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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 7, SEPTEMBER 2014
Transmit Antenna Selection for Interference
Management in Cognitive Relay Networks
Phee Lep Yeoh, Member, IEEE, Maged Elkashlan, Member, IEEE, Trung Q. Duong, Senior Member, IEEE,
Nan Yang, Member, IEEE, and Daniel Benevides da Costa, Senior Member, IEEE
Abstract—We propose transmit antenna selection (TAS) in
decode-and-forward (DF) relaying as an effective approach to
reduce the interference in underlay spectrum sharing networks
with multiple primary users (PUs) and multiple antennas at the
secondary users (SUs). We compare two distinct protocols: 1) TAS
with receiver maximal-ratio combining (TAS/MRC) and 2) TAS
with receiver selection combining (TAS/SC). For each protocol, we
derive new closed-form expressions for the exact and asymptotic
outage probability with independent Nakagami-m fading in the
primary and secondary networks. Our results are valid for two
scenarios related to the maximum SU transmit power, i.e., P,
and the peak PU interference temperature, i.e., Q. When P
is proportional to Q, our results confirm that TAS/MRC and
TAS/SC relaying achieve the same full diversity gain. As such,
the signal-to-noise ratio (SNR) advantage of TAS/MRC relaying
relative to TAS/SC relaying is characterized as a simple ratio of
their respective SNR gains. When P is independent of Q, we find
that an outage floor is obtained in the large P regime where the SU
transmit power is constrained by a fixed value of Q. This outage
floor is accurately characterized by our exact and asymptotic
results.
Index Terms—Cognitive radio, relays, spectrum sharing.
I. I NTRODUCTION
C
OGNITIVE relaying is an exciting application to increase
spectrum utilization and extend the reach of the secondary
network [1]. The underlying idea is to introduce network cooperation in opportunistic spectrum access in order to aid the
transmission between secondary users (SUs) over large network
areas [2], [3]. In doing so, cognitive relaying is applied, from a
power perspective, to address fundamental constraints on the
transmit power at the secondary network while keeping the
interference power at the primary network (or the so-called
interference temperature) to a minimum [4], [5]. The challenge
is how to effectively manage the transmit power relative to
Manuscript received November 28, 2012; revised April 29, 2013 and
August 12, 2013; accepted December 27, 2013. Date of publication January 9,
2014; date of current version September 11, 2014. This work was presented
in part at the IEEE International Communications Conference, Budapest,
Hungary, June 2013. The review of this paper was coordinated by Dr. C. Ibars.
P. L. Yeoh is with the University of Melbourne, Parkville, VIC 3010,
Australia (e-mail: phee.yeoh@unimelb.edu.au).
M. Elkashlan is with Queen Mary University of London, London E1 4NS,
U.K. (e-mail: maged.elkashlan@qmul.ac.uk).
T. Q. Duong was with Blekinge Institute of Technology, 371 41 Karlskrona,
Sweden. He is currently with the Queen’s University Belfast, Belfast BT7 1NN,
U.K. (e-mail: trung.q.duong@qub.ac.uk).
N. Yang is with the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia (e-mail:
nan.yang@unsw.edu.au).
D. B. da Costa is with the Federal University of Ceara (UFC), 62010-560
Sobral, Brazil (e-mail: danielbcosta@ieee.org).
Digital Object Identifier 10.1109/TVT.2014.2298387
the interference power in large-scale cognitive relay networks
(CRNs) with multiple primary users (PUs).
Underlay spectrum sharing is a common class of CRNs in
which the secondary network may access the primary licensed
spectrum provided that the primary network performance is
not compromised. To do so, the interference at the PUs due
to the SU transmit power must be managed under a maximum
interference temperature to guarantee reliable communication
in the primary network. In this respect, a wealth of existing
literature has considered single antennas in the secondary network (see, e.g., [6]–[11] and the citations therein). Among
them, the exact outage probability of CRNs was derived in
[6] for decode-and-forward (DF) relaying in Rayleigh fading.
Further insights into the diversity gain of CRNs were presented
in [7] for DF relaying and amplify-and-forward (AF) relaying.
The more general case of DF relaying in Nakagami-m fading
was analyzed in [8]. Considering AF relaying in Rayleigh
fading, the exact outage probability was examined in [9]. It
was shown in [9] that CRNs offer a lower outage probability
relative to their direct transmission counterpart when the relay
is placed between the source and the destination. In [10], AF
relaying was found to achieve a full diversity gain when the SU
transmit power is managed according to the peak interference
temperature at the PU. More recently, in [11], the impact of
multiple PUs on the outage probability was addressed. To do so,
the SU transmit power was adapted to comply with the added
interference constraints related to the multiple PUs.
Here, we view CRNs from the viewpoint of multiple antennas in the secondary network. The findings in this direction
are instructional due to the prominence of multiple antennas
in future cognitive networks [12]–[17]. We note that the outage
probability is positively impacted by the transmit power and
negatively impacted by the interference temperature. As such,
the interplay between transmit power with multiple antennas
in the secondary network and interference temperature with
multiple users in the primary network is not intuitively obvious.
Recent papers have considered cognitive relaying with multiple
antennas from various perspectives, including relay precoding
design [14], green energy harvesting [15], superposition coding
[16], and game theory [17].
In this paper, we propose transmit antenna selection (TAS) in
DF relaying as an effective interference management design in
underlay spectrum sharing networks. We consider large-scale
CRNs where the coverage of the multiple-antenna secondary
network is much larger than that of the single-antenna primary
network [18], [19]. As such, the multiple-antenna SUs may opportunistically access the licensed spectrum of small-coverage
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YEOH et al.: TAS FOR INTERFERENCE MANAGEMENT IN COGNITIVE RELAY NETWORKS
single-antenna PUs [20], [21]. We seek to answer fundamental questions surrounding the joint impact of two key power
constraints, namely, 1) maximum transmit power at the SUs,
i.e., P, and 2) peak interference temperature at the PUs, i.e.,
Q. To address these constraints, we derive new closed-form
expressions for the exact and asymptotic outage probability
with an arbitrary number of users in the primary network and
an arbitrary number of antennas in the secondary network. The
purpose is to showcase a unified comparative analysis of two
multiple-antenna relaying protocols, namely, TAS with receive
maximal-ratio combining (TAS/MRC) relaying and TAS with
receive selection combining (TAS/SC) relaying. In TAS/MRC
relaying, the strongest antenna at the source and the relay is
selected for transmission, and all the receive antennas at the
relay and the destination are combined with MRC. This results in a low-complexity transceiver design with low-feedback
overheads in the secondary network. In TAS/SC relaying, the
strongest transmit–receive antenna pairs are jointly selected
at the source, relay, and destination. This further reduces the
number of active radio-frequency (RF) chains in the secondary
network. We note that selecting the strongest transmit antenna
at the source and the relay is optimal for the secondary network
since it fully exploits multiantenna diversity and maximizes the
instantaneous SNR at the relay and the destination. From an
interference perspective, the strongest transmit antenna in the
secondary network corresponds to a random transmit antenna in
the primary network. As such, the interference does not increase
with the number of antennas in the secondary network.
Capitalizing on our closed-form expressions, new conceptual
insights are drawn. For the scenario where P is proportional to
Q, we confirm that TAS/MRC and TAS/SC relaying achieve
the same maximum diversity gain. As such, we can further
characterize the performance gap between the two relaying
protocols as a concise ratio of their signal-to-noise ratio (SNR)
gains. We also highlight that the diversity–multiplexing tradeoff
(DMT) of TAS/MRC and TAS/SC relaying is independent of
the primary network and entirely dependent on the secondary
network. For the scenario where P is independent of Q, we
find that an outage floor is obtained in the large P regime when
the SU transmit power is constrained by a fixed value of Q. We
also demonstrate that the threshold SNR for the outage floor
increases with Q. In each case, the outage floor is accurately
characterized by our exact and asymptotic results.
II. S YSTEM AND C HANNEL M ODELS
Consider the CRN in Fig. 1 where the secondary network
is allowed to reuse the spectrum band licensed to the primary
network. The primary network comprises L PUs equipped
with a single antenna. The secondary network consists of a
secondary source (S), a secondary relay (R), and a secondary
destination (D), equipped with NS , NR , and ND antennas,
respectively. We consider the scenario where R is activated
based on the quality and/or presence of the direct link. This
is a realistic scenario in cognitive underlay spectrum sharing,
where the transmit power at S is usually severely restricted,
and therefore, R assists in extending the range of the secondary
network.
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Fig. 1. CRN with multiple PUs and multiple antennas in the secondary
network.
Let G1 denote the NS × NR channels from the source to
the relay with channel coefficients g1ij , i ∈ {1, . . . NS }, j ∈
{1, . . . , NR }; G2 denote the NR × ND channels from the
relay to the destination with channel coefficients g2jk , j ∈
{1, . . . NR }, k ∈ {1, . . . , ND }; H1 denote the NS × L channels from the source to the PUs with channel coefficients h1il ,
i ∈ {1, . . . NS }, l ∈ {1, . . . , L}; and H2 denote the NR × L
channels from the relay to the PUs with channel coefficients
h2jl , j ∈ {1, . . . NR }, l ∈ {1, . . . , L}. The channel coefficients
in G1 , G2 , H1 , and H2 follow a Nakagami-m distribution with
fading parameters mg1 , mg2 , mh1 , mh2 , and channel powers
Ωg1 , Ωg2 , Ωh1 , Ωh2 , respectively. In the following, · is
the Euclidean norm, | · | is the absolute value, and E[·] is the
expectation.
In such an underlay spectrum sharing network, the interference power at the PUs originating from the SUs must not
exceed a predetermined threshold level. The transmit powers at
S and R are constrained according to [22]
Q
(1)
PS = min P,
|h1i∗ |2
Q
PR = min P,
(2)
|h2j ∗ |2
respectively, where P is the maximum SU transmit power,
and Q is the peak PU interference temperature. We denote
|h1i∗ | = maxl {|h1i∗ l |} as the largest channel coefficient from
the selected transmit antenna at S to the L PUs and |h2j ∗ | =
maxl {|h2j ∗ l |} as the largest channel coefficient from the selected transmit antenna at R to the L PUs. Channel state
information (CSI) of |h1i∗ l | and |h2j ∗ l | is assumed to be known
at S and R, respectively.
A. TAS/MRC Relaying
In the source-to-relay link, a single transmit antenna is selected at the source, and all the receive antennas at the relay are
combined using MRC. In the relay-to-destination link, a single
transmit antenna is selected at the relay, and all the receive
antennas at the destination are combined using MRC. The
instantaneous end-to-end SNR for TAS/MRC in DF relaying
is given as
γD = min(γ̃1 , γ̃2 )
(3)
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where
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 7, SEPTEMBER 2014
g1i∗ 2 γ Q
2
∗
γ̃1 = min g1i γ P ,
|h1i∗ |2 2
g
2j ∗ γ Q
γ̃2 = min g2j ∗ 2 γ P ,
.
|h2j ∗ |2
A. TAS/MRC Relaying
(4)
(5)
In (4) and (5), we define γ P = (P/N0 ) and γ Q = (Q/N0 ),
where N0 represents the noise variance. We also define
g1i∗ = maxi {[g1i1 , . . . , g1iNR ]} as the largest channel
vector between the source and the relay and g2j ∗ =
maxj {[g2j1 , . . . , g2jND ]} as the largest channel vector between the relay and the destination. In each link, we assume
that the CSI is estimated at the secondary receiver using pilot
symbols sent by the secondary transmitter. In the source-torelay link, S transmits pilot symbols, and R feeds back the
index of the strongest transmit antenna to S. In the relay-todestination link, R broadcasts pilot symbols, and D feeds back
the index of the strongest transmit antenna to R. As such, S
and R only need the index of the strongest transmit antenna to
perform the transmission.
Pout,TAS/MRC = Fγ̃1 (γ) + Fγ̃2 (γ) − Fγ̃1 (γ)Fγ̃2 (γ)
In this protocol, a single antenna pair with the highest
received SNR is selected in the source-to-relay link and the
relay-to-destination link. The instantaneous end-to-end SNR of
TAS/SC in DF relaying is given as
γD = min(γ̂1 , γ̂2 )
|g1i∗ j ∗ |2 γ Q
γ̂1 = min |g1i∗ j ∗ |2 γ P ,
|h1i∗ |2
|g2j ∗ k∗ |2 γ Q
2
γ̂2 = min |g2j ∗ k∗ | γ P ,
.
|h2j ∗ |2
(6)
(7)
(8)
In (7) and (8), we define |g1i∗ j ∗ | = maxi,j |g1ij | as the largest
channel coefficient between the source and the relay, and
|g2j ∗ k∗ | = maxj,k |g2jk | as the largest channel coefficient between the relay and the destination. As in TAS/MRC relaying,
CSI is estimated in each link at the secondary receiver using
pilot symbols sent by the secondary transmitter.
Fγ̃1 (γ)
1−e
−γ
γQ
Pout = Pr{γD ≤ γth } = FγD (γth )
(9)
where FγD (γth ) is the cumulative distribution function (cdf) of
γD . In the sequel, we derive new analytical expressions for the
outage probability with TAS/MRC and TAS/SC relaying.
1−
N
R −1
r=0
+
NS N
L−1
R −1
l=0 n=0 r=1
−
γ
e Ωg1 γ P γ r
r! (Ωg1 γ P )r
N S
nr−1 nr−1 1 nr −nr+1 L − 1
nr =0
nr
l
r!
NR −1
(−1)l+n Lγ r=1 nr
NR −1
×
Ωh1 (Ωg1 γ Q ) r=1 nr
−1−NR −1 nr
r=1
l+1
nγ
×
+
Ωh1
Ωg1 γ Q
N
R −1
(l + 1)γ Q
nγ
×Γ 1+
nr ,
+
Ωh1 γ P
Ωg1 γ P
r=1
NS n
Fγ̃2 (γ)
=
1−e
−γ
γQ
P Ωh2
L 1−
N
D −1
r=0
+
NR N
L−1
D −1
−
γ
e Ωg2 γ P γ r
r! (Ωg2 γ P )r
(12)
N R
nr−1 nr−1 1 nr −nr+1 L − 1
nr =0
nr
r!
ND −1
(−1)l+n Lγ r=1 nr
ND −1
×
Ωh2 (Ωg2 γ Q ) r=1 nr
−1−ND −1 nr
r=1
l+1
nγ
×
+
Ωh2
Ωg2 γ Q
N
D −1
(l + 1)γ Q
nγ
×Γ 1+
nr ,
+
.
Ωh2 γ P
Ωg2 γ P
r=1
NR Here, we seek to address the impact of the maximum transmit
power P and the peak interference temperature Q on the outage
probability of CRNs with multiple antennas. Our results are
valid for the two scenarios that P is proportional to Q and that
P is independent of Q.
The CRN is considered to be in outage when the instantaneous end-to-end SNR falls below a minimum threshold γth .
As such, the outage probability is
L P Ωh1
l=0 n=0 r=1
III. E XACT O UTAGE P ROBABILITY
(11)
where
=
B. TAS/SC Relaying
where
Here, we present a new closed-form expression for the exact outage probability of TAS/MRC relaying in the following
theorem.
Theorem 1: The exact outage probability of CRNs with
TAS/MRC relaying is given in (10), shown at the bottom of
the next page.
Proof: See Appendix A.
Note that our result in Theorem 1 consists of easyto-evaluate finite summations of the gamma function Γ(·)
[23, eq. (8.310.1)] and the upper incomplete gamma function
Γ(·, ·) [23, eq. (8.350.2)].
Corollary 1: Based on Theorem 1, the exact outage probability of TAS/MRC relaying for Rayleigh fading is given by
l
n
(13)
Proof: The result directly follows by setting mg1 = mg2 =
mh1 = mh2 = 1 in (10).
TAS/SC Relaying: Next, we present a new closed-form expression for the exact outage probability of TAS/SC relaying in
the following theorem.
YEOH et al.: TAS FOR INTERFERENCE MANAGEMENT IN COGNITIVE RELAY NETWORKS
Theorem 2: The exact outage probability of CRNs with TAS/
SC relaying is given in (14), shown at the bottom of the next page.
Proof: See Appendix B.
Comparing our expressions in Theorem 1 and Theorem 2, the
main difference lies in the limits of the summations and the
statistics of the channel coefficients.
Corollary 2: Based on Theorem 2, the exact outage probability of TAS/SC relaying in Rayleigh fading is given by
Pout,TAS/SC = Fγ̂1 (γ) + Fγ̂2 (γ) − Fγ̂1 (γ)Fγ̂2 (γ)
where
N S N R
γ
−
Fγ̂1 (γ) = 1 − e Ωg1 γ P
+
L−1
S NR
N
1−e
−γ
+
×
l
P Ωh1
l=0 n=0
= 1 − ⎝1 − Fg1i∗ 2
(16)
F|h1i∗ |2
γQ
γP
−
NS L−1
NS L − 1 L(−1)n+l
n=0 l=0
⎤
n
l
mh1 −1
⎣
lp−1
× ⎝1 − Fg2i∗ 2
⎡
γ
γP
F|h2i∗ |2
γQ
γP
−
NR L−1
NR L − 1 L(−1)n+l
n=0 l=0
⎤
n
l
mh2 −1
lp
lp−1 1 lp −lp+1 mh
p=1
2
⎦
lp
p!
Ωh2
p=1
lp =0
mg N −1
mg2 ND −1 nr−1 nr−1 1 nr −nr+1 γmg r=12 D nr
2
×
nr
r!
Ωg2 γ Q
r=1
nr =0
mh2 −1
N
−1
m
g2 D
−mh2 −
nr −
lp
p=1
r=1
(l + 1)mh2
nγmg2
×
+
Ω
Ωg2 γ Q
⎞⎞
⎛ h2
mh2 −1
mg2 ND −1
(l
+
1)m
γ
nγm
h
g
Q
2
2
⎠⎠
× Γ ⎝ mh 2 +
nr +
lp ,
+
Ωh2 γ P
Ωg2 γ P
r=1
p=1
mh2 −1
×
⎣
lp−1
m h1
Ω h1
m h 1
Γ (mh1 )
lp
lp−1 1 lp −lp+1 mh
p=1
1
⎦
lp
p!
Ωh1
p=1
lp =0
mg N −1
mg1 NR −1 nr−1 nr−1 1 nr −nr+1 γmg r=11 R nr
1
×
nr
r!
Ωg1 γ Q
r=1
nr =0
h1 −1
−mh1 − mg1 NR −1 nr −m
lp
p=1
r=1
(l + 1)mh1
nγmg1
×
+
Ω
Ωg1 γ Q
⎞⎞
⎛ h1
mh1 −1
mg1 NR −1
(l
+
1)m
γ
nγm
h
g
Q
1
1 ⎠⎠
× Γ ⎝ mh 1 +
nr +
lp ,
+
Ω
γ
Ω
γ
h
g
P
P
1
1
r=1
p=1
mh1 −1
×
⎛
⎡
γ
γP
n=0
Here, we apply our exact closed-form expressions to present
a unified comparative analysis of TAS/MRC and TAS/SC
relaying. The comparison is based on our new asymptotic
expressions, which we derive for the two relaying protocols at
high-SNR operating regions. Similar to our exact expressions,
we note that our asymptotic results encompass the two scenarios that P is proportional to Q and that P is independent
of Q. A natural question arises as to what are the underlying
network parameters that determine the SNR difference between
TAS/MRC and TAS/SC relaying. The comparison is examined from three perspectives: diversity gain, SNR gain, and
diversity–multiplexing tradeoff.
(−1)l+n L
l
IV. A SYMPTOTIC O UTAGE P ROBABILITY
(−1)l+n L
Pout,TAS/MRC
⎛
n
Proof: The result is obtained by setting mg1 = mg2 =
mh1 = mh2 = 1 in (14).
(15)
Ωh1
−1 (l+1)γ Q
− Ω γ + Ω nγγ
l+1
nγ
g1 P
h1 P
×
+
e
Ωh1
Ωg1 γ Q
L
γQ
N R N D
−γ Ω
− Ω γγ
1 − e P h2
Fγ̂2 (γ) = 1 − e g2 P
NR ND L−1
Ωh2
−1 (l+1)γ Q
− Ω γ + Ω nγγ
l+1
nγ
g2 P
h2 P
+
e
. (17)
Ωh2
Ωg2 γ Q
l=0
NS NR L−1
n
L−1
R ND
N
L
γQ
3253
m h2
Ω h2
m h 2
Γ (mh2 )
(10)
3254
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 7, SEPTEMBER 2014
A. TAS/MRC Relaying
B. TAS/SC Relaying
Here, we present the asymptotic outage probability of
TAS/MRC relaying in the following theorem.
Theorem 3: The asymptotic outage probability of TAS/MRC
relaying in (10) as γ P → ∞ is derived as
Next, we present the asymptotic outage probability of
TAS/SC relaying in the following theorem.
Theorem 4: The asymptotic outage probability of TAS/SC
relaying in (14) as γ P → ∞ is derived as
∞
Pout,TAS/MRC
⎧ m g1 NS NR
⎪
⎪
α1 γγth
⎪
⎪
P
⎪
m g 1 N S N R
⎪
⎪
⎪
γ
⎪
,
⎪ + β1 γth
⎪
Q
⎪
⎪
m
N
N
⎪
g2 R D
⎪
⎨ α2 γth
γP
=
m g 2 N R N D
⎪
γth
⎪
+
β
,
⎪
2
γQ
⎪
⎪
⎪
m g 1 N S N R
⎪
⎪
⎪
(α1 +α2 ) γγth
⎪
⎪
⎪
⎪
P mg1 NS NR
⎪
⎪
⎩ + (β1 +β2 ) γth
,
γ
∞
Pout,TAS/SC
⎧ m g1 NS NR
⎪
⎪
κ1 γγth
⎪
⎪
P
⎪
m g 1 N S N R
⎪
⎪
⎪
γ
⎪
,
⎪ + λ1 γth
⎪
Q
⎪
⎪
m
N
N
⎪
g2 R D
⎪
⎨ κ2 γth
γP
=
m g 2 N R N D
⎪
γth
⎪
+
λ
,
⎪
2
γQ
⎪
⎪
⎪
m g 1 N S N R
⎪
⎪
⎪
(κ1 +κ2 ) γγth
⎪
⎪
P
⎪
⎪
m g 1 N S N R
⎪
⎪
⎩ + (λ1 +λ2 ) γth
,
γ
mg 1 NS NR < mg 2 NR ND
mg 1 NS NR > mg 2 NR ND
mg 1 N S N R = m g 2 N R N D
Q
Q
mg 1 N S N R < m g 2 N R N D
mg 1 NS NR > m g 2 NR ND
mg 1 N S N R = m g 2 N R N D
(18)
(23)
where α1 , β1 , α2 , and β2 are given as in (19)–(22), shown at
the bottom of the next page.
Proof: See Appendix C.
where κ1 , λ1 , κ2 , and λ2 are given as in (24)–(27), shown at the
bottom of the next page.
Proof: See Appendix D.
Pout,TAS/SC
⎛
= 1 − ⎝1 − F|g1i∗ j ∗ |2
⎛
γ
γP
F|h1i∗ |2
γQ
γP
−
N
S NR L−1
k=0 l=0
NS N R
k
m h 1
(−1)k+l L mh1
Ω h1
L−1
l
Γ(mh1 )
⎤
h1 −1
m
lp −lp+1 lp
p=1
m
l
1
p−1
h1
⎣
⎦
×
lp
p!
Ωh1
p=1
l =0
⎡p
⎤
mg −1
mg1 −1 kj−1 kj−1 1 kj −kj+1 γmg j=11 kj
1
⎣
⎦
×
kj
j!
Ωg1 γ Q
j=1
kj =0
mg1 −1
h1 −1
−mh1 − m
lp −
kj
p=1
j=1
(l + 1)mh1
kγmg1
×
+
Ω
Ωg1 γ Q
⎞⎞
⎛ h1
mh1 −1
mg1 −1
(l
+
1)m
γ
kγm
h1 Q
g1 ⎠⎠
× Γ ⎝ mh 1 +
lp +
kj ,
+
Ω
γ
Ω
γ
h
g
P
P
1
1
p=1
j=1
mh1 −1
⎡
lp−1 × ⎝1 − F|g2i∗ j ∗ |2
γ
γP
F|h2i∗ |2
γQ
γP
−
N
R ND L−1
k=0
l=0
NR N D
k
m h2 m h2
k+l
L − 1 (−1) L Ωh2
l
Γ (mh2 )
⎤
h2 −1
m
lp −lp+1 lp
p=1
m
l
1
p−1
h
2
⎣
⎦
×
lp
p!
Ωh2
p=1
l =0
⎡p
⎤
mg −1
mg2 −1 kj−1 kj−1 1 kj −kj+1 γmg j=12 kj
2
⎣
⎦
×
k
j!
Ω
γ
j
g
Q
2
j=1
kj =0
mh −1
−mh2 − p=12 lp − mg2 −1 kj
j=1
(l + 1)mh2
kγmg2
×
+
Ω
Ωg2 γ Q
⎞⎞
⎛ h2
mh2 −1
mg2 −1
(l
+
1)m
γ
kγm
h
g
Q
2
2
⎠⎠
× Γ ⎝ mh 2 +
lp +
kj ,
+
Ωh2 γ P
Ωg2 γ P
p=1
j=1
mh2 −1
⎡
lp−1
(14)
YEOH et al.: TAS FOR INTERFERENCE MANAGEMENT IN COGNITIVE RELAY NETWORKS
Based on Theorem 3 and Theorem 4, we present the following fundamental comparisons of TAS/MRC and TAS/SC
relaying. Specifically, we focus on the scenario where P is
directly proportional to Q according to γ P = μγ Q , where μ is
a positive constant [24].
α1 =
β1 =
m g 1 N S N R
m g1
Ωg1
l=0
L−1
L(−1)l
l
p=1
lp =0
α2 =
β2 =
m g 2 N R N D
L−1
l=0
l
L(−1)l
p=1
lp =0
mh2 −1
p=1
κ1 =
λ1 =
L−1
l=0
L(−1)
l
l
κ2 =
λ2 =
l=0
p=1
m g 2 N R N D
L−1
l
⎛
L(−1)l
mg2 Ωh2
mh2 Ωg2
m g 2 N R N D
(l + 1)−mh2 −mg2 NR ND −
mh2 −1
p=1
lp
(22)
(24)
mh1 −1 lp−1 lp−1 1 lp −lp+1
lp =0
lp
p!
mh1 −1
lp ,
mg1 Ωh1
mh1 Ωg1
m g 1 N S N R
(l + 1)−mh1 −mg1 NS NR −
mh1 −1
p=1
lp
⎞
Q(l + 1)mh1 ⎠
PΩh1
(25)
⎞L
Qm
Γ mh2 , PΩhh2
2
⎠
⎝1 −
Γ (mh2 )
⎛
(Γ (mg2 + 1))NR ND
L−1
lp
⎞
Q(l + 1)mh2 ⎠
lp ,
PΩh2
p=1
m g2
Ωg2
p=1
⎞L
Qm
Γ mh1 , PΩhh1
1
⎠
⎝1 −
Γ (mh1 )
× Γ ⎝ m h 1 + mg 1 NS NR +
p!
lp
Γ (mh1 ) (Γ (mg1 + 1))NS NR
⎛
mh1 −1
⎛
(Γ (mg1 + 1))NS NR
L−1
(l + 1)−mh1 −mg1 NS NR −
(21)
mh2 −1 lp−1 lp−1 1 lp −lp+1
m g 1 N S N R
m g 1 N S N R
(20)
Γ (mh2 ) (Γ (mg2 ND + 1))NR
⎛
m g1
Ωg1
NS
mg1 Ωh1
mh1 Ωg1
⎞L
Qm
Γ mh2 , PΩhh2
2
⎠
⎝1 −
Γ (mh2 )
× Γ ⎝ m h 2 + mg 2 NR ND +
⎛
(Γ (mg2 ND + 1))NR
L−1
p!
lp
⎞
Q(l + 1)mh1 ⎠
lp ,
PΩh1
mh1 −1
p=1
m g2
Ωg2
(28)
(19)
mh1 −1 lp−1 lp−1 1 lp −lp+1
× Γ ⎝ m h 1 + mg 1 NS NR +
GD = min (mg1 NS NR , mg2 NR ND ) .
⎞L
Qm
Γ mh1 , PΩhh1
1
⎠
⎝1 −
Γ (mh1 )
Γ (mh1 ) (Γ (mg1 NR + 1))
⎛
Corollary 3: The diversity gain of TAS/MRC and TAS/SC
relaying is given by
⎛
(Γ (mg1 NR + 1))NS
L−1
3255
mh2 −1 lp−1 lp−1 1 lp −lp+1
p=1
lp =0
lp
Γ (mh2 ) (Γ (mg2 + 1))
× Γ ⎝ m h 2 + mg 2 NR ND +
mh2 −1
p=1
p!
NR ND
⎞
Q(l + 1)mh2 ⎠
lp ,
PΩh2
(26)
mg2 Ωh2
mh2 Ωg2
m g 2 N R N D
(l + 1)−mh2 −mg2 NR ND −
mh2 −1
p=1
lp
(27)
3256
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 7, SEPTEMBER 2014
Proof: The proof follows by reexpressing the asymp∞
=
totic outage probability in (18) and (23) according to Pout
−GD
, where GA is the SNR gain, and GD is the diversity
(GA γ P )
gain.
The main insight to be taken from Corollary 3 is that
TAS/MRC and TAS/SC relaying achieves the same diversity
gain at high-SNR operating regions.
Corollary 4: The SNR gap between TAS/MRC and TAS/SC
is given by
GA,TAS/MRC
GA,TAS/SC
⎧ 10
⎪
mg1 NR log10
⎪
⎪
⎪
⎪
Γ(mg1 NR +1)
⎪
⎪
×
dB,
⎪
N
⎪
Γ(mg1 +1) R
⎪
⎪
⎪ 10
⎪
⎨ m N log10
g2 D
=
Γ(mg2 ND +1)
⎪
⎪
×
dB,
N
⎪
⎪
Γ(mg2 +1) D
⎪
⎪
⎪
10
⎪
⎪
mg1 NS NR log10
⎪
⎪
⎪
⎪
⎩ × κ1 +κ2 +λ1 +λ2 dB,
α1 +α2 +β1 +β2
mg 1 N S N R < m g 2 N R N D
mg1 NS NR > mg2 NR ND
mg1 NS NR = mg2 NR ND .
(29)
Proof: The proof follows by extracting the SNR gains
GA,TAS/MRC from (18) and GA,TAS/SC from (23) according
∞
= (GA γ P )−GD . The SNR gap between TAS/MRC and
to Pout
TAS/SC relaying is the ratio of their respective SNR gains as
ΔGA = 10 log10 (GA,TAS/MRC /GA,TAS/SC ) dB.
We observe from Corollary 4 that the SNR gap between
TAS/MRC and TAS/SC relaying is independent of the primary
network.
Corollary 5: The DMT of TAS/MRC and TAS/SC relaying
is given by
d(r̂) = min (mg1 NS NR , mg2 NR ND ) × (1 − 2r̂)
(30)
where r̂ is the normalized spectral efficiency with respect to the
channel capacity.
Proof: We evaluate the DMT of TAS/MRC and TAS/SC
relaying according to
− log Pout (r̂, γ P )
γ P →∞
log γ P
d(r̂) = lim
(31)
where r̂ = R/ log2 (1 + γ P ) is the normalized spectral efficiency with respect to the channel capacity, and R =
(1/2) log2 (1 + γth ) is the spectral efficiency in bits/s/Hz with
pre-log factor due to the half-duplex operation at the relay.
Reexpressing (18) and (23) in terms of r̂ and substituting the
resulting expressions into (31) yields the same expression for
TAS/MRC and TAS/SC relaying given by
d(r̂) = lim min (mg1 NS NR , mg2 NR ND )
γ P →∞
log (1 + γ P )2r̂ − 1
× 1−
.
log γ P
Applying L’Hôpital’s rule to (32) yields the DMT in (30).
(32)
Fig. 2. CRN with TAS/SC and TAS/MRC relaying, where P is proportional
to Q. We set Q = P, L = 3, NS = ND = 2, mh1 = mh2 = 3, and mg1 =
mg2 = 1.
From Corollary 5, we can see that when the normalized
spectral efficiency r̂ → 0, the maximum diversity order of
min(mg1 NS NR , mg2 NR ND ) is achieved. When d(r̂) → 0, the
maximum normalized spectral efficiency is r̂ = (1/2). Furthermore, we see that the DMT is entirely dependent on the
secondary network and is independent of the primary network.
V. N UMERICAL E XAMPLES
Numerical examples are provided to highlight the impact
of TAS/MRC and TAS/SC relaying on the outage probability
of CRNs. We consider large-scale underlay spectrum sharing
networks with multiple PUs and multiple antennas at the SUs.
In the examples, we assume that the fading in the secondary
network is more severe than the fading between the SUs and
the PUs. This is a realistic assumption in large-scale networks
where the SUs are widely distributed and in close proximity to
the PUs. As such, we set the channel powers to Ωh1 = Ωh2 = 5
and Ωg1 = Ωg2 = 2. We set the outage threshold SNR as γth =
10 dB.
We first consider the scenario where P = Q in Figs. 2–5. In
Fig. 2, we compare the exact outage probability of TAS/MRC
and TAS/SC relaying from (10) and (14), respectively. We see
that the exact analytical curves are well validated by the simulation points. We also plot the asymptotic curves for TAS/MRC
and TAS/SC relaying from (18) and (23), respectively. It is
important to note that our asymptotic results correctly predict
the behavior of the outage probability at high-SNR operating
regions. The plots confirm the observation in Corollary 3 that
TAS/MRC and TAS/SC relaying achieve the same diversity
gain. We further note that the SNR gap between TAS/MRC and
TAS/SC relaying increases with NR .
In Fig. 3, we consider the impact of the PUs on the outage
probability of TAS/MRC relaying. As expected, the outage
probability increases with L. This increase can be easily evaluated using our asymptotic expression in (18). We also observe
that the diversity gain remains unchanged with L.
YEOH et al.: TAS FOR INTERFERENCE MANAGEMENT IN COGNITIVE RELAY NETWORKS
Fig. 3. CRN with TAS/MRC relaying, where P is proportional to Q. We set
Q = P, NR = 2, NS = ND = 1, mh1 = mh2 = 3, and mg1 = mg2 = 2.
Fig. 4. CRN with TAS/SC relaying, where P is proportional to Q. We set
Q = P, L = 3, NS = ND = 2, NR = 1, and mh1 = mh2 = 2.
Fig. 5. CRN with TAS/MRC relaying, where P is proportional to Q. We set
Q = P, L = 3, NS = NR = ND = 2, and mg1 = mg2 = 1.
3257
Fig. 6. CRN with TAS/MRC and TAS/SC relaying, where P is independent
of Q. We set Q = 30 dB, L = 2, NS = ND = 1, mh1 = mh2 = 3, and
mg1 = mg2 = 1.
Fig. 7. CRN with TAS/MRC relaying, where P is independent of Q. We
set Q = 30 dB, NS = ND = 2, NR = 1, mh1 = mh2 = 3, and mg1 =
mg2 = 1.
In Figs. 4 and 5, we consider the impact of the fading severity
on the outage probability of TAS/SC and TAS/MRC relaying,
respectively. We see in Fig. 4 that increasing mg1 and mg2
brings a prominent increase in the diversity gain. By contrast,
increasing mh1 and mh2 has no impact on the diversity gain,
as shown in Fig. 5. This serves as a validation to Corollary 5
that the diversity gain is entirely dependent on the secondary
network and independent of the primary network.
Next, in Figs. 6–9, we consider the scenario where P is
independent of Q. We note that in both figures, the asymptotic
curves accurately predict the exact outage probability at high
SNRs.
In Fig. 6, we compare the outage probability of TAS/MRC
and TAS/SC relaying. The plots show that the outage probability initially decreases with increasing γ P . However, an outage
floor is obtained when γ P is large. This is due to the fact that
the transmit power at the secondary source and secondary relay
are constrained by the fixed peak interference temperature.
3258
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 7, SEPTEMBER 2014
VI. C ONCLUSION
Fig. 8. CRN with TAS/MRC and TAS/SC relaying, where P is independent of
Q. We set Q = 30 dB, L = 3, NS = ND = 2, NR = 1, mh1 = mh2 = 1,
and mg1 = mg2 = 1, 2.
We have proposed TAS with DF relaying in underlay spectrum sharing networks with multiple PUs. For such networks,
we derived new closed-form expressions for the exact and
asymptotic outage probability with arbitrary L PUs and NS ,
NR , and ND antennas at the secondary source, relay, and destination users, respectively. In the secondary network, we have
presented a comparative analysis of TAS/MRC and TAS/SC
relaying. Our results are valid for general Nakagami-m fading
with distinct fading parameters in the primary and secondary
networks. Based on our new analytical expressions, important
design insights are reached into the relationship between the
maximum SU transmit power, i.e., P, and the peak interference
temperature, i.e., Q. When P is independent of Q, we find that
a full diversity gain of GD = min(mg1 NS NR , mg2 NR ND ) is
attained for both TAS/MRC and TAS/SC relaying. When P is
independent of Q, an outage floor is displayed in the large P
regime where the SU transmit power is constraint by a fixed
value of Q. This outage floor is accurately characterized by our
exact and asymptotic results. Interestingly, we highlight that the
threshold SNR at which the outage floor occurs increases with
increasing Q.
A PPENDIX A
P ROOF OF T HEOREM 1
Based on (3) and (9), the outage probability of TAS/MRC is
derived according to
Pout = 1 − (1 − Fγ̃1 (γ)) (1 − Fγ̃2 (γ))
Fig. 9. CRN with TAS/MRC and TAS/SC relaying, where P is independent
of Q. We set L = 3, NS = ND = 2, NR = 1, mh1 = mh2 = 3, and mg1 =
mg2 = 1.
As such, no further improvement in the outage probability is
attained. The same outage floor is observed in Fig. 7, as the
number of PUs is varied from L = 1 to 3. As expected, the
outage probability increases with increasing L.
In Fig. 8, we examine the impact of increasing the fading
parameters mg1 and mg2 on the outage probability with fixed
Q. Similar to Fig. 4, we observe a prominent decrease in the
outage probability due to the increase in the diversity gain.
However, we clearly see that the diversity gain is lost in the
large γ P regime due to the constraint on the SU transmit power
imposed by the fixed Q. Finally, in Fig. 7, we consider the
impact of different fixed values of Q on the outage probability.
Interestingly, we note that the threshold SNR for γ P at which
the outage floor occurs increases with increasing value of Q.
This is due to the fact that relaxing the peak interference
temperature constraint for the primary network yields a lower
outage floor for the secondary network.
(33)
where Fγ̃1 (γ) is the cdf of γ̃1 in (4), and Fγ̃2 (γ) is the cdf of γ̃2
in (5). The cdf of γ̃1 is derived as
γQ
γ
2
2
& |h1i∗ | ≤
Fγ̃1 (γ) = Pr g1i∗ ≤
γP
γP
!"
#
I1
γQ
g1i∗ 2
γ
2
∗
+ Pr
≤
&
|h
|
≥
. (34)
1i
|h1i∗ |2
γQ
γP
!"
#
I2
The first term I1 is evaluated as
γQ
γ
F|h1i∗ |2
I1 = Fg1i∗ 2
γP
γP
(35)
where Fg1i∗ 2 (·) is the cdf of g1i∗ 2 , and F|h1i∗ |2 (·) is the cdf
of |h1i∗ |2 . The cdf of g1i∗ 2 is given by
⎞NS
⎛
m g1 r
mg1 NR −1
mg
x
1
Ω
−x
g1
⎠
Fg1i∗ 2 (x) = ⎝1 − e Ωg1
(36)
r!
r=0
where the channel gains in g1i∗ follow a Gamma distribution
with Nakagami-m fading parameter mg1 and channel power
Ωg1 . The cdf of |h1i∗ |2 can be written as
p ⎞ L
⎛
m
mh1 −1
mh
x Ωhh1
−x Ω 1 1
h1
⎠
F|h1i∗ |2 (x) = ⎝1 − e
(37)
p!
p=0
YEOH et al.: TAS FOR INTERFERENCE MANAGEMENT IN COGNITIVE RELAY NETWORKS
where |h1i∗ |2 follows a Gamma distribution with Nakagami-m
fading parameter mh1 and channel power Ωh1 . The second term
I2 is evaluated as
$∞
I2 =
f|h1i∗ |2 (y)Fg1i∗ 2
γQ
yγ
γQ
dy
where Fg1i∗ 2 (·) is given in (36), and f|h1i∗ |2 (·) is the probability density function (pdf) of |h1i∗ |2 given by
m h1
−x
mh
1
xmh1 −1 e Ωh1
Γ (mh1 )
⎞
mh1 p L−1
mh1 −1
mh
x
1
Ω h1
−x
⎠
× ⎝1 − e Ωh1
.
p!
p=0
mh 1
f|h1i∗ |2 (x) = L
Ωh1
⎛
(39)
×
r=1
γmg1
×
Ωg1 γ Q
nr−1 1 nr −nr+1
nr
r!
nr =0
N −1
r=1
(l+1)mh1 γ Q nγmg1
+
Ωh1 γ P
Ωg1 γ P
γ
γP
F|h1i∗ |2
γQ
γP
.
(40)
In (40), we expand the power sum according to
a N −1 an−1 N −1
xn
an−1 1 an −an+1 N −1 a
=
x n=1 n
n!
a
n!
n
n=0
n=1 an =0
(41)
when N > 1, and aN = 0. The resulting integral is solved by
applying [23, 3.351.2]. The cdf of γ̃2 is derived based on (38)
and (40) by carefully substituting the parameters for the sourceto-relay link with their relay-to-destination counterparts (i.e.,
mh1 → mh2 , mg1 → mg2 , Ωh1 → Ωh2 , Ωg1 → Ωg2 , NS →
NR , and NR → ND ). Substituting the resulting expressions for
Fγ̃1 (γ) and Fγ̃2 (γ) into (33) yields the closed-form outage
probability for TAS/MRC relaying in (10).
(44)
and F|h1i∗ |2 (·) is given in (37). The I4 term is evaluated as
$∞
yγ
f|h1i∗ |2 (y)F|g1i∗ j ∗ |2
I4 =
dy
γQ
=
where F|g1i∗ j ∗ |2 (·) is the cdf of |g1i∗ j ∗ |2 given by
⎞NS NR
⎛
m g1 r
mg1 −1
mg
x
1
Ωg1
−x
⎠
F|g1i∗ j ∗ |2 (x) = ⎝1 − e Ωg1
(45)
r!
r=0
γP
nr
p=1
The I3 term is evaluated as
γQ
h1 −1
−mh1−mg1 NR −1 nr−m
lp
p=1
r=1
(l+1)mh1 nγmg1
×
+
Ωh1
Ωg1 γ Q
mh1−1
mg1 NR −1
×Γ mh1 +
nr +
lp ,
r=1
(42)
where Fγ̂1 (γ) is the cdf of γ̂1 in (7), and Fγ̂2 (γ) is the cdf of γ̂2
in (8). The cdf of γ̂1 is derived as
γ
γ
Fγ̂1 (γ) = Pr |g1i∗ j ∗ |2 ≤
, |h1i∗ |2 ≤ Q
γP
γP
!"
#
I3
γQ
|g1i∗ j ∗ |2
γ
2
∗
+ Pr
≤
, |h1i | ≥
. (43)
|h1i∗ |2
γQ
γP
!"
#
I3 = F|g1i∗ j ∗ |2
lp =0
Pout = 1 − (1 − Fγ̂1 (γth )) (1 − Fγ̂2 (γth ))
I4
Substituting (36) and (39) into (38) results in
m h 1
mh
NS L−1
NS L − 1L(−1)n+l Ωh 1
1
I2 =
n
l
Γ(m
)
h
1
n=0 l=0
⎡
⎤
mh −1
mh1 −1 lp−1 lp−1 1 lp −lp+1 mh p=11 lp
1
⎣
⎦
×
lp
p!
Ωh1
p=1
mg1 NR −1 nr−1 A PPENDIX B
P ROOF OF T HEOREM 2
Based on (6) and (9), the outage probability of TAS/SC is
derived according to
(38)
γP
3259
N
S NR L−1
(−1)k+l L
m h1
Ω h1
m h 1
NS N R
L−1
k
l
Γ (mh1 )
k=0 l=0
⎡
⎤
h1 −1
mh1 −1 lp−1 m
lp −lp+1
lp
lp−1
p=1
m
1
h
1
⎣
⎦
×
lp
p!
Ωh1
p=1
⎡lp =0
⎤
mg1 −1 kj−1 kj−1 1 kj −kj+1
⎣
⎦
×
k
j!
j
j=1
kj =0
mg1 −1 kj
j=1
γmg1
×
Ωg1 γ Q
mg1−1
h1−1
−mh1−m
lp−
kj
p=1
j=1
(l+1)mh1 kγmg1
×
+
Ωh1
Ωg1 γ Q
mh1 −1
mg1 −1
× Γ mh 1 +
lp +
kj ,
p=1
j=1
(l + 1)mh1 γ Q
kγmg1
+
Ωh1 γ P
Ωg1 γ P
(46)
where f|h1i∗ |2 (·) is given in (39), and F|g1i∗ j ∗ |2 (·) is given
in (45). The cdf of γ̂2 is obtained from (44) and (46) by
substituting the source-to-relay link parameters with their relayto-destination counterparts (i.e., mh1 → mh2 , mg1 → mg2 ,
Ωh1 → Ωh2 , Ωg1 → Ωg2 , NS → NR , and NR → ND ). Substituting the expressions for Fγ̂1 (γ) and Fγ̂2 (γ) into (42) results
in our new closed-form expression for the outage probability of
TAS/SC relaying in (14).
3260
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 7, SEPTEMBER 2014
A PPENDIX C
P ROOF OF T HEOREM 3
matical manipulation, results in our new asymptotic expression
for the outage probability of TAS/MRC relaying in (18).
To derive the asymptotic outage probability of TAS/MRC relaying, we first present the first-order expansion of Fg1i∗ 2 (x)
as x → 0 given by
m g1 m g1 NS NR
x
Ωg1
x→0
Fg1i∗ 2 (x) =
.
(47)
(Γ (mg1 NR + 1))NS
We consider that the interference temperature at the PUs is fixed
and independent of the SU transmit power. As such, the firstorder expansion of Fγ̃1 (γ) in (34) as γ P → ∞ is derived as
Fγ̃∞1 (γ) = I1 + I2
(48)
where I1 in (35) as γ P → ∞ results in
m g 1 N S N R ⎛
I1
γ P →∞
=
m g1 γ
Ωg1 γ P
(Γ (mg1 NR + 1))NS
⎞L
Qm
Γ mh1 , PΩhh1
1
⎠ .
⎝1 −
Γ (mh1 )
(49)
Next, we consider I2 as γ P → ∞ and perform a change of
variables y = (tQ/P) in (38), which results in
tQ
tγ Q
dt
F|g1i∗ j ∗ |2
P
γP P
1
L−1 L(−1)l
γ P →∞ L − 1
=
l
Γ (mh1 ) (Γ (mg1 NR + 1))NS
l=0
⎡
⎤
mh1 −1 lp−1 lp−1 1 lp −lP +1
⎣
⎦
×
l
p!
p
p=1
lp =0
mh1 −1 γ Q mh1 mh1 + p=1 lp γmg1 mg1 NS NR
×
γ P Ωh1
Ωg1 γ P
Q(l+1) mh
$∞
mh1 −1
1
−t
P
Ωh
1 dt.
× tmg1 NS NR + p=1 lp +mh1 −1 e
$∞
I2 =
f|h1i∗ |2
1
(50)
We solve the integral according to [23, 3.351/2], which results in
L−1 L(−1)l
γ P →∞ L − 1
I2 =
l
Γ (mh1 ) (Γ (mg1 NR + 1))NS
l=0
⎡
⎤
mh1 −1 lp−1 lp−1 1 lp −lP +1
⎣
⎦
×
lp
p!
p=1
lp =0
m g 1 N S N R
mg1 Ωh1 γ
×
mh1 Ωg1 γ Q
mh1 −1
× (l + 1)−mg1 NS NR − p=1 lp −mh1
mh1 −1
× Γ mg 1 NS NR +
lp + mh 1 ,
p=1
Q(l + 1)mh1
PΩh1
.
(51)
The first-order expansion of Fγ̃2 (γ) as γ P → ∞ is derived
following the same steps as above, which, after some mathe-
A PPENDIX D
P ROOF OF T HEOREM 4
To derive the asymptotic outage probability of TAS/SC relaying, we first present the asymptotic expansion of F|g1i∗ j ∗ |2 (x)
as x → 0 given by
m g1 m g1 NS NR
x
Ω
g1
x→0
.
(52)
F|g1i∗ j ∗ |2 (x) =
(Γ (mg1 + 1))NS NR
Next, we derive the first-order expansion of Fγ̂1 (·) in (43) as
γ P → ∞. As such, I3 in (44) results in
⎞L
⎛
Qmh1
m g1 γ m g1 NS NR
Γ
m
,
h1 PΩh
Ωg1 γ P
γ →∞
1
⎠
⎝1 −
I3 P=
NS NR
Γ
(mh1 )
(Γ (mg1 + 1))
(53)
and I4 in (46) yields
L−1 L(−1)l
γ P →∞ L − 1
I4 =
l
Γ (mh1 ) (Γ (mg1 + 1))NS NR
l=0
⎡
⎤
mh1 −1 lp−1 lp−1 1 lp −lp+1
⎣
⎦
×
lp
p!
p=1
lp =0
m g 1 N S N R
mg1 Ωh1 γ
×
mh1 Ωg1 γ Q
mh1 −1
× (l+ 1)−mh1 −mg1 NS NR − p=1 lp
× Γ mh 1 + mg 1 NS NR
mh1 −1
+
p=1
Q(l + 1)mh1
lp ,
PΩh1
.
(54)
The first-order expansion of Fγ̂2 (γ) as γ P → ∞ is derived in
the same fashion as (53) and (54). Finally, the first-order expansion of Pout,TAS/SC is presented in (23) by considering the
joint impacts of Fγ̂1 (γ) and Fγ̂2 (γ) on the outage probability.
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Phee Lep Yeoh (S’08–M’12) received the B.E. degree with University Medal from the University of
Sydney, Sydney, Australia, in 2004 and the Ph.D.
degree, also from the University of Sydney, in 2012.
From 2004 to 2008, he worked at Telstra Australia
as a radio network design and optimization engineer.
From 2008 to 2012, he was with the Telecommunications Laboratory, University of Sydney, and the
Wireless and Networking Technologies Laboratory,
the Commonwealth Scientific and Industrial Research Organization (CSIRO), Sydney. In 2012, he
joined the Department of Electrical and Electronic Engineering, University of
Melbourne, Melbourne, Australia. His research interests include heterogeneous
networks, large-scale multiple-input–multiple-output, cooperative communications, and cognitive networks.
Dr. Yeoh received the Australian Research Council Discovery Early
Career Researcher Award, the University of Sydney Postgraduate Award, the
Norman I Price Scholarship, and the CSIRO Postgraduate Scholarship.
3261
Maged Elkashlan (M’06) received the Ph.D. degree in electrical engineering from the University of
British Columbia, Vancouver, BC, Canada, in 2006.
From 2006 to 2007, he was with the Laboratory for Advanced Networking, University of British
Columbia. From 2007 to 2011, he was with the
Wireless and Networking Technologies Laboratory,
Commonwealth Scientific and Industrial Research
Organization, Sydney, Australia. During this time, he
held an adjunct appointment with the University of
Technology Sydney. In 2011, he joined the School
of Electronic Engineering and Computer Science, Queen Mary University of
London, London, U.K., as an Assistant Professor. He also holds visiting faculty
appointments with the University of New South Wales, Sydney, and the Beijing
University of Posts and Telecommunications, Beijing, China. His research
interests include communication theory, wireless communications, and statistical signal processing for distributed data processing, large-scale multipleinput multiple-output, millimeter-wave communications, cognitive radio, and
network security.
Dr. Elkashlan currently serves as an Editor for the IEEE T RANSACTIONS ON
W IRELESS C OMMUNICATIONS, the IEEE T RANSACTIONS ON V EHICULAR
T ECHNOLOGY, and the IEEE C OMMUNICATIONS L ETTERS. He also serves
as the Lead Guest Editor for the Special Issue on “Green Media: The Future of
Wireless Multimedia Networks” of the IEEE W IRELESS C OMMUNICATIONS
M AGAZINE, the Lead Guest Editor for the Special Issue on “Millimeter Wave
Communications for 5G” of the IEEE C OMMUNICATIONS M AGAZINE, and
a Guest Editor for the Special Issue on “Location Awareness for Radios and
Networks” of the IEEE J OURNAL ON S ELECTED A REAS IN C OMMUNICA TIONS . He received the Best Paper Award at the IEEE Vehicular Technology
Conference (VTC-Spring) in 2013 and the Exemplary Reviewer Certificate of
the IEEE C OMMUNICATIONS L ETTERS in 2012.
Trung Q. Duong (S’05–M’12–SM’13) received
the Ph.D. degree in telecommunications systems
from the Blekinge Institute of Technology (BTH),
Karlskrona, Sweden, in 2012.
He continued working at the BTH as a Project
Manager. In 2013, he joined Queen’s University
Belfast, Belfast, U.K., as a Lecturer (Assistant Professor). He held a visiting position with the Polytechnic Institute of New York University, Brooklyn, NY,
USA, and Singapore University of Technology and
Design, Singapore, in 2009 and 2011, respectively.
His current research interests include cooperative communications, cognitive
radio networks, physical-layer security, massive multiple-input multiple-output,
cross-layer design, millimeter-wave communications, and localization for radios and networks.
Dr. Duong has been a Technical Program Committee Chair for several
IEEE international conferences and workshops, including the most recent IEEE
GLOBECOM13 Workshop on Trusted Communications with Physical Layer
Security. He currently serves as an Editor for the IEEE C OMMUNICATIONS
L ETTERS and the Wiley Transactions on Emerging Telecommunications Technologies, the Lead Guest Editor for the Special Issue on “Secure Physical
Layer Communications” of the IET COMMUNICATIONS, a Guest Editor for the
Special Issue on “Green Media: Toward Bringing the Gap between Wireless and
Visual Networks” of the IEEE WIRELESS COMMUNICATIONS MAGAZINE,
a Guest Editor for the Special Issue on “Millimeter Wave Communications
for 5G” of the IEEE COMMUNICATIONS MAGAZINE, a Guest Editor for the
Special Issue on “Cooperative Cognitive Networks” of the EURASIP J OURNAL
ON W IRELESS C OMMUNICATIONS AND N ETWORKING , and a Guest Editor
for the Special Issue on “Security Challenges and Issues in Cognitive Radio
Networks” of the EURASIP Journal on Advances in Signal Processing. He
received the Best Paper Award at the IEEE Vehicular Technology Conference
(VTC-Spring) in 2013 and the Exemplary Reviewer Certificate of the IEEE
C OMMUNICATIONS L ETTERS in 2012.
3262
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 7, SEPTEMBER 2014
Nan Yang (S’09–M’11) received the B.S. degree
in electronics from China Agricultural University,
Beijing, China, in 2005 and the M.S. and Ph.D. degrees in electronic engineering from Beijing Institute
of Technology in 2007 and 2011, respectively.
From 2008 to 2010, he was a visiting Ph.D.
student with the School of Electrical Engineering
and Telecommunications, University of New South
Wales, Sydney, Australia. From 2010 to 2012, he was
a Postdoctoral Research Fellow with the Wireless
and Networking Technologies Laboratory, Commonwealth Scientific and Industrial Research Organization, Marsfield, Australia.
Since 2012, he has been with the School of Electrical Engineering and Telecommunications, University of New South Wales, where he is currently a Postdoctoral Research Fellow. His general research interests include communications
theory and signal processing, with specific interests in collaborative networks,
multiple-antenna systems, network security, and distributed data processing.
Dr. Yang received the Exemplary Reviewer Certificate of the IEEE
COMMUNICATIONS LETTERS in 2012 and the Best Paper Award at the IEEE
77th Vehicular Technology Conference (VTC-Spring) in 2013. He is currently
serving as the Editor for the Wiley Transactions on Emerging Telecommunications Technologies.
Daniel Benevides da Costa (M’09–SM’13) was
born in Fortaleza, Ceará, Brazil, in 1981. He received
the B.Sc. degree in telecommunications from the
Military Institute of Engineering, Rio de Janeiro,
Brazil, in 2003 and the M.Sc. and Ph.D. degrees in telecommunications from the University
of Campinas, Campinas, Brazil, in 2006 and 2008,
respectively.
From 2008 to 2009, he was a Postdoctoral Research Fellow with INRS-EMT, University of Quebec, Montreal, QC, Canada. At that time, he received
two scholarships, namely, the Merit Scholarship Program for Foreign Students
in Quebec and the Natural Sciences and Engineering Research Council of
Canada Postdoctoral Scholarship. Since 2010, he has been with the Federal
University of Ceará, Brazil, where he is currently an Assistant Professor.
He has authored or coauthored more than 55 papers in IEEE/IET journals
and more than 45 papers in international conferences. His research interests
include wireless communications, particularly channel modeling and characterization, relaying/multihop/mesh networks, cooperative systems, cognitive
radio networks, tensor modeling, physical-layer security, and performance
analysis/design of multiple-input–multiple-output systems.
Dr. da Costa is currently an Editor of the IEEE C OMMUNICATIONS
L ETTERS, the IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY, the
EURASIP Journal on Wireless Communications and Networking, and the KSII
Transactions on Internet and Information Systems. He has also served as an
Associate Technical Editor for the IEEE C OMMUNICATIONS M AGAZINE, the
Lead Guest Editor for the EURASIP Journal on Wireless Communications and
Networking in the Special Issue on “Cooperative Cognitive Networks,” and
a Guest Editor for the IET Communications in the Special Issue on “Secure
Physical Layer Communications.” He is currently serving as Workshop Chair
of the 2nd International Conference on Computing, Management, and Telecommunications (ComManTel 2014). He is currently a Scientific Consultant of the
National Council of Scientific and Technological Development (CNPq), Brazil,
and of the Brazilian Ministry of Education (CAPES). He is also a Productivity
Research Fellow of CNPq. From 2010 to 2012, he was a Productivity Research
Fellow of the Ceará Council of Scientific and Technological Development
(FUNCAP). Currently, he is a member of the Advisory Board of FUNCAP
in the area of Telecommunications. He also received three conference paper
awards: one at the 2009 IEEE International Symposium on Computers and
Communications, one at the 13th International Symposium on Wireless Personal Multimedia Communications in 2010, and another at the XXIX Brazilian
Telecommunications Symposium in 2011. His Ph.D. dissertation received the
Best Ph.D. Thesis in Electrical Engineering from the Brazilian Ministry of
Education (CAPES) at the 2009 CAPES Thesis Contest.