optimal power allocation in cooperative networks
TRANSCRIPT
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TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
Trans. Emerging Tel. Tech. (2014)
Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.2834
RESEARCH ARTICLE
Efficient multiple antenna–relay selection algorithms
for MIMO unidirectional–bidirectionalcognitive relay networks
Ahmad Alsharoa, Hakim Ghazzai and Mohamed-Slim Alouini*
Computer, Electrical, and Mathematical Science of Engineering (CEMSE) Division, King Abdullah University of Science and
Technology (KAUST), Thuwal, Makkah Province, Kingdom of Saudi Arabia
ABSTRACT
In this paper,we consider a multiple-input multiple-output (MIMO) cooperative cognitive radio (CR) system using
amplify-and-forward protocol under a spectrum sharing scenario, where licensed users and unlicensed users operate on the
same frequency band. Indeed, combined CR, cooperative communication and MIMO antennas provide a smart solution fora more efficient usage of the frequency band and the data rate. The main objective of this work is to maximise the sum rate
of the unlicensed users allowed to share the spectrum with the licensed users by respecting a tolerated interference thresh-
old under perfect and imperfect channel state information scenarios. Practical approaches based on iterative and genetic
algorithms for multiple antenna–relay selections with generalised MIMO model for both unidirectional and bidirectional
transmissions are proposed to solve our formulated optimization problems. Interestingly, selected numerical results show
that our proposed approaches reach a performance close to the performance of the optimal solution either with discrete or
continuous power distributions while providing a considerable saving in terms of computational complexity. Copyright ©
2014 John Wiley & Sons, Ltd.
*Correspondence
M.-S. Alouini, Computer, Electrical, and Mathematical Science of Engineering (CEMSE) Division, King Abdullah University of Science
and Technology (KAUST), Thuwal, Makkah Province, Kingdom of Saudi Arabia.
E-mail: [email protected]
Received 29 September 2013; Revised 27 February 2014; Accepted 24 March 2014
1. INTRODUCTION
During the last decade, a light of improving both the spec-
trum usage and the data rate has been shed by wireless
communication researchers in both academic centres and
industrial companies. Several schemes including cognitive
radio (CR), cooperative communication and multi-input
multi-output (MIMO) antennas have been proposed and
discussed. The ideas have centred around incorporating
two or more of these schemes together to solve the spectral
limitation and the high data rate demand issues.The first idea of CR was proposed by Joseph Mitola III
and Gerald Q. Maguire Jr in late 1990s [3, 4]. This novel
approach of using an intelligent wireless system paved the
way for future research in wireless communication towards
a more efficient usage of the radio spectrum [5]. CR spec-
trum sharing allows secondary users (SUs), known also as
unlicensed users, to access the frequency band allocated by
§Parts of the material in this paper were presented in [1, 2].
primary users (PUs), known also as licensed users. As such
and in order to protect the PUs, the sum of the interference
power due to the secondary network (SN) should be kept
below a certain tolerated threshold called the interference
temperature limit [6], while the SN might be subjected to a
non-limited interference caused by the PUs [7, 8].
Relay techniques were proposed to increase the over-
all system throughput and extend the network coverage
area. Also, with relays, there is a considerable reduction
in transmission powers that can lead to the decrease of the
interference to neighbouring networks. In addition to that,in some cases, absence of the direct link between terminals
can be covered by relays to maintain the communication
link between the terminals [9]. In traditional unidirectional
transmission, known also as one-way relaying (OWR),
four time slots are required to accomplish the transmis-
sion of different messages between two terminals [10]. To
perform this, several relay strategies are used: decode-and-
forward (DF), compress-and-forward (CF) and amplify-
and-forward (AF) [11, 12]. In DF protocol, the relay
decodes the received signal and removes the noise before
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2. SYSTEM MODEL
We consider a cognitive system consisting of a primary
pairs and a SN. The SN is constituted of two cognitive
transceiver terminals T 1 and T 2, and L cognitive half-
duplex relays. The primary receiver, T 1, T 2, and the ith
relay are equipped by M PU
, M T 1
, M T 2
and M Ri
antennas,
respectively. A non-line of sight link between T 1 and T 2 is
considered. In this work, we assume that the PUs and SUs
utilise the spectrum simultaneously. Mutual interference is
considered between PUs and SUs. As, in this work, we
are focusing on maximising the secondary sum rate with-
out affecting the PU QoS, we consider that the secondary
receivers treat the primary interference as a noise and com-
bine it with the additive white Gaussiannoise [26]. Without
loss of generality, all the noise variances are assumed to be
equal to 2n . In order to protect the PU, the average received
interference power due the secondary nodes should be
below a specific interference threshold denoted I th [6].
Let us define NP, NPr ,H 1r i 2 C M Ri M T 1 ,H 2r i 2
C M Ri M T 2 ,H r i p 2 C M Ri M PU ,H 1 p 2 C M T 1 M PU andH 2 p 2 C
M T 2 M PU as the peak power at the transceiver
terminals, peak power at each relay, the complex chan-
nel mapping matrix between T 1 and the ith relay, the
complex channel mapping matrix between T 2 and the ith
relay, the complex channel mapping matrix between the
ith relay and the PU, the complex channel mapping matrix
between T 1 and the PU and the complex channel map-
ping matrix between T 2 and the PU, respectively. All the
channel gains adopted in our framework are assumed to
follow a Rayleigh distribution and constant during the
coherence time with elements h xyab
representing the fad-
ing coefficients between transmit antenna y at node a
and receive antenna x at node b. It is also assumed that
E
jjxmjj2 D TrC xm
6 NP whereC xm is the covariance
matrix of the signal xm, m D 1, 2. In an imperfect CSI sce-
nario, the relay fading channel matrices can be modelled
as follows
H mr i D OH mr i C H mr i , m D 1,2,
H r i p D OH r i p C H r i p,
H mp D OH mp C H mp, m D 1,2,
(1)
where OH mr i , OH r i p and OH mp are the estimated CSI at the
nodes, and H mr i , H r i p and H mp are the correspond-
ing CSI errors. Entries of all estimated errors matrices are
assumed to be independent and identically distributed with
zero mean complex Gaussian and variances equal to 2e(see [27] for more details). Note that when the CSI errors
go to zero, we obtain the perfect CSI case.
2.1. One-way relaying
Figure 1 illustrates a system model of OWR-CR networks.
During the first time slot t 1, T 1 transmits its signal x1 to
the relays with a diagonal matrix power denoted P1.t 1/
Figure 1. Cooperative communication multiple-input multiple-
output system under cognitive radio (CR) scenario for one-way-
relaying-CR networks: (a) first two time slots and (b) last two
time slots.
with elementsh
P11.t 1/, : : : , P
M T 1
1 .t 1/i
, where P x a denotes
the transmit power of antenna x at node a. The complex
baseband received vector in the first time slot at the ith relay
is given by
yri .t 1/ D H 1rix1 C nri .t 1/ (2)
where nri is the additive Gaussian noise vector at the ith
relay. During the second time slot, each active relay ampli-
fies yri by multiplying it by a diagonal matrix W i with
diagonal entries wk i and broadcasts it to the terminals T 2,
where wk i denotes the amplification factor at the k th antenna
of the ith relay.
Then, in the second time slot t 2, the selected
relays broadcast the amplified signal to T 2 with a
diagonal matrix power denoted Pri .t 2/ with elementshP1
r i.t 2/, : : : , P
M Rir i .t 2/
i, where i D 1, : : : , L. The received
signal at terminal T 2 is given by
y2.t 2/ D A2. H /x1 C z2 (3)
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where A2. H / D LP
iD1
H T 2ri
i .t 2/W i .t 2/H 1ri , z2 D
LPiD1
H T
2rii.t 2/W i .t 2/nri .t 1/
C n2, n2 is the additive
Gaussian noise vector at T 2 and i is a diagonal binary
variable matrix denoting whether the k th antenna at the ith
relay is active or not and its diagonal elements are given by
k i D
1 if the k th antenna at the i th relay is active,
0 otherwise (4)
Similarly, during the third time slot t 3, T 2 transmits its
signal x2 to the relays with a diagonal matrix power
denoted P2.t 3/ with elementsh
P12.t 3/, : : : , P
M T 2
2 .t 3/i
.
Finally, in the fourth time slot t 4, the selected relays broad-
cast the amplified signals to T 2 with a diagonal matrix
power Pri .t 4/ with elementsh
P1r i.t 4/, : : : , P
M Rir i .t 4/
i. The
received signal at terminal T 1 is given by
y1.t 4/ D A1. H /x2 C z1 (5)
where A1. H / D LP
iD1
H T 1ri
i .t 4/W i .t 4/H 2ri , z1 D
LPiD1
H
T 1ri i .t 4/W i .t 4/nri .t 3/
C n1 and n1 is the addi-
tive Gaussian noise vector at T 1.
The noise covariance matrix for OWR transmission at T mcan be given as
C zm D EŒzmz H m
D
2
n
L
XiD1
H
T
mri iW i H T mriiW i H
C
2
n I
(6)
where i and W i can be determined from the context.
2.2. Two-way relaying
Figure 2 illustrates a system model of TWR-CR networks.
During the first time slot, known also as the multiple-access
channel phase, T 1 and T 2 transmit their signals x1 and x2
to the relays simultaneously, with a power denoted P1, and
P2, respectively. In the second time slot, known also as the
broadcast channel phase, the selected relays transmit the
amplified signals to the terminals, with a power denoted
Pri , where i D 1, : : : , L.
In the first time slot, the complex baseband received
signal at the ith relay is given by
yri .t 1/ D H 1rix1 C H 2rix2 C nri (7)
During the second time slot, each relay amplifies yri by
multiplying it by W i and broadcasts it to the terminals T 1and T 2. The received signals in the broadcast channel phase
are given as
Figure 2. Cooperative communication multiple-input multiple-
output system under cognitive radio (CR) scenario for two-way-
relaying-CR networks.
y1.t 2/ D QA1. H /x1„ ƒ‚ …Self Interference
CA1. H /x2 C Qn1 (8)
y2.t 2/ D A2. H /x1 C QA2. H /x2„ ƒ‚ …Self Interference
C Qn2 (9)
respectively, where
A1. H / D
LXiD1
H T 1rii .t 2/W i .t 2/H 2ri ,
A2. H / D
L
XiD1
H T 2rii .t 2/W i .t 2/H 1ri ,
QA1. H / D
LXiD1
H T 1rii .t 2/W i .t 2/H 1ri ,
QA2. H / D
LXiD1
H T 2rii .t 2/W i .t 2/H 2ri ,
Qn1 D
LXiD1
H T 1ri
i .t 2/W i .t 2/nri .t 1/
C n1 and
Qn2 D
L
XiD1 H T 2ri
i .t 2/W i .t 2/nri .t 1/C n2
By using the available knowledge of the CSI that might
be erroneous, the terminals can remove the estimated
self interference. Thus, the received signals at T 1 and T 2becomes
r1 D y1.t 2/ QA1
O H x1 D A1. H /x2 C z1 (10)
r2 D y2.t 2/ QA2
O H x2 D A2. H /x1 C z2 (11)
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A. Alsharoa et al.
where z1 D Qn1 C
QA1. H / QA1
O H x1 and z2 D Qn2 C
QA2. H / QA2
O H x2. The noise covariance matrix for
TWR transmission at T m can be given as
C zm D E
zmz
H m
D 2n
LXiD1
H T mriiW i
H T mri
iW i
H C 2n I
C
QAm. H / QAm
O H C xm
QAm. H / QAm
O H H
(12)
where i and W i can be determined from the context.
Note that if perfect CSI is available at the terminals,
QAm. H / D QAm
O H
and the noise covariance matrix
becomes dependent only on the noise variance.
3. MULTIPLE ANTENNA–RELAYSELECTION AND PROBLEMFORMULATION
In this section, we formulate the optimization problems
that maximise the secondary sum rate for both OWR-CR
and TWR-CR networks without affecting the QoS of the
PUs. For simplicity, we assume that M Ri D M R, 8i D
1, : : : , L, i.e. all the relays equipped with the same number
of antennas.
3.1. One-way relaying
The relay power at the k th antenna of the i th relay can be
expressed as
Pk r i.t 2/ D E
ˇ̌̌wk
i .t 2/ yk r i
ˇ̌̌2
D
0@ M T 1X
zD1
P z1
ˇ̌̌hkz
1r i
ˇ̌̌2C 2n
1A ˇ̌̌
wk i .t 2/
ˇ̌̌2(13)
From Equation (13), the value of ˇ̌wk
i .t 2/ˇ̌
can be expressed
as
ˇ̌̌wk i .t 2/ˇ̌̌ D vuuuutPk
r i.t 2/
M T 1P zD1
P z1
ˇ̌̌hkz
1r i
ˇ̌̌2C 2n
(14)
Similarly, the value of jwk i .t 4/j can be expressed as
ˇ̌̌wk
i .t 4/ˇ̌̌ D
vuuuutPk
r i.t 4/
M T 2P zD1
P z2
ˇ̌̌hkz
2r i
ˇ̌̌2C 2n
(15)
Thus, the sum rate of the MIMO-OWR can be written as
R.OWR/. H / D 1
4log2
det
I C
A2. H /P1A
H 2 . H /
C z1
2
C 1
4log2
det
IC
A1. H /P2A
H 1 . H /
C z1
1
(16)
where the factor 14 is due to the four time slots that are
needed to accomplish the OWR transmission. Therefore,
the sum rate maximisation problem of OWR-CR multiple
antenna–relay selection can be formulated as follows
maximiseP1.t 1/,Pr.t 2/,P2.t 3/,Pr.t 4/,V .t 2/,V .t 4/
R.OWR/
O H
(17)
s.t 0 6
M T 1XvD1
Pv1 6
NP, 0 6
M T 2XuD1
Pu2 6
NP (18)
0 6
M RXk D1
Pk r i.t s/ 6 NPr , 8i D 1, .., L, s D f2, 4g (19)
M T 1XvD1
M PU X jD1
Pv1
ˇ̌̌Oh jv1 p
ˇ̌̌26 I th,
M T 2XuD1
M PU X jD1
Pu2
ˇ̌̌Oh ju2 p
ˇ̌̌26 I th (20)
LXiD1
M PU X jD1
M RXk D1
k i .t s/Pk
r i.t s/
ˇ̌̌Oh jk
r i p
ˇ̌̌26 I th, s D f2, 4g (21)
k i .t s/ 2 f0, 1g, 8i D 1, .., L, 8k D 1, .., M R, s D f2, 4g
(22)
where V .t s/ Dh1
1.t s/,.., M R1 .t s/,.., 1
L.t s/,.., M R L .t s/
iand Pr .t s/ D
hP1
r 1.t s/, .., P
M Rr 1 .t s/,.., P1
r L.t s/,.., P
M Rr L .t s/
i,
are the decision variable vectors of our formulated opti-
mization problem that contain the state and the transmit
power vector of each relay for the second and fourth time
slots, respectively. The constraints (18) and (19) represent
the power budget constraints at the terminals and at the
relays, respectively, while the constraints (20) and (21) rep-
resent the average interference constraints imposed to the
terminals and relays, respectively.
3.2. Two-way relaying
The relay power at the k th antenna of the i th relay can be
expressed as
Pk r i.t 2/ D E
ˇ̌̌wk
i .t 2/ yk r i
ˇ̌̌2
D
0@ M T 1X
zD1
P z1
ˇ̌̌hkz
1r i
ˇ̌̌2C
M T 2X zD1
P z2
ˇ̌̌hkz
2r i
ˇ̌̌2C 2n
1A ˇ̌̌
wk i .t 2/
ˇ̌̌2
(23)
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From Equation (23), the value of ˇ̌wk
i
ˇ̌can be expressed as
ˇ̌̌wk
i .t 2/ˇ̌̌ D
vuuuutPk
r i.t 2/
M T 1P zD1
P z1
ˇ̌
ˇhkz
1r i
ˇ̌
ˇ2
C M T 2P zD1
P z2
ˇ̌
ˇhkz
2r i
ˇ̌
ˇ2
C 2n
(24)
Thus, the sum rate of the MIMO-TWR can be written as
R.TWR/. H / D 1
2log2
det
IC
A2. H /P1A
H 2 . H /
C z1
2
C 1
2log2
det
IC
A1. H /P2A
H 1 . H /
C z1
1
(25)
where the factor 12
is due to the two time slots that are
needed to accomplish the TWR transmission. Thus, the
sum rate maximisation problem of TWR-CR multiple relay
selection can now be formulated as
maximiseP1.t 1/,P2.t 1/,Pr.t 2/,V .t 2/
R.TWR/ O H
(26)
s.t 0 6
M T 1XvD1
Pv1 6
NP, 0 6
M T 2XuD1
Pu2 6
NP (27)
0 6
M RXk D1
Pk r i.t 2/ 6 NPr , 8i D 1, .., L (28)
M T 1
XvD1
M PU
X jD1
Pv1 ˇ̌̌
Oh jv1 p ˇ̌̌
2C
M T 2
XuD1
M PU
X jD1
Pu2 ˇ̌̌
Oh ju2 p ˇ̌̌
26 I th (29)
LXiD1
M PU X jD1
M RXk D1
k i P
k r i.t 2/
ˇ̌̌Oh jk
r i p
ˇ̌̌26 I th (30)
k i .t 2/ 2 f0, 1g, 8i D 1, .., L, 8k D 1, .., M R (31)
where the constraints (29) and (30) represent the average
interference constraint in the first and second time slots,
respectively.
4. MULTIPLE ANTENNA–RELAYSELECTION ALGORITHMS
The optimal solution using continuous power distribu-
tion for our nonlinear optimization problems formulated
in Section 3 are difficult to find because of the exis-
tence of binary variables k i , where i D 1, : : : , L and
k D 1, : : : , M R [28]. Therefore, we employ heuristic
approaches to find suboptimal solutions to the problems.
For simplicity, we handle this problem by solving it in
a time slot per time slot fashion for both OWR and
TWR transmissions.
4.1. Quantisation and relay
power distributions
In this section, we propose to use a quantization set
with discrete number of power levels from zero to
the peak relay antenna power (i.e. it is assumed that
the peak power budget allocated at the relays is uni-
formly distributed at each antenna; NPar D NPr
M R). In
fact, each antenna at the relay can transmit the ampli-
fied signal using one of the power level between 0 and
NPar
Pa
r i2 S D
n0,
NPar
N 1,
2 NPar
N 1, : : : ,
. N 2/ NPar
N 1 , NPa
r
o, where N
is the number of quantization levels. By this way, cognitive
relays have more flexibility to allocate their powers in the
case where continuous power distribution is not available,
which is the case of actual existing systems. This method
is considered as a generalisation of the ON–OFF mode
where antennas can either transmit or keep silent. There-
fore, our goal is to find the optimal power allocation and
antenna–relay selection at the relay side. We assume that
the terminal powers at each antenna are equal.
For OWR transmission, the power allocated at the
each antenna of both terminals depends essentially on
two constraints: the peak power constraint (18) and the
interference constraint (20), and their optimal values are
given by
Pa1 D min
0BBBB@
I th
M T 1PvD1
M PU P jD1
ˇ̌̌Oh jv1 p
ˇ̌̌2, NPa
1
1CCCCA (32)
Pa2 D min
0BBBB@ I th
M T 2PuD1
M PU P jD1
ˇ̌̌Oh ju2 p
ˇ̌̌2, NPa
2
1CCCCA (33)
where NPa1 D
NP M T 1
and NPa2 D
NP M T 2
are the antenna peak
power at antenna a associated with T 1 and T 2, respectively.
The resulting simplified sum rate maximisation prob-
lem of OWR-CR multiple relay selection can now be
formulated as
maximisePr.t 2/,Pr.t 4/,V .t 2/,V .t 4/
R.OWR/
O H
(34)
s.t (19), (21), (22) (35)
Similarly, the optimal power allocated at the each
antenna of T 1 and T 2 for TWR transmission can be given
as
Pac D min
0BBBB@
I th
M T 1PvD1
M PU P jD1
ˇ̌̌Oh jv1 p
ˇ̌̌2C
M T 2PuD1
M PU P jD1
ˇ̌̌Oh ju2 p
ˇ̌̌2, NPa
c
1CCCCA (36)
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where c D f1, 2g. Thus, the simplified sum rate maximisa-
tion problem of TWR-CR multiple relay selection can now
be formulated as
maximisePr.t 2/,V .t 2/
R.TWR/
O H
(37)
s.t (28), (30), (31) (38)
The objective becomes now to find the optimal power allo-
cation over relay antennas in order to solve the OWR-CR
and TWR-CR problems expressed in Equations (34) and
(37), respectively. Two approaches are proposed to deal
with these maximisation problems: iterative algorithm and
GA. A comparison between both approaches are given in
Section 5.
4.2. Iteration algorithm
We assume that each antenna has N power levels from zero
to the maximum power, i.e. an antenna cooperates withone of the quantized power in S without interfering with
the PU. In the proposed algorithm, we aim to maximise
the sum rate by transmitting the signals with the maximum
number of antennas powered with the maximum possible
power without affecting the PUs QoS. At the beginning,
the transmit powers of all antennas at all relays are fixed
to NPar (i.e. the highest power level in the discrete quanti-
zation set S ). The algorithm selects the antenna that offers
the highest R and satisfies the interference constraint at
the same time. Then, it tries to add the maximum num-
ber of antennas that can contribute in maximising the sum
rate. If, during this process, the interference constraint is
not satisfied, then the new active antennas have to be pow-
ered with the next lower power existing in the discretequantized power set
Pr i 2 S
. At the end, the algorithm
converges when Pr reaches 0 (i.e. no more antenna can
be selected even with the lowest non-zero power). The
proposed algorithm is summarised in Algorithm 1.
4.3. Genetic algorithm
In order to employ the GA, we propose to encode the
power levels into binary words b.k /i , 8i D 1, , L and
8k D 1, , M R such that each power levels is designed
by a binary word. The length of the binary words b.k /i
depends on N (i.e. the number of quantization levels) as
follows: length.b.k /i / D dlog2 N e where d.e denotes the
integer round towards C1. For instance, if N D 4, two
bits are sufficient to encode these levels. If N D 11, four
bits are used to encode the code levels. In the last case,
the number of required words is not a power of 2, some
binary words are redundant and they correspond to any
valid word. Several solutions were proposed to solve this
problem by discarding these words as illegal, assigning
them a low utility or mapping them to a valid word with
fixed, random or probabilistic remapping [29].
Algorithm 1 Proposed iterative algorithm for OWR-CR
and TWR-CR networks with discrete power levels
Input: N , M T 1 , M T 2 , M R, I th, 2n , NP, NPr , L, OH 1ri , OH 2ri ,
OH rip , OH 1p and OH 2p .
Compute P1 and P
2 using (32) and (33) respectively, for
OWR, or compute P using (36) for TWR.
Initialization: Rmax D 0, Pk r D NPar , V D Œ0, : : : , 0,LV opt D ¿.
while Pk r D 0 do
l D 1.
while l 6 M R L and l 62 LV opt do
int D V .
int .l/ D 1.
Compute the sum rate R.t / using (16) for OWR or
(25) for TWR.
l D l C 1.
end while
Find lopt s.t Ropt D max l
Rl.
if Ropt > Rmax then
.lopt / D 1.
Rmax D Ropt .
LV opt D LV
opt [ flopt g.
else
Pk r D Pk
r NPa
r
N 1.
end if
end while
In our GA based approach, we generate randomly T
binary strings to form the initial population set where
T denotes the population length. Each string S t , 8t D
1, , T , is built by concatenating LM R binary words b.k /i
corresponding to a power level of each relay antenna. Thus,
the length of a string is equal to LM R log2 N . Once the
power level of each relay in a string S t is known and thus
the values of k i , 8i D 1, , L, k D 1, , M R, (i.e. if
b.k /i refers to a zero power level, then k
i D 0, otherwise,
k i D 1), the algorithm verifies whether the interference
constraint is satisfied or not. If it is the case, the GA com-
putes the corresponding data rate R.t /, which plays the role
of the fitness of the string S t . Otherwise, R.t / D 0. Then,
the algorithm selects .1 6 6 T ) strings that provide
the highest data rates and keeps them to the next pop-
ulation while the T remaining strings are generated
by applying crossovers and mutations to the survived
parents. Crossovers consist in cutting two selected ran-
dom parent strings at a correspond point that is chosen
randomly between 1 and LM R dlog2. N /e. The obtained
fragments are then swapped and recombined to produce
two new strings. After that, mutation (i.e. changing a bit
value of the string randomly) is applied with a probability
p. This procedure is repeated until reaching convergence
or reaching the maximum iteration number denoted I .
The proposed GA with discrete power levels is detailed
in Algorithm 2.
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Algorithm 2 Proposed GA for OWR-CR and TWR-CR
networks with discrete power levels
Input: N , M T 1 , M T 2 , M R, I th, 2n , NP, NPr , L, OH 1ri , OH 2ri ,
OH rip , OH 1p and OH 2p.
Compute P1 and P
2 using (32) and (33) respectively, for
OWR, or compute P using (36) for TWR.
Initialization: Rmax D 0.Generate a random initial population containing all
S t , 8t D 1, , T .
itr D 1.
while (itr 6 I or not converge) do
for t D 1 : T do
Find Pk r i
, 8i D 1, , L, k D 1, , M R corre-
sponding to the string S t .
if interference constraint is satisfied then
Compute the sum rate R.t / using (16) for OWR
or (25) for TWR.
else
Set R.t / to 0.
end if
end for
Save Rmax such that Rmax D max t
R.t/.
Keep the best strings providing the highest data rates
to the next population.
From the survived strings, generate T new strings
by applying crossovers and mutations to generate a
new population set.
itr D itr C 1.
end while
4.4. Complexity analysis
The formulated problems in Equations (34) and (37) canbe of course solved via an ES by investigating all possible
combinations. This depends on L (i.e. the number of relays
in SN), M R (i.e. the number of relay antennas) and N (i.e.
the number of quantization levels). Therefore, the ES algo-
rithm requires LP
iD0
LM R
i
. N 1/i D O. N LM R/ operations
to find the optimal solution [30] while our proposed itera-
tion algorithm (IA) and GA require . N 1/. LM R/2 and TI
times at most to compute the possible achievable rate until
reaching a suboptimal solution, respectively. However, it is
worth to notice that GA requires more central processing
unit (CPU) time than IA because GA applies crossover and
mutation operations at each step while IA does not require
these operations as it is shown in Table I. Indeed, Table I
shows a comparison between the proposed algorithms and
ES algorithm with average CPU time for 100 channel real-
isations and fixed I th and NPr . It is clear from this table that
the GA requires more processing time than IA even with a
lower rate computations.
Also, it can be seen that the ES algorithm is not a
practical choice because of its high complexity espe-
cially for a large number of relays L, a large number of
relays antenna M R and/or a high quantization level N .
Table I. : Central processing unit times for two-way relaying.
ES IA GA
RC, CPU time RC, CPU time (s) RC, CPU time (s)
fM R , L, N g D f1,4,64g
2 107, 1 1008, 0.13 1120, 0.45
fM R , L, N g D f2,4,64g
3 1014, 1 4032, 0.17 1120, 0.6fM R , L, N g D f4,4,64g
8 1028, 1 16128, 0.23 1120, 0.76
ES, exhaustive search; RC, rate computation; CPU, central
processing unit; IA, iteration algorithm; GA, genetic algorithm.
Table II. : Complexity comparison for two-way relaying.
M R , L, N ES IA GA
M R D 1, L D 4, N D 64 2 107 1008 1120
M R D 1, L D 4, N D 256 4 109 4080 1120
M R D 1, L D 8, N D 64 3 1014 4032 1120
M R D 1, L D 8, N D 256 2 1019 16320 1120
M R D 2, L D 4, N D 64 3 1014 4032 1120M R D 2, L D 4, N D 256 2 1019 16320 1120
M R D 2, L D 8, N D 64 8 1028 16 12 8 112 0
M R D 2, L D 8, N D 256 3 1038 65280 1120
M R D 4, L D 4, N D 64 8 1028 16 12 8 112 0
M R D 4, L D 4, N D 256 3 1038 65280 1120
M R D 4, L D 8, N D 64 6 1057 64512 1120
M R D 4, L D 8, N D 256 1 1077 261120 1120
ES, exhaustive search; IA, iteration algorithm; GA, genetic
algorithm.
Hence, our proposed algorithms are able to reach a sub-
optimal solution with a considerable saving in terms of
computational complexity as detailed in Table II wherewe compute the required number of iterations to achieve
the suboptimal solution for different values of L, M Rand N . In addition to that, as will be shown in the sequel,
our numerical results show that our proposed algorithms
achieve almost the same performance as the ES method.
Concerning the convergence of the algorithms, by experi-
ments and for a large number of channel realisations, the
proposed algorithms always converge successfully to their
suboptimal solutions.
5. SIMULATION RESULTS
The simulations are executed under the following assump-
tions: (i) all channels are assumed to be independent and
identically distributed (i.i.d) Rayleigh fading channels; (ii)
all cognitive elements have the same peak power, i.e.NPr D NP; (iii) all the communication nodes of the sys-
tem are equipped with the same number of antennas, i.e.
M T 1 D M T 2 D M PU D M R D M with 2n D 104; and (iv)
the GA is executed using these parameters: the mutation
probability p is set to 0.5, D 0.25 T, and the maximum
iteration number is I D 35.
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−20 −15 −10 −5 0 5 10 15 20 25 300
2
4
6
8
10
12
(a)
S u m R a
t e ( B i t s / s / H z )
−20 −15 −10 −5 0 5 10 15 20 25 300
5
10
15
(b)
S u m R
a t e ( B i t s / s / H z )
Figure 3. Achieved sum rate versus the peak power NP r for the
optimal and iteration algorithm (IA) with I th D 10 dBm and
different values of M and N : (a) L D 4 and (b) L D 8.
5.1. Performance of the proposed
algorithms for TWR-CR networks
The merits of MIMO system over single antenna system
are investigated in Figure 3, we plot the TWR secondary
sum rate for different values of M D f1, 4g, different values
of N D f256,64, 16, 2g and different values of L D f4, 8g.
It is noticed that we can improve the performance signifi-
cantly using the multi-antenna scheme than using the sin-
gle antenna scheme. The benefits of using MIMO system
appears clearly with a considerable data rate improvement
when M increases. When N D 16, NPr
D 10 dBm, L D 8,
and using M D 4 instead of M D 1, our proposed algo-
rithm improves the rate by around 136% because the sum
rate increases from 5.5 to about 13 bits/s/Hz.
In low-SNR region, IA and the optimal solution have
almost the same sum rate, while in the high SNR region, a
gap between both methods is obtained. This gap is increas-
ing with higher NPr values. This is justified by the fact that
starting from a certain value of NPr the system can not sup-
ply the relays with the whole power budget. Hence, more
relays are deactivated. In fact, at high values of NPr , the
−20 −15 −10 −5 0 5 10 15 20 25 300
1
2
3
4
5
6
7
8
9
Pr Peak Power [dBm]
S u m R a
t e ( B i t s / s / H z )
Optimal
GA with N=256
IA with N=256
Best antenna selection
Ith
=10dBm
Ith
=0dBm
Figure 4. Achieved sum rate versus the peak power NP r for the
optimal and the proposed algorithms with M D 2, N D 256 and
different values of I th and L D 4.
−20 −10 0 10 20 30 40
0
2
4
6
8
10
12
Pr Peak Power [dBm]
(a)
S u m R
a t e ( B i t s / s / H z )
Optimal
IA with N=512
IA with N=64
IA with N=16
IA with N=2 (ON−OFF mode)
−20 −10 0 10 20 30 400
2
4
6
8
10
12
Pr Peak Power [dBm]
(b)
S u m R
a t e ( B i t s / s / H z )
Optimal
GA with N=512
GA with N=64
GA with N=16
GA with N=2 (ON−OFF mode)
Figure 5. Achieved sum rate versus the peak power NP r for the
optimal and the proposed algorithms with different values of I th
and N with L D 10, T D 32, and M D 1: (a) iteration algorithm
(IA) and (b) genetic algorithm (GA).
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interference constraint can be affected. For this reason, we
have introduced the discretization set to get more degrees
of freedom by increasing N as such we enhance the SN
sum rate. It should be noted that with the proposed algo-
rithm, when N ! 1, we achieve the performance of the
optimal solution.
To further improve the performance of the system, we
proposed to employ the GA (with T D 32 random ini-
tial strings) to achieve better sum rate than IA but with
more complexity (CPU time) as discussed in Section 4.4.
In the low-SNR region, we can notice in Figure 4 that
both algorithms and the optimal solution have almost the
same sum rate, while in the high SNR region, the benefit of
using GA is clearly observed. Indeed, IA is a deterministic
approach that reaches always the same suboptimal solu-
tion for the same channel realisation while thanks to its
random behaviour, the GA achieves different suboptimal
solutions even for the same channel realisation: it explores
several additional options than IA. In this figure, we com-
pare the performances of the IA and GA with the best
antenna selection. The best antenna selection presented in
[24] attempts to exchange the information between the ter-
minals via the best antenna with the maximum allowed
power that achieves maximum sum rate while respecting
both the interference and peak constraints.
The effect of varying I th for different algorithms with
fixed M D 2 and N D 256 is also shown in Figure 4
where we plot the TWR secondary sum rate versus NPr for
different values of I th D f0,10g, dBm.
Figure 5 shows a comparison between the TWR-CR
network performance of the proposed algorithms and the
optimal solution with continuous power distributions for
−20 −10 0 10 20 30 400
2
4
6
8
10
Pr Peak Power [dBm] Pr Peak Power [dBm]
Pr Peak Power [dBm]
Pr Peak Power [dBm]
(a)
S u m R
a t e ( B i t s / s / H z )
L=6, N=2
−20 −10 0 10 20 30 400
1
2
3
4
5
6
(b)
A v e r a g e A c t i v e R e
l a y s
−20 −10 0 10 20 30 400
2
4
6
8
10
Pr Peak Power [dBm]
(c)
S u m R
a t e ( B i t s
/ s / H z )
L=4, N=8
−20 −10 0 10 20 30 400
1
2
3
4
(d)
A v e r a g e A c t i v e R
e l a y s
−20 −10 0 10 20 30 400
2
4
6
8
10
Pr Peak Power [dBm]
(e)
S u m R
a t e ( B i t s / s / H z )
L=6, N=8
−20 −10 0 10 20 30 400
1
2
3
4
5
6
(f)
A v e r a g e A c t i v e R e l a y s
ES algorithm
GA
IA
Single Relay
Ith
= 20dBm
Ith
= 20dBm
Ith
= 10dBm
Ith
= 10dBm
Ith
= 20dBm
Ith
= 10dBm
Ith
= 10dBm
Ith
= 20dBm
Ith
= 20dBmIth
= 10dBm
Ith
= 10dBm
Ith
= 20dBm
Figure 6. The performance of the exhaustive search (ES) algorithm, the iteration algorithm (IA) and the genetic algorithm (GA) with
different values of I th, L and N versus NP r : (a,c,e) achieved sum rate and (b,d,f) average active relays.
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single antenna case. We plot the achieved secondary sum
rate versus NPr for different values of I th D f10, 20g dBm
and L D 10. For instance, with L D 10, I th D 20 dBm
and N D 64, we were able to improve the achievable
data rate by around 16% going from 8.7 bits/s/Hz to more
than 10 bits/s/Hz by using GA instead of IA when NPr D
30 dBm. We also notice that with the same quantiza-
tion level, GA is able is able to more maintain the same
slope as the optimal solution with continuous power levels
than IA.
The performances of the ES algorithm, IA, GA (with
T D 32) and the single relay selection with discrete Pr i
under TWR-CR network scenario with M D 1 are depicted
in Figure 6. It is worth to mention that we can achieve
higher cognitive sum rate by increasing the relay power
budget for a fixed interference threshold up to a certain
level. This can be justified by the fact that increasing the
relay power budget will amplify the interference power due
unlicensed users. For instance, Figure 6(a) and (b) plot the
cognitive sum rate and the average number of active relays
versus the peak relay power for L D 6 and N D 2. Itis shown that the proposed algorithms achieve almost the
same secondary sum rate of the ES algorithm by powering
−20 −10 0 10 20 30 400
2
4
6
8
10
12
14
16
18
20
Pr Peak Power [dBm]
Pr Peak Power [dBm]
(a)
S u m R
a t e ( B i t s / s / H z )
OWR
TWR
−20 −10 0 10 20 30 400
10
20
30
40
50
60
(b)
S u m R
a t e ( B i t s / s / H z )
Optimal with peak power constraint only
Optimal with interference constraint only
Optimal with peak power and interference constraints
IA with N=256
IA with N=32
IA with N=8
OWR
TWR
Figure 7. Achieved sum rate of the optimal and iteration algo-
rithm (IA) versus NP r with L D 6, I th D 20 dBm for one-way
relaying (OWR) and tow-way relaying (TWR): (a) M D 1 and (b)
M D 4.
almost the same number of relays. However, by increas-
ing N , we notice a degradation of around 0.5 bits/s/Hz of
IA at the secondary sum rate peak comparing to GA and
ES algorithm while the same performance is reached oth-
erwise as shown in Figure 6(c)–(f). However, our proposed
GA maintains the same performance as ES method even for
high values of L and N . Indeed, thanks to its random evo-
lution process, GA provides more chance to find a better
combination than IA. In terms of computational complex-
ity, an important saving mainly for large values of N and
L is obtained comparing to the ES algorithm as detailed in
Section 4.4.
In general, by increasing N , M and L, a degradation of
the performance comparing to the ES method at the peak
of the cognitive sum rate is noticed. This can be explained
by the fact that the number of combinations that accommo-
date the interference constraint is very large in that region
and optimal solutions can be reached with ES, which is not
the case with the proposed heuristic approach. In addition
to the performance achieved by the proposed algorithms,
−20 −10 0 10 20 30 400
2
4
6
8
10
12
14
16
18
20
Pr Peak Power [dBm]
(a)
S u m R
a t e ( B i t s / s / H z )
OWR
TWR
−20 −10 0 10 20 30 400
10
20
30
40
50
60
Pr Peak Power [dBm]
(b)
S u m R
a t e ( B i t s / s / H z )
Optimal with peak power constraint only
Optimal with interference constraint only
Optimal with peak power and interference constraints
GA with N=256
GA with N=32
GA with N=8
OWR
TWR
Figure 8. Achieved sum rate of the optimal and genetic algo-
rithm (GA) versus NP r with L D 6, I th D 20 dBm for one-way
relaying (OWR) and tow-way relaying (TWR): (a) M D 1 and (b)
M D 4.
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an important complexity saving is obtained comparing to
the ES algorithm for TWR transmission as summarised
in Table II.
5.2. OWR transmission versus
TWR transmission
Figures 7 and 8 depict the achieved sum rate of the optimal
and proposed algorithms versus the peak power constraintNPr with L D 6, I th D 20 dBm and different values of
M D f1, 4g for both OWR and TWR transmissions for IA
and GA, respectively. The sum rate of both OWR and TWR
schemes is compared to the case when only one constraint
is applied (either peak power constraint or interference
constraint). It can be shown that the optimal solution with
interference constraint only is an upper bound for the case
when both constraints are considered. It can be seen that,
we can almost double the secondary sum rate by using
TWR transmission instead of using OWR transmission.
In addition to that, OWR transmission requires more rate
computational analysis than TWR transmission. Indeed, itrequires the double number of operations to solve the opti-
mization problem, because it has to execute the algorithm
twice (i.e. every two time slots).
To investigate the effect of the interference caused by
PUs to the SN for OWR and TWR networks, we plot in
Figure 9 the secondary achievable sum rate as a function
of 2n for fixed NPr D 10 dBm, I th D 20 dBm, L D 4 and
M D 2. It is deduced from this figure that when the value
of 2n increases (i.e. the interference from the PUs to SN
increases), the secondary achievable rate reduces. Also, we
notice that the PU interference has no significant impact on
the proposed algorithm performance. Indeed, the gap of the
achieved sum rate between the algorithms and the optimal
solution is maintained even for high values of 2n .
Finally, Figure 10 deals with the effect of an erroneous
CSI on the system performance. We vary the variance of
the CSI error 2e between 0 and 1 (i.e. 2e D 0 corresponds
to the perfect CSI scenario) for both algorithms (IA and
GA). We plot the achievable secondary rate versus the error
variance 2e with the following parameters NPr D 10 dBm,
1 1.5 2 2.5 3 3.5 4
x 10−4
4
5
6
7
8
9
10
11
12
S u m R
a t e
( B i t s / s / H z )
Optimal
GA with N=256
IA with N=256
TWR
OWR
Figure 9. Achieved sum rate using genetic algorithm (GA) and
iteration algorithm (IA) as a function of 2n for NP r D 10 dBm,
I th D 20 dBm, L D 4 and M D 2.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
S u m
R a t e ( B i t s / s / H z )
GA with perfect CSI, σ =0
IA with perfect CSI, σ =0
GA with imperfect CSI
IA with imperfect CSI
TWR
OWR
Figure 10. Achieved sum rate t wo-way relaying (TWR) transmis-
sion using genetic algorithm (GA) and iteration algorithm (IA)
as a function of 2e under imperfect CSI for NP r D 10 dBm,
I th D 10 dBm, L D 3, N D 256 and M D 2.
I th D 10 dBm, L D 3, N D 256 and M D 2. We notice that
the scheme performance is highly affected by the increase
of the CSI error for both algorithms. Indeed, it can be
noticed that for 2e D 0.1, the TWR secondary sum ratedegrades by 27% going from 3.5 Bits/s/Hz to 4.8 Bits/s/Hz
by having imperfect CSI instead of perfect CSI. However,
we can see that TWR network is more affected by the CSI
error than the OWR network. This is because the additional
error observed during the self interference elimination in
Equations (10) and (11).
6. CONCLUSION
In this paper, practical approaches (iterative algorithm and
GA) are designed to maximise the achievable secondary
sum rate by employing a multiple antenna–relay selection
scheme for both OWR-CR and TWR-CR networks withdiscrete power distributions. We have analysed the perfor-
mance of the proposed algorithms and compared them with
the optimal solution using continuous power distributions
and an ES method for discrete power levels. In many sit-
uations, the proposed algorithms are able to reach a close
solution to both optimal schemes with a considerable sav-
ing in terms of computational complexity. In addition to
that, we have showed that thanks to its random evolution,
the GA provides a better performance than the iterative
one. Furthermore, we showed that comparing to the opti-
mal solution, the performance of our proposed algorithms
follow the same behaviour for high primary interference
and erroneous channel state information. In our ongoing
task, we are working on applying continuous power allo-cation algorithm based on the particle swarm optimization
technique to our multi-antenna system model.
ACKNOWLEDGEMENT
The work of M.-S. Alouini was made possible by NPRP
grant #5 250 2 087 from the Qatar National Research
Fund (a member of Qatar Foundation). The statements
made herein are solely the responsibility of the authors.
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REFERENCES
1. Alsharoa A, Ghazzai H, Alouini M-S. A low complex-
ity algorithm for multiple relay selection in two-way
relaying cognitive radio networks. In Proceedings of
the 5th IEEE Workshop on Cooperative and Cogni-
tive Mobile Networks (COCONET’2013) in Conjunction
with IEEE International Conference on Communications
(ICC’2013), Budapest, Hungary, June 2013; 327–331.
2. Alsharoa A, Ghazzai H, Alouini M-S. A genetic algo-
rithm for multiple relay selection in two-way relaying
cognitive radio networks. In IEEE Vehicular Technol-
ogy Conference (VTC Fall’2013), Las Vegas, USA,
September 2013.
3. Mitola J, III, Maguire GQ, Jr. Cognitive radio: making
software radios more personal. IEEE Personal Commu-
nications 1999; 6(4): 13–18.
4. Mitola J, III. Cognitive radio: an integrated agent
architecture for software defined radio. Ph.D. Disserta-
tion, Royal Institute of Technology (KTH), Stockholm,
Sweden, 2000.
5. Haykin S. Cognitive radio: brain-empowered wireless
communications. IEEE Journal on Selected Areas in
Communications 2005; 23(2): 201–220.
6. Kang X, Liang Y-C, Nallanathan A, Garg HK, Zhang R.
Optimal power allocation for fading channels in cogni-
tive radio networks: Ergodic capacity and outage capac-
ity. IEEE Transactions on Wireless Communications
2009; 8(2): 940–950.
7. Zou Y, Yao Y-D, Zheng B. Cooperative relay tech-
niques for cognitive radio systems: Spectrum sensing
and secondary user transmissions. IEEE Communica-tions Magazine 2012; 50(4): 98–103.
8. Zou Y, Zhu J, Zheng B, Yao Y-D. An adaptive coop-
eration diversity scheme with best-relay selection in
cognitive radio networks. IEEE Transactions on Signal
Processing 2010; 58(10): 5438–5445.
9. Hasna MO, Alouini M-S. Optimal power allocation for
relayed transmissions over Rayleigh-fading channels.
IEEE Transactions on Wireless Communications 2004;
3(6): 1999–2004.
10. Hasna MO, Alouini M-S. End-to-end performance of
transmission systems with relays over Rayleigh-fading
channels. IEEE Transactions on Wireless Communica-tions 2003; 2(6): 1126–1131.
11. Kramer G, Gastpar M, Gupta P. Cooperative strate-
gies and capacity theorems for relay networks. IEEE
Transactions on Information Theory 2005; 51(9):
3037–3063.
12. Laneman JN, Tse DNC, Wornell GW. Cooperative
diversity in wireless networks: efficient protocols and
outage behavior. IEEE Transactions on Information
Theory 2004; 50(12): 3062–3080.
13. Rankov B, Wittneben A. Spectral efficient protocols
for half-duplex fading relay channels. IEEE Journal
on Selected Areas in Communications 2007; 25(2):
379–389.
14. Jitvanichphaibool K, Zhang R, Liang Y-C. Optimal
resource allocation for two-way relay-assisted OFDMA.
IEEE Transactions on Vehicular Technology 2009;58(7): 3311–3321.
15. Li L, Zhou X, Xu H, Li GY, Wang D, Soong A. Simpli-
fied relay selection and power allocation in cooperative
cognitive radio systems. IEEE Transactions on Wireless
Communications 2011; 10(1): 33–36.
16. Luo C, Yu FR, Ji H, Leung VCM. Distributed relay
selection and power control in cognitive radio net-
works with cooperative transmission. In Proceedings
of IEEE International Conference on Communications
(ICC’2010), Cape Town, South Africa, May 2010; 1–5.
17. Xu J, Zhang H, Yuan D, Jin Q, Wang C-X. Novel mul-
tiple relay selection schemes in two-hop cognitive relaynetworks. In Proceedings of IEEE 3rd International
Conference on Communications and Mobile Computing
(CMC’2011), Qingdao, China, April 2011; 307–310.
18. Bayat S, Louie RH, Vucetic B, Li Y. Dynamic decen-
tralised algorithms for cognitive radio relay networks
with multiple primary and secondary users utilising
matching theory. Transactions on Emerging Telecommu-
nications Technologies 2013; 24(5): 486–502.
19. Choi M, Park J, Choi S. Low complexity multiple
relay selection scheme for cognitive relay networks. In
Proceedings of IEEE Vehicular Technology Conference
(VTC Fall’2011), San Francisco, USA, 2011; 1–5.20. Naeem M, Lee DC, Pareek U. An efficient multiple
relay selection scheme for cognitive radio systems. In
Proceedings of IEEE International Conference on Com-
munications Workshops (ICC’2010), Cape Town, South
Africa, May 2010; 1–5.
21. Wang B, Zhang J, Host-Madsen A. On the capacity of
MIMO relay channels. IEEE Transactions on Informa-
tion Theory 2005; 51(1): 29–43.
22. Fan Y, Thompson J. MIMO configurations for relay
channels: theory and practice. IEEE Transactions on
Wireless Communications 2007; 6(5): 1774–1786.
23. Cui T, Gao F, Ho T, Nallanathan A. Distributed space-
time coding for two-way wireless relay networks. In
Proceedings IEEE International Conference on Com-
munications (ICC’2008), Beijing, China, May 2008;
3888–3892.
24. Amarasuriya G, Tellambura C, Ardakani M. Two-way
amplify-and-forward multiple-input multiple-output
relay networks with antenna selection. IEEE Journal
on Selected Areas in Communications 2012; 30(8):
1513–1529.
Trans. Emerging Tel. Tech. (2014) © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett
8/11/2019 optimal power allocation in cooperative networks
http://slidepdf.com/reader/full/optimal-power-allocation-in-cooperative-networks 14/14
A. Alsharoa et al.
25. Park H, Chun J, Adve R. Computationally efficient relay
antenna selection for af MIMO two-way relay channels.
IEEE Transactions on Signal Processing 2012; 60 (11):
6091–6097.
26. Taki M, Lahouti F. Discrete rate interfering cogni-
tive link adaptation design with primary link spectral
efficiency provisioning. IEEE Transactions on WirelessCommunications 2011; 10(9): 2929–2939.
27. Lee N, Simeone O, Kang J. The effect of imper-
fect channel knowledge on a MIMO system with
interference. IEEE Transactions on Communications
2012; 60(8): 2221–2229.
28. Boyd S, Vandenberghe L. Convex Optimization.
Cambridge University Press: New York, NY, USA,
2004.
29. Beasley D, Bull DR, Martin RR. An overview of genetic
algorithms: part 2, research topics. University Comput-ing 1993; 15(4): 170–181.
30. Rosen KH. Discrete Mathematics and Its Applications
(6th edn). McGraw-Hill: New York, NY, 2007.
Trans. Emerging Tel. Tech. (2014) © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett