Distributed Relay Beamforming in Cognitive Two-Way Networks: SINR Balancing Approach

doi:10.4236/ijcns.2012.510070

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Int. J. Communications, Network and System Sciences, 2012, 5, 678-683

http://dx.doi.org/10.4236/ijcns.2012.510070 Published Online October 2012 (http://www.SciRP.org/journal/ijcns)

Distributed Relay Beamforming in Cognitive Two-Way

Networks: SINR Balancing Approach

Seyed Hamid Safavi, Mehrdad Ardebilipour

Faculty of Electrical and Computer Engineering, K.N.Toosi University of Technology, Tehran, Iran

Email: [email protected], [email protected]

Received August 16, 2012; revised September 14, 2012; accepted September 24, 2012

ABSTRACT

In this paper, we study the problem of distributed relay beamforming for a bidirectional cognitive relay netwo rk which

consists of two secondary transceive rs and K ognitive relay nodes and a primary network with a transmitter and receiver,

using underlay model. For effective use of spectrum, we propose a Multiple Access Broadcasting (MABC) two-way

relaying scheme for cogn itive networks. The two transceivers transmit their data towards the relays and then relays re-

transmit the processed form of signal towards the receiver. Our aim is to design the beamforming coefficients to maxi-

mize quality of service (QoS) for the secondary network while satisfying tolerable interference constraint for the pri-

mary network. We show that this approach yields a closed-form solution. Our simulation results show that the maxi-

mum achievable SINR improved while the tolerable interference temperature becomes not strict for primary receiver.

Keywords: Cognitive Radio; Two-Way Relay Networks; Beamforming

1. Introduction

With the explosive proliferation of wireless systems, the

demand for radio spectrum has been increasing rapidly.

As a result, the radio spectrum has become a scarce re-

source. Cognitive radio (CR) has recently emerged as a

promising technology to address the need for intelligent

spectrum allocation [1]. In cognitive radio networks, un-

licensed (secondary) users can access the licensed (pri-

mary) spectrum either on non-interference or interference

tolerant basis. There are three main cognitive radio net-

work paradigms: underlay, overlay, and interweave [2].

In the interweave approach, cognitive transmitters are

required to sense the spectrum and transmit signals only

when frequency holes are available. Spectrum holes are

the most obvious opportunities to be exploited by CR,

but higher spectrum utilization is anticipated in overlay

and underlay approaches where coexistence between the

primary user (PU) and secondary users (SUs) is permit-

ted. We have adopted the underlay paradigm due to its

advantages from an implementation viewpoint [3] in this

work. In the underlay approach, the SUs are allowed to

utilize the spectrum of the PU only if the interference

generated by the SUs at the primary receivers is below

some acceptable threshold which is commonly known as

interference temperature [2,4]. This constraint limits the

allowed transmit power of SUs and consequently the

QoS of the secondary network. To address this issue,

cooperation between SUs is a potential way to improve

the secondary network QoS while performance of the

primary network is not affected. A variety of cooperative

strategies have been proposed with different design crite-

ria and assumptions. Among them, distributed beaform-

ing is an efficient technique to enable concurrent trans-

mission of SUs and PUs. Also, in the overlay approach,

the SU shares part of its power resources with the PU to

provide a relay-assisted transmission.

Recently, motivated by cognitive radio and coopera-

tive communications, cognitive relay networks have gai-

ned considerable research interest. As we explained be-

fore, distributed relay beamforming, in which the objec-

tive is to determine the beamforming weights according

to some optimality criterion, have received a lot of atten-

tion in non-cognitive relay networks [5-8]. However, the

literature on cooperativ e relaying techniques such as dis-

tributed relay beamforming with explicit in corpor ation of

cognitive radio concepts is very sparse. Especially, the

use of beamforming in cognitive relay networks is much

more challenging because of the existence of the bidirec-

tional interferences between the primary and secondary

networks. In addition, two-way relaying technique along

with beamforming can further improve the spectrum ef-

ficiency in cognitive relay networks [9,1 0]. Two-way re-

laying scheme can be categorized in three main groups;

i.e. two one way relaying, time division broadcasting

(TDBC) and multiple access broadcasting (MABC). The

MABC approach which is used in this paper, provides a

throughput sign ificantly higher than the other app roaches

S. H. SAFAVI, M. ARDEBILIPOUR 679

and well investigated in [11]. A beamforming technique

has been proposed in [9] to maximize achievable sum

rate in a multi-antenna cognitive two-way relaying net-

work without considering the mutual interference. To the

best of our knowledge, the problem of optimal distrib-

uted beamforming for an u nderlay cognitive two-way re-

lay network has not been well addressed.

In this work, we propose a beamforming approach to

maximize QoS requirements for the secondary network

while satisfying interference temperature constraint for

the primary network in an underlay cognitive two-way

relay network. Our goal is to obtain beamforming coeffi-

cients of the secondary relays as the design parameters,

such that the secondary network QoS measured by the

signal-to-interference-plus-noise ratio (SINR) at the sec-

ondary destination is maximized while interference from

secondary network to primary network is constrainted to

a predefined value.

Throughout this paper, we use the following standard

notations: and



T









diag a

represent the transpose and

the hermitian transpose, respectively. The notation

is a vector which contains the diagonal entries

of the square matrix A and is a diagonal ma-

trix whose diagonal elements are different entries of the

vector a. max and













max represent principal

eigenvalue and eigenvector of matrix A, respectively.

denotes the statistical expectation and I is the

identity matrix.



E

The reminder of paper is organized as follows. In the

next section system model and problem formulation for

cognitive two-way relaying scheme are described. In

Section 3, the SINR balancing under interference con-

straint is developed. Simulation results are given in Sec-

tion 4 and finally, the main results are summarized in

Section 5.

2. System Model

As shown in Figure 1, we consider a set of SUs coexist

and operate in the licenced primary band. The secondary

Figure 1. A Two-way cognitive relay network.

network consists of a pair of source node exchange in-

formation with the assistance of K randomly located re-

lay nodes via MABC two-way relaying scheme. As we

consider the underlay paradigm in the model, the secon-

dary network utilizes the primary network’s spectrum to

transmit its data under a simple two-phase amplify-and-

phase-adjust-and-forward protocol simultaneously with

the primary transmission. It is reasonable for secondary

network that have the full channel state information (CSI)

by a band manager that interpose between the primary

and secondary networks [12].

We denote the channel vector between the n’th





1, 2n



transceiver and the relays by

12nn

nkn

fff

ff f



f

gg g

and channel coefficients between the

primary transmitter and receiver by hp. We also consider

mutual interference between the primary and secondary

networks in this work. Hence 12pp

pkp



de-

note the interference channel vector from PU transmitter

to the relays, while 12pp

pkp







 is the channel

vector between relays and PU receiver. We assume that

the forward channels from each transceiver to the relay

nodes are reciprocal to the backward channels from the

relay nodes to each corresponding transceiver [13]. Also,

a flat fading condition is considered so that the channel

realizations vary independently from one frame to an-

other while they remain fixed within each frame. Any

interference from the secondary transceivers at the pri-

mary receiver in the first time slot as well as interference

from the primary transmitter at the secondary transceiv-

ers in the second time slot is considered as additive white

Gaussian noise (AWGN ) [4] .

g

During the first time slot (multiple access phase), both

transceivers simultaneously transmit their data to the

relays. The received signals in relays from transceivers as

well as interference from PU transmitter can be repre-

sented, in vector form, as



1112 22ppp

PsPsPs



 xfff υ

(1.1)

where x is the



complex vector of the received

signals at the relays, P1, P2 and Pp are the transmit pow-

ers of Transceivers 1, 2 and PU transmitter, respectively.

Let S1, S2 represent the information symbols transmitted

by transceivers 1, 2 and







represent the infor-

mation symbols transmitted by PU transmitter in the first

and second time slot respectively. v is the



com-

plex vector of the relay noises with covariance matrix



In the second time slot (broadcasting phase), the i’th

relay multiplies its received signal by a complex weight

i and transmits the so-obtained signal can be ex-

pressed as



tWx

** *

,,,

ww w

(1.2)







where





W. The received signal in two

S. H. SAFAVI, M. ARDEBILIPOUR

680

transceivers can be written as:





11ppp

s n



fυ



11 1

1111222

PsP sP



fWx

fW ff (1.3)



12ppp

s nfυ

22 2

2111222

PsPsP



fWx

fW ff (1.4)

Using







diagba

diagab , we rewrite (3 ) and (4)



11111

yP s





wFf

2122

111

P s

n

wFf

wFυ (1.5)



21211

yP s





wFf

2222

222

P s

n

wFf

wFυ







(1.6)

where , 11

, diagwW diagFf





diagFf

The noise process is assumed to be zero-mean and spa-

tially white with variance σ2. We will later explain how

each relay can compute its own optimal beamforming

weight. Since the knowledge of f1 and s1 are available at

Transceiver 1, thus transceiver 1 can subtracts the first

term in (5) and manipulate the remaining term to have



111 111

2122 1

desiredsignal interference

yy Ps

PsP





wFf

wFf wFf



   11

noise

s nwFυ

 (1.7)

and similarly



222 222

12112

desiredsignal interference

yy Ps

PsP





wFf

wFf wFf



   22

noise

s nwFυ

 (1.8)

The received signal at the primary receiver can be ex-

pressed as







1112 2 2

noise

desiredsignal

1112

interferencefromsecondaryne

self interference

ppppp p

ppp p

twork

p p

s n





fυ

f wGυ



yPhs n

Phs

PsP sP

Phs n

PsP













gWx

wGf wG

wGf

 



 

(1.9)

3. SINR Balancing

In this section, our goal is to find the beamforming

weight vector W in order to SINR balancing at the sec-

ondary network subject to an interference power con-

straint at the primary network. Mathematically, the opti-

mization problem can be represented as follows





max min,

SINR SINR

SubjecttoP I

w (1.10)

where SINRm is defined as the ratio of the desired signal

power to the interference plus noise power at the m’th

transceiver for m = 1, 2 and PI denotes the interference

power. These parameters can be calculated as follows

1, 2

min

SINR m



 (1.11)







2122221

21221 2

HHH

PEP ss

PEE s



wFf fFw

wFffFw

whhw

wAw



12 21

=hFf Ff

(1.12)

Ahh

 

. where ,











21 1

HHH

ipppp

HHH

ppp p

PEP ss

PEE s



wFf fFw

wFffFw

wkkw



(1.13)

where

KFf.







11 1

HHH

PE En







wFυυ Fw

wF υυ Fw

wDw

111

(1.14)

DFF

, similarly where

















wAw

wLLw

wDw

where

LFf222

DFF

, .



122 1

HHH

SINR P









wAw

wDw wkkw

wAw

wDkkw

wAw

wBw

(1.15)

and similarly

S. H. SAFAVI, M. ARDEBILIPOUR 681



1222

SINR









wDw

wAw

wCw

wLLw

LLw

(1.16)

where



BDkk

CD LL















Using (9) so the interference component power which

consists of secondary network interference and self in-

terference can be written as



 



 





1 1111

22222

HHH

Ipp

HHH

ppppp

HH H

PEPss

EP ss

PEsP

PEs











wGffGw

wGυυ Gw

wGffGw

wUUw wY

wZZw wG

wQw









2 2

H H





υυ Gw





(1.17)

where











UGf

YGf

ZGf

and

HH H



Z GG

NR SINR

PPPQUU YYZ (1.18)

Note that at the optimum, it is required that

SI (1.19)

Otherwise, if, for example, SINR1 > SINR2, then P2

can be reduced such that SINR1 = SINR2 and this reduc-

tion of P2 will not violate the power constraint. Using (15)

and (19) the optimization problem (10) can be written as

Hth







wAw

wBw

wQw

max

(1.20)

to solve (20), let us write the weight vector w as

I

















(1.21)

then we can rewrite the optimization problem as

max

.. 1,

StI I







wAw

wBw











(1.22)

It is easy to show that the inequality constraint in (22)

will be satisfied with equality at the optimum. As the

objective function in (22) is monotonically increasing in

I, for any value of w, this objective function is maxi-

mized for I - Ith.

max

.. 1

th H







wAw

wBw

















BIA





(1.23)

It is obvious that the optimization problem (23) is in

the form of Rayleigh-Ritz ratio, in which objective func-

tion is globally maximized when WH chosen as the con-

stant factor of the principal eigenvector of the matrix





max th





wBIA



 (1.24)

as a result, the beamforming weight vector can be written





12 max

1212 21212







 





QBQIQAQ (1.25)

and the maximum achievable SINR can be expressed as





max 2

1212 21212

max

SINRP I





 



QBQIQAQ (1.26)

As the level of interference temperature can be esti-

mated at the secondary network [2] and we assume that

the secondary network have full CSI, optimal beam-

forming coefficient in each relay can be calculated from

(25).

4. Simulation Results

In our simulation results we consider a secondary net-

work with K = 20, 30, 40 relay nodes, and the channel

coefficients are generated independently as complex

Gaussian random variables with unit variance in each

simulation run. All noise powers including relay noises,

secondary and primary receiver noises is assumed to be 0

dBW. Throughout our numerical examples, the transmit

power of transceivers and PU is also considered to be

equal to 0 dBW. The average value of each quantity is

obtained by averaging the corresponding quantity over

104 simulation runs.

Figure 2 illustrates the average values of the maxi-

S. H. SAFAVI, M. ARDEBILIPOUR

682

mum achievable SINRs versus the maximum interfer-

ence power that primary receiver can tolerate for three

different values of K. As can be seen from this figure, as

we increase K, the maximum achievable SINRs increase.

The achieved improvement from 30 relays to 40 has be-

come lower than the improvement of 20 to 30.

Figure 3 shows the average values of the relay trans-

mit power for three different values of K. It is reasonable

that, as we increase the number of relays, total power

dissipated in the relays doesn’t change considerably for

fixed tolerable interference. However because of the

beamforming effect and phase compensation, SINR of

each transceiver’s is improved.

Figure 4 illustrates the average values of the maxi-

mum achievable SINRs versus the maximum interfer-

ence power that primary receiver can tolerate for 30 re-

lays and two different scenarios: 1) 12

and 2) . As can be seen from this figur e ,

==0dB



==3d



B

Figure 2. The average values of the maximum achievable

SINRs versus the interference temperature for three dif-

ferent values of K.

Figure 3. Total relay Power dissipated in the network ver-

sus the interference temperature for three different values

of K.

Figure 4. The average values of the maximum achievable

SINRs versus the interference temperature for two different

scenarios; 1) ; 2) .

==0 dB

σσ 22

==3 dB

σσ

by increasing the interference temperature and improving

the quality of secondary channels, SINR improvement

decreases. Because the interference constraint become

strict.

5. Conclