS
1
j=1
MS1,j
k=1
mh
i=0 mh
iλjkΓ(k+i)
Γ(k)¯γk+i
S1,j
(73)
Th,g =1−
mh−1
n=0
ηmgΓ(mg+n)
Γ(n+1)Γ(mg)2βhβ−1
gnγn
×1+2βhβ−1
gγ−(mg+n)1−βhN0E−1
Sγ
(74)
WS1,h,R,λjk =a⎡
⎣1−!b
π
LFS
1
j=1
MS1,j
k=1
mh−1
n=0
λjkΓ(n+k)Γ n+1
2
Γ(n+1)Γ(k)ES1,j
βS1,j k)βS1,jER
βhES1,j
×Φn+1,3/2−k, bβS1,jER
(βhES1,j )& (67)
ℵg,h =a1−!b
π)βg
2βh
mh−1
n=0
Γ(mg+n)Γ n+1
2
Γ(n+1)Γ(mg)Φn+1,3/2−mg,bβg
(2βh)(68)
HATAMNIA et al.: TWO-WAY RELAYING IN SPECTRUM-SHARING SYSTEMS WITH QoS REQUIREMENTS 1307
Fig. 2. OP of the PU for different numbers of cochannel interferers.
and ηmg=(2¯γ−1
g,R)mgη0mg. Accordingly, using the cdf-based
approach as in Proposition 2, we obtain
Pb(γR,S1)=aΓmh+1
2
bmh√πZS1,h,S,λjk (75)
PbγS1,R|¯eγS2,R =aΓmh+1
2
bmh√πZR,h,R,μjk (76)
PbγS1,R|eγS2,R =a1−!b
πYg,h(77)
where
Yg,h =)βg
2βh
mh−1
n=0
ηmgΓ(mg+n)Γ n+1
2
Γ(n+1)Γ(mg)
×*Φn+1
2;3
2−mg;bβg
2βh−n+1
2βg
2βh
ׯγh,RΦn+3
2;5
2−mg;bβg
2βh&.(78)
Finally, by substituting the results into (16), a simpler closed-
form expression for the average SEP of the system can be
obtained.
VI. NUMERICAL RESULTS AND DISCUSSION
Monte Carlo simulations are performed to validate the an-
alytical results. For ease, we denote the number of interferers
affecting the secondary nodes by L=[LS1,L
S2,L
R]and that
impacting the PU by L=[LP]. In the following simulation
evaluations, γth is set to 3 dB, and noise power is normalized to
0 dB. Moreover,in all figures, the horizontal axis is the primary
transmit SNR, i.e., ¯γP.
The outage and error performance comparison between the
analytical results and the simulation results corresponding to
the intended PU is shown in Figs. 2 and 3, respectively, for dif-
ferent values of Land fading parameter m=2. In these figures,
the useful power of the PU and the interference power profile
satisfy EP−EP,j =30 dB, where EP,j is the transmit energy
Fig. 3. SEP of the PU for different numbers of cochannel interferers.
Fig. 4. SEP of the secondary in the i.i.d. case for different primary OP
thresholds λ∈{0.1, 0.01}and numbers of interferers (L).
at the jth (j∈{1, 2,...,L
P})primary interferer in the prox-
imity of node P. First, the agreement between the plots from
the analysis and those from simulations confirm the accuracy of
the analysis. As observed, the interference from the other PUs
has an adverse influence on the outage and the SEP of the
intended PU. It is evident that the OP and SEP improve with
increasing received SNR at the PU. The transmit power of the
SUs is controlled for the target reliability at the primary. There-
fore, as the primary OP threshold λdecreases, the performance
of the SUs would degrade.
Figs. 4–8 show SEP versus SNR forthe two-way PNC cogni-
tive relaying system, for Case 1, i.e.,when EIES. To examine
the accuracy of the expressions in Corollaries 1–3, Fig. 4 shows
the results for the i.i.d. case with the corresponding lower bound
and asymptotic results, as well as the SEP obtained throughsim-
ulations. Two sets of plots are presented, for a primary OP
threshold λ=0.1 and 0.01, while m=2. Fig. 5 shows a similar
set of results for λ=0.01 and m=1, 2. As observed, the analyti-
cal results yield an excellent match across the entire SNR range.
Fig. 6 shows the corresponding sets of results for the i.n.i.d.
case, for m=1 and 2 and with λ=0.01. Similar conclusions
as above can be drawn. For completeness, the case of Rayleigh
fading is shown. From Figs. 5 and 6, it can be deduced that
when the interferers’ channels are i.n.i.d., the performance
1308 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017
Fig. 5. SEP of the secondary in the i.i.d. case and for different fading parame-
ters m∈{1, 2}and numbers of interferers (L).
Fig. 6. SEP of the two-way PNC relay network in the i.n.i.d. case for m∈
{1, 2}and different numbers of interferers.
Fig. 7. SEP of the secondary in the i.i.d. and i.n.i.d. cases for m∈{1, 2}and
different numbers of interferers.
improvement is significant compared with the case when the
interferers’ channels are i.i.d.
Figs. 7 and 8 show the results when the channels consist
of a combination of i.i.d. and i.n.i.d. Nakagami-mfading to
examine Corollaries 1–3, for m=1, 2 and λ=0.1, 0.01. In
Fig. 8. SEP of the secondary in the i.i.d. and i.n.i.d. cases for different primary
OP thresholds λ∈{0.1, 0.01}and numbers of interferers.
addition, the average SEP performance under Case 2, i.e., when
ESEI, is a horizontal line matched exactly at 1/2 shown
in Figs. 4–8. As observed for these two practical Cases 1 and 2,
when ESEI, the secondary network is almost in outage and
exhibits poor error performance (see the parts of the curves
before the cutoff points), whereas when EIES(Case 1)
and assuming that the interference power is increasing with
the transmit power of the relay and the secondary sources, the
SEP improvement is visible only in the medium-SNR range.
With an increase in transmit power ES, the error probability
reaches a floor at a high SNR. Therefore, the PNC cognitive
relaying system is more vulnerable to noise than to interference
for low and moderate SNRs, whereas it is more susceptible to
interference at a high SNR.
Additionally, some interesting observations are drawn from
Figs. 4–8, which are summarized as follows: 1) There is a close
match between the asymptotic results and the simulations, even
for low SNRs. Moreover, in the low-to-medium-SNR range,
as the SNR increases, the SEP performance improves because
the dominant factor is the AWGN. 2) The performance of the
interference-free system (L=[0, 0, 0]), as well as that of the
single-interferer case (L=[1, 1, 1]) are included as benchmark.
In these two special cases, the simulation results are in good
agreement with the analytical results (Corollaries 1 and 2,
respectively). 3) For the special scenario where the SU’s ter-
minals transmit with the same power characteristics as the
interfering terminals, implying that the interference-to-noise
ratio (INR) and the SNR tend to infinity simultaneously as
the additive noise power becomes negligible, the presence of
interference at the secondary nodes induces a floor level at
a high SNR in the SEP performance, which is reflected in a
zero diversity order (as indicated by the slope of the curves),
whereas for the interference-free case, error floors do not occur.
This demonstrates that the use of interference cancelation is
crucial for attaining the beneficial effects of diversity. 4) It can
be concluded from the results in Figs. 4–8 that the number
of interfering signals has no effect on the SEP in the low-
SNR range, whereas a degradation can be seen as the SNR
increases. 5) As expected, there is a significant improvement
in performance as the fading parameters (m)and the primary’s
OP threshold (λ)increase. 6) Since both the source nodes and
the relay experience interferences from the primary side, the
HATAMNIA et al.: TWO-WAY RELAYING IN SPECTRUM-SHARING SYSTEMS WITH QoS REQUIREMENTS 1309
Fig. 9. Achievable rate for different primary OP thresholds λ∈{0.1, 0.01}
and numbers of interferers.
floor point on the error performance is reached at lower SNR
values.
We now turn our attention to Fig. 9, which shows the achiev-
able rate performance of the system for different distributions
of interferers, when their total is constant (fixed to 27), and
different values of λ,form=2. It can be clearly seen that with
theincreaseofλ, a better performance is achieved. The gap
between the simulation and analytical results is due to the use of
Jensen’s inequality in the derivation of expressions (51)–(54).
The unmarked curve shows the rate R1of the system when
CγR,S1,CγR,S2,CγS1,andCγS2are computed by simulation
(for clarity, only the case of L=[27, 0, 0]is shown). As
expected, an equal number of interferers at each node of the
secondary network gives better performance. Moreover, the
worse performance occurs for L=[27, 0, 0], i.e., when only
S1is affected by interference.
VII. CONCLUSION
This paper has considered a traditional primary network coex-
isting with a two-way cognitive relay network where two SU
source nodes communicate with each other through a relay using
a PNC protocol while sharing the spectrum with multiple PUs.
