optimal power allocation in cooperative networks

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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

Copyright © 2014 John Wiley & Sons, Ltd.



A. Alsharoa et al.

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)

Trans. Emerging Tel. Tech. (2014) © 2014 John Wiley & Sons, Ltd.DOI: 10.1002/ett



A. Alsharoa et al.

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


QA1. H / D

LXiD1


QA2. H / D

LXiD1


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)




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)




A. Alsharoa et al.

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)




A. Alsharoa et al.

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.




A. Alsharoa et al.

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.




A. Alsharoa et al.

−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


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)


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).




A. Alsharoa et al.

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.




A. Alsharoa et al.

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.




A. Alsharoa et al.

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.




A. Alsharoa et al.

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