We investigated the effects of interference created by multiple
primary transceiversand by the CRN on the performance of both
a target PU and the SUs. The desired signals were assumed to be
subject to Nakagami-mfading. Furthermore, it was assumed that
thereis an arbitrary number of interfererssubjectto bothi.i.d. and
i.n.i.d. Nakagami-mfading, with each interfering signal having
a different power level and undergoing a different amount of
fading. Exact closed-form expressions for the OP and SEP of a
target PU were derived. For the SUs, closed-form expressions
for the SEP and its lower bound, as well as an upper bound
on the achievable rates were derived. Cases of interference-free
and single-interference reception at the SUs were studied by
deriving new expressions for the average SEP valid for BPSK
modulation. Simple asymptotic expressions for the error per-
formance were also developed. It was shown that interference
at the secondary nodes leads to floor levels in the SEP, which
occur because the higher the SNR, the higher the interference
on an information-bearing link. The simulation results indicate
that the fading parameters have a significant impact on the OP
and SEP performances. Furthermore, for low SNR values, the
error performance is not sensitive to the number of cochan-
nel interfering signals. Comparisons with simulation results
showed that the newly developed analytical expressions for the
average SEP accurately predict the system’s performance.
APPENDIX A
PROOF OF PROPOSITION 1
According to (10) and making the change of variables x=
(EP/N0)|hP|2,y=LFP
j=1 EP,j|fP,j |2,andz=ES(|fP,S1|2+
|fP,S2|2), the pdfs of these RVs are given by fX(x)=¯γmP
P(xmP−1
/
Γ(mP)) exp(−¯γPx),fY(y)=LFP
j=1 MP,j
k=1 (αjk/Γ(k))yk−1
exp(−¯γP,j y),andfZ(z)=LFSP
t=1 MP,St
w=1 (θtw /Γ(w))zw−1
exp(−¯γP,Stz). According to (10), the cdf of the primary SINR
is obtained as
FP(γ)
=Ey$Ez$Ew$Pr x≤γy+w+z+σ2
Pi|y, z, w%%%
=
∞
0
∞
0
γ(y+z+1)
0
fX(x)fY(y)fZ(z)dx dy dz
=
∞
0
∞
0
Fx(γ(y+z+1)) fY(y)fZ(z)fW(w)dy dz dw
=
∞
0
∞
01−
mP−1
n=0
(¯γP(y+z+1)γ)n
Γ(n+1)
×exp (−¯γP(y+z+1)γ)fY(y)fZ(z)dy dz
=
∞
0
∞
0
⎡
⎣1−
mP−1
j=1
n
r=0
r
q=0
¯γn
Pγn
Γ(n+1)n
rr
q
×exp(−¯γPγ)zqexp(−¯γPzγ)yn−rexp(−¯γPyγ)⎤
⎦
×fY(y)fZ(z)dy dz (79)
where E[.]represents expectation. Equation (79) can be split
into two separate integrals as follows:
I0=
∞
0
∞
0
fY(y)fZ(z)dy dz =1 (80)
I1=
mP−1
j=1
n
r=0
r
q=0
¯γn
Pγn
Γ(n+1)n
rr
qexp(−¯γPγ)
×
∞
0
zqexp(−¯γPzγ)fZ(z)dz
×
∞
0
yn−rexp(−¯γPyγ)fY(y)dy. (81)
1310 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017
FP(γ)=1−
LFP
j=1
MP,j
k=1
LFSP
t=1
MP,St
w=1
mP−1
n=0
n
r=0
r
q=0
¯γn
PΓ(n+k−r)Γ(t+q)θtwαjk
Γ(n+1)Γ(w)Γ(k)n
rr
q
×γn
(¯γPγ+¯γP,j )n+k−r(¯γPγ+¯γP,St)w+qexp(−¯γPγ)(82)
Pb(γS1,R)= PbγS1,R |¯eγS2,R +PbγS2,R|¯eγS1,R PbγS1,R |eγS2,R −PbγS1,R|¯eγS2,R
1−$PbγS1,R|eγS2,R −PbγS1,R |¯eγS2,R %$PbγS2,R |eγS1,R −PbγS2,R|¯eγS1,R % (90)
Pb(γS2,R)= PbγS2,R |¯eγS1,R +PbγS1,R|¯eγS2,R PbγS2,R |eγS1,R −PbγS2,R|¯eγS1,R
1−$PbγS1,R|eγS2,R −PbγS1,R |¯eγS2,R %$PbγS2,R |eγS1,R −PbγS2,R|¯eγS1,R % (91)
Finally, the cdf of the primary SINR is expressed as (82), shown
at the top of the page. In terms of (82), the OP of the SINR of
the PU can be directly expressed as
Pout
Pri =FP(γth).(83)
To ensure that the primary’s communications is reliable, the
corresponding OP shall remain below a threshold λ,andwe
must have
Pout
Pri ≤λ⇒Pout
Pri −λ≤0.(84)
Finally, by solving (84) w.r.t. ES, the power constraint of S1
and S2can be achieved as shown in (11).
APPENDIX B
PROOF OF PROPOSITION 2
To begin, the cdf of γR,S1in (8) is obtained as
FγR,S1(γ)=KS1,h,S,λjk (85)
where
KS1,h,S,λjk =1−
LFS
1
j=1
MS1,j
k=1
mh−1
n=0
n
i=0
¯γn
h,S λjkΓ(k+i)
Γ(n+1)Γ(k)
×n
iγn
(¯γh,S γ+¯γS1,j )k+iexp(−¯γh,Sγ).(86)
By substituting (85) into (13), with [45, eq. (9.211.4)], and
doing some manipulations, we arrive at (18). Next, we derive
Pb(γR).Wehave
Pb(γR)=PbγS1,R|¯eγS2,R ¯
Pb(γS2,R)
+PbγS2,R|¯eγS1,R ¯
Pb(γS1,R).(87)
Pb(γS1,R)and Pb(γS2,R )can be further expressed as
Pb(γS1,R)=PbγS1,R|eγS2,R Pb(γS2,R )
+PbγS1,R|¯eγS2,R ¯
Pb(γS2,R)(88)
Pb(γS2,R)=PbγS2,R|eγS1,R Pb(γS1,R )
+PbγS2,R|¯eγS1,R ¯
Pb(γS1,R).(89)
With the help of (88) and (89), we obtain (90) and (91),
shown at the top of the page. To find Pb(γS1,R |¯eγS2,R ),
Pb(γS1,R|eγS2,R ),Pb(γS2,R|¯eγS1,R ),andPb(γS2,R|eγS1,R ),we
make use of the cdf-based approach. To this end, the SINRs
γS1,R|¯eS2,R ,γS1,R|eS2,R ,γS2,R|¯eS1,R,andγS2,R|eS1,R need to
be obtained. According to (3), these SINRs at the relay are
given by
γS1,R|¯eS2,R =ES|h|2
LR
j=1 ER,j |fR,j |2+N0
(92)
γS1,R|eS2,R =ES|h|2
2ES|g|2+LR
j=1 ER,j |fR,j |2+N0
(93)
and their corresponding cdfs can be obtained as
FγS1,R|¯eS2,R (γ)=KR,h,R,μjk (94)
FγS1,R|eS2,R (γ)=Nh,g (95)
where
Nh,g =1−
mh−1
n=0
mg
k=1
n
i=0
¯γn
h,Rη0kΓ(k+i)
Γ(n+1)Γ(k)n
i
×γn
¯γh,Rγ+¯γg,R
2k+iexp(−¯γh,Rγ)
−
LFR
j=1
MR,j
k=1
mh−1
n=0
n
i=0
¯γn
h,Rηjk Γ(k+i)
Γ(n+1)Γ(k)n
i
×γn
(¯γh,R γ+¯γR,j )k+iexp(−¯γh,Rγ).(96)
Substituting (94), (95), FγS2,R |¯eS1,R (γ),andFγS2,R|eS1,R (γ)
into (13), we reach the equations shown in Proposition 2.
REFERENCES
[1] “Mobile and wireless communications enablers for the Twenty-Twenty
Information Society,” EU Funded Res. Project FP7 METIS, Stockholm,
Sweden, Nov. 2012–Apr. 2015. [Online]. Available: https://www.
metis2020.com
[2] “2020: Beyond 4G, radio evolution for the gigabit experience,” Nokia
Siemens Netw., Espoo, Finland, Aug. 2011.
[3] “50 billion connections 2020,” Ericsson Telecommun. Inc., Stockholm,
Sweden, Aug. 2013. [Online]. Available: http://www.ericsson.com/news/
1403231
[4] S. Vahidian, S. Aïssa, and S. Hatamnia, “Relay selection for security-
constrained cooperative communication in the presence of eavesdropper’s
overhearing and interference,” IEEE Wireless Commun. Lett.,vol.4,
no. 6, pp. 577–580, Dec. 2015.
HATAMNIA et al.: TWO-WAY RELAYING IN SPECTRUM-SHARING SYSTEMS WITH QoS REQUIREMENTS 1311
[5] S. Hatamnia, S. Vahidian, and M. Ahmadian-Attari, “Performance analy-
sis of two-way decode-and-forward relaying in the presence of co-channel
interferences,” in Proc. 22nd ICEE, May 2014, pp. 1817–1822.
[6] S. Haykin, “Cognitive radio: Brain-empowered wireless communica-
tions,” IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201–220,
Feb. 2005.
[7] A. Goldsmith, S. A. Jafar, I. Maric, and S. Srinivasa, “Breaking spectrum
gridlock with cognitive radios: An information theoretic perspective,”
Proc. IEEE, vol. 97, no. 5, pp. 894–914, May 2009.
[8] T. Q. Duong, P. L. Yeoh, V. N. Q. Bao, M. Elkashlan, and
N. J. Yang, “Cognitive relay networks with multiple primary transceivers
under spectrum-sharing,” IEEE Signal Process. Lett., vol. 19, no. 11,
pp. 741–744, Nov. 2012.
[9] T. Q. Duong, K. J. Kim, H.-J. Zepernick, and C. Tellambura, “Oppor-
tunistic relaying for cognitive network with multiple primary users over
Nakagami-mfading,” in Proc. IEEE ICC, Jun. 2013, pp. 5668–5673.
[10] V. N. Q. Bao, T. Q. Duong, D. B. da Costa, G. C. Alexandropoulos, and
A. Nallanathan, “Cognitive amplify-and-forward relaying with best relay
selection in non-identical Rayleigh fading,” IEEE Commun. Lett., vol. 17,
no. 3, pp. 475–478, Mar. 2013.
[11] Y. Zou, J. Zhu, B. Zheng, and Y.-D. Yao, “An adaptive cooperation
diversity scheme with best-relay selection in cognitive radio networks,”
IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5438–5445, Oct. 2010.
[12] Y. Huang et al., “Cognitive MIMO relaying networks with primary
user’s interference and outdated channel state information,” IEEE Trans.
Commun., vol. 62, no. 12, pp. 4241–4254, Dec. 2014.
[13] H. Ding, J. Ge, D. B. da Costa, and Z. Jiang, “Asymptotic analysis
of cooperative diversity systems with relay selection in a spectrum-
sharing scenario,” IEEE Trans. Veh. Technol., vol. 60, no. 2, pp. 457–472,
Feb. 2011.
[14] W. Xu, J. Zhang, P. Zhang, and C. Tellambura, “Outage probability
of decode-and-forward cognitive relay in presence of primary user’s
interference,” IEEE Commun. Lett., vol. 16, no. 8, pp. 1252–1255,
Aug. 2012.
[15] M. Xia and S. Aïssa, “Cooperative AF relaying in spectrum-sharing
systems: Performance analysis under average interference power con-
straints and Nakagami-mfading,” IEEE Trans. Commun., vol. 60, no. 6,
pp. 1523–1533, Jun. 2012.
[16] M. Xia and S. Aïssa, “Spectrum-sharing multi-hop cooperative relaying:
Performance analysis using extreme value theory,” IEEE Trans. Wireless
Commun., vol. 13, no. 1, pp. 234–245, Jan. 2014.
[17] Y. Huang et al., “Outage probability of spectrum sharing relay systems
with multi-secondary destinations under primary user’s interference,”
IEEE Trans. Veh. Technol., vol. 63, no. 7, pp. 3456–3464, Sep. 2014.
[18] B. Rankov and A. Wittneben, “Spectral efficient protocols for half-duplex
fading relay channels,” IEEE J. Sel. Areas Commun., vol. 25, no. 2,
pp. 379–389, Feb. 2007.
[19] D. B. da Costa, H. Ding, M. D. Yacoub, and J. Ge, “Two-way relaying in
interference-limited AF cooperative networks over Nakagami-mfading,”
IEEE Trans. Veh. Technol., vol. 61, no. 8, pp. 3766–3771, Oct. 2012.
[20] S. S. Ikki and S. Aïssa, “Performance analysis of two-way amplify-
and-forward relaying in the presence of co-channel interferences,” IEEE
Trans. Commun., vol. 60, no. 4, pp. 933–939, Apr. 2012.
[21] X. Liang, S. Jin, W. Wang, X. Gao, and K.-K. Wong, “Outage probabil-
ity of amplify-and-forward two-way relay interference-limited systems,”
IEEE Trans. Veh. Technol., vol. 61, no. 7, pp. 3038–3049, Sep. 2012.
[22] X. Liang, S. Jin, W. Wang, X. Gao, and K.-K. Wong, “Outage per-
formance for decode-and-forward two-way relay network with multiple
interferers and noisy relay,” IEEE Trans. Commun., vol. 61, no. 2,
pp. 521–531, Feb. 2013.
[23] E. Soleimani-Nasab, M. Matthaiou, M. Ardebilipour, and
G. K. Karragiannidis, “Two-way AF relaying in the presence of
co-channel interference,” IEEE Trans. Commun., vol. 61, no. 8,
pp. 3156–3169, Aug. 2013.
[24] A. Alsharoa, F. Bader, and M.-S. Alouini, “Relay selection and resource
allocation for two way DF–AF cognitive radio networks,” IEEE Wireless
Commun. Lett., vol. 2, no. 4, pp. 427–430, Aug. 2013.
[25] K. Hamdi, M. O. Hasna, A. Ghrayeb, and K. B. Letaief, “Opportunis-
tic spectrum sharing in relay-assisted cognitive systems with imper-
fect CSI,” IEEE Trans. Veh. Technol., vol. 63, no. 5, pp. 2224–2235,
Jun. 2014.
[26] P. Ubaidulla, M.-S. Alouini, and S. Aïssa, “Cognitive relaying and power
allocation under channel state uncertainties,” in Proc. IEEE WCNC,
Apr. 2013, pp. 3358–3363.
[27] A. Alsharoa, H. Ghazzai, and M.-S. Alouini, “A low complexity algo-
rithm for multiple relay selection in two-way relaying cognitive radio
networks,” in Proc. IEEE ICC, Jun. 2013, pp. 327–331.
[28] S.-I. Chu, “Outage probability and DMT performance of underlay cogni-
tive networks with incremental DF and AF relaying over Nakagami-m
fading channels,” IEEE Commun. Lett., vol. 18, no. 1, pp. 62–65,
Jan. 2014.
[29] A. Alsharoa, H. Ghazzai, and M.-S. Alouini, “Optimal transmit power
allocation for MIMO two-way cognitive relay networks with multiple
relays using AF strategy,” IEEE Wireless Commun. Lett., vol. 3, no. 1,
pp. 30–33, Feb. 2014.
[30] H. A. Suraweera, H. K. Garg, and A. Nallanathan, “Performance analysis
of two hop amplify-and-forward systems with interference at the relay,”
IEEE Commun. Lett., vol. 14, no. 8, pp. 692–694, Aug. 2010.
[31] H. Phan, T. Q. Duong, M. Elkashlan, and H.-J. Zepernick, “Beamforming
amplify-and-forward relay networks with feedback delay and interfer-
ence,” IEEE Signal Process. Lett., vol. 19, no. 1, pp. 16–19, Jan. 2012.
[32] N. J. Yang, P. L. Yeoh, M. Elkashlan, I. B. Collings, and Z. Chen,
“Two-way relaying with multi-antenna sources: Beamforming and an-
tenna selection,” IEEE Trans. Veh. Technol., vol. 61, no. 9, pp. 3996–4008,
Nov. 2012.
[33] R. H. Y. Louie, Y. Li, and B. Vucetic, “Practical physical layer net-
work coding for two-way relay channels: Performance analysis and com-
parison,” IEEE Trans. Wireless Commun., vol. 9, no. 2, pp. 764–777,
Feb. 2010.
[34] S. Hataminia, S. Vahidian, M. Mohammadi, and M. Ahmadian-Attari,
“Performance analysis of two-way decode-and-forward relaying in the
presence of co-channel interferences,” IET Commun., vol. 8, no. 18,
pp. 3349–3356, Dec. 2014.
[35] M. Najafi, M. Ardebilipour, E. Soleimani-Nasab, and S. Vahidian, “Multi-
hop cooperative communication technique for cognitive DF and AF relay
networks,” Wireless Pers. Commun., vol. 83, no. 4, pp. 3209–3221, 2015.
[36] P. Ubaidulla and S. Aïssa, “Optimal relay selection and power allocation
for cognitive two-way relaying networks,” IEEE Commun. Lett.,vol.1,
no. 3, pp. 225–228, Jun. 2012.
[37] Y. Chen and C. Tellambura, “Distribution function of selection com-
biner output in equally correlated Rayleigh, Rician, and Nakagami-m
fading channels,” IEEE Trans. Commun., vol. 52, no. 11, pp. 1948–1956,
Nov. 2004.
[38] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Prod-
ucts, 7th ed., A. Jeffrey and D. Zwillinger, Eds. San Diego, CA, USA:
Academic, 2007.
[39] T. Wang, A. Cano, G. B. Giannakis, and J. N. Laneman, “High-
performance cooperative demodulation with decode-and-forward relays,”
IEEE Trans. Commun., vol. 55, no. 7, pp. 1427–1438, Jul. 2007.
[40] M. Ju and I.-M. Kim, “Error performance analysis of BPSK modulation in
physical-layer network-coded bidirectional relay networks,” IEEE Trans.
Commun., vol. 58, no. 10, pp. 2770–2775, Oct. 2010.
[41] Z. Ding, M. Xu, J. Lu, and F. Liu, “Improving wireless security
for bidirectional communication scenarios,” IEEE Trans. Veh. Technol.,
vol. 61, no. 6, pp. 2842–2848, Jul. 2012.
[42] T. M. Cover and J. A. Thomas, Elements of Information Theory.
New York, NY, USA: Wiley, 1991.
[43] L. Ong, C. M. Kellett, and S. J. Johnson, “On achievable rate regions
of the asymmetric AWGN two-way relay channel,” in Proc. ISIT, 2011,
pp. 84–88.
[44] Z. Wang and G. B. Giannakis, “A simple and general parameterization
quantifying performance in fading channels,” IEEE Trans. Commun.,
vol. 51, no. 8, pp. 1389–1398, Aug. 2003.
[45] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products,
7th ed. New York, NY, USA: Academic, 2007.
Sajad Hatamnia was born in Iran in 1988. He
received the B.Sc. degree in electrical engineering
from Razi University, Kermanshah, Iran, in 2012
and the M.Sc. degree in electrical engineering from
K. N. Toosi University of Technology, Tehran, Iran,
in 2014.
His research interests include statistical signal
processing, wireless communications, multiple-
input–multiple-output (MIMO) networks, and coop-
erative and cognitive radio networks.
1312 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 2, FEBRUARY2017
Saeed Vahidian was born in Iran. He received the
B.Sc. degree in electrical engineering from Ferdowsi
University of Mashhad, Mashhad, Iran, in 2012
and the M.Sc. degree in electrical engineering from
K. N. Toosi University of Technology, Tehran, Iran,
in 2014.
Since then, he has workedasaRadioNetwork
Planning and Optimization Engineer with Ericsson
Telecommunications Company, Iran. His current re-
search interests include wireless and mobile com-
munications, signal processing, design and analysis
of multiple-antenna (MIMO) systems, cooperative communications, cognitive
radio networks, space–time coding, and convex optimization.
Mr. Vahidian served as a Reviewer for the IEEE TRANSACTIONS ON
VEHICULAR TECHNOLOGY, the IEEE SIGNAL PROCESSING LETTERS,and
the IEEE International Symposium on Computers and Communication.
Sonia Aïssa (S’93–M’00–SM’03) received the Ph.D.
degree in electrical and computer engineering from
McGill University, Montréal, QC, Canada, in 1998.
Since then, she has been with the Institut National
de la Recherche Scientifique— Energy, Materials
and Telecommunications Center (INRS-EMT), Uni-
versity of Quebec, Montréal, where she is a Full
Professor. From 1996 to 1997, she was a Researcher
with the Department of Electronics and Communi-
cations, Kyoto University, Kyoto, Japan, and with
the Wireless Systems Laboratories, NTT, Japan.
From 1998 to 2000, she was a Research Associate with INRS-EMT. During
2000–2002, while she was an Assistant Professor, she was a Principal In-
vestigator in the major program of personal and mobile communications of
the Canadian Institute for Telecommunications Research, leading research in
radio resource management for wireless networks. From 2004 to 2007, she was
an Adjunct Professor with Concordia University, Montréal. She was Visiting
Invited Professor with Kyoto University in 2006 and Universiti Sains Malaysia
in 2015. Her research interests include the modeling, design, and performance
analysis of wireless communication systems and networks.
Dr. Aïssa was the Founding Chair of the IEEE Women in Engineering
Affinity Group in Montréal during 2004–2007; a Technical Program Committee
(TPC) Symposium Chair or Cochair at the 2006, 2009, 2011, and 2012 IEEE
International Conference on Communications; a Program Cochair at the 2007
IEEE Wireless Communications and Networking Conference; a TPC Cochair
at the 2013 IEEE Vehicular Technology Conference (Spring); and a TPC
Symposia Chair at the 2014 IEEE Global Telecommunications. She also served
as an Editor for the IEE E TRANSACTIONSON WI RELESS COMMUNICATIONS
during 2004–2012, an Associate Editor and a Technical Editor for the IE EE
COMMUNICATIONS MAGAZINE during 2004–2015, a Technical Editor for the
IEEE WIRELESS COMMUNICATIONS MAGAZINE during 2006–2010, and an
Associate Editor for the Wiley Security and Communication Networks Journal
during 2007–2012. She currently serves as an Area Editor for the IEEE
TRANSACTIONS ON WIRELESS COMMUNICATIONS. Awards to her credit
include the Natural Sciences and Engineering Research Council (NSERC)
University Faculty Award in 1999; the Quebec Government FRQNT Strategic
Faculty Fellowship during 2001–2006; the INRS-EMT Performance Award,
multiple times since 2004, for outstanding achievements in research, teaching,
and service; and the Technical Community Service Award from the FQRNT
Center for Advanced Systems and Technologies in Communications in 2007.
She has coreceived five IEEE Best Paper Awards and the 2012 IEICE Best
Paper Award. She also received the NSERC Discovery Accelerator Supplement
Award. She is a Distinguished Lecturer of the IEEE Communications Society
(ComSoc) and an Elected Member of the ComSoc Board of Governors. She is
a Fellow of the Canadian Academy of Engineering.
Benoit Champagne (SM’03) received the B.Ing. de-
gree in engineering physics from the École Polytech-
nique de Montréal, Montréal, QC, Canada, in 1983;
the M.Sc. degree in physics from the Université de
Montréal, in 1985; and the Ph.D. degree in electrical
engineering from the University of Toronto, Toronto,
ON, Canada, in 1990.
From 1990 to 1999, he was an Assistant
Professor and then an Associate Professor with the
Institut National de la Recherche Scientifique—
Telecommunications, Université du Quebec,
Montréal. In 1999, he joined McGill University, Montréal, where he is currently
a Full Professor with the Department of Electrical and Computer Engineering,
as well as served as an Associate Chairman of Graduate Studies from 2004
to 2007. His research focuses on the study of advanced algorithms for
the processing of communication signals by digital means. He has coauthored
nearly 250 referred publications in his areas of interest. His interests span many
areas of statistical signal processing, including detection and estimation, sensor
array processing, adaptive filtering, and applications thereof to broadband
communications and audio processing. His research was funded by the
Natural Sciences and Engineering Research Council of Canada, the “Fonds de
Recherche sur la Nature et les Technologies” from the Government of Quebec,
and some major industrial sponsors, including Nortel Networks, Bell Canada,
InterDigital, and Microsemi.
Dr. Champagne was an Associate Editor of the EURASIP Journal on
Applied Signal Processing from 2005 to 2007, the IE EE SIGNAL PROCESSING
LETTERS from 2006 to 2008, and the IEEE TRANSACTIONS ON SIGNAL
PROCESSINGfrom 2010 to 2012 and a Guest Editor of two Special Issues of the
EURASIP Journal on Applied Signal Processing published in 2007 and 2014,
respectively. He also served on the Technical Committee of several interna-
tional conferences in the fields of communications and signal processing. In
particular, he served as a Registration Chair for the 2004 IEEE International
Conference on Acoustics, Speech, and Signal Processing; a Cochair, Antennas
and Propagation Track, for the 2004 IEEE Vehicular Technology Conference
(VTC’Fall); a Cochair, Wide Area Cellular Communications Track, for the
2011 IEEE International Symposium on Personal, Indoor, and Mobile Radio
Communications; a Cochair, Workshop on D2D Communications, for the 2015
IEEE International Conference on Communications; and a Publicity Chair for
the 2016 IEEE VTC (Fall).
Mahmoud Ahmadian-Attari was born in Tehran,
Iran, on April 15, 1953. He received the joint B.Sc.
and M.Sc. degree in electrical engineering and elec-
tronics from the University of Tehran, Tehran, and
the Ph.D. degree in electrical engineering from the
University of Manchester, Manchester, U.K.
Since 1989, he has been a faculty member with
K. N. Toosi University of Technology (KNTU),
Tehran. He taught electronics, communication the-
ory, digital communications, data communications,
information theory and coding, and advanced chan-
nel coding courses and founded the Coding Laboratory at KNTU in 2003.
He is currently a Professor, supervising research activities in related fields in
this laboratory. He is the author of Error Control and Correcting Codes in
Telecommunication Systems (in Persian: K. N. Toosi University of Technology,
2013). His research interests include error control coding schemes, secure
communications, cognitive radio, and sensor networks.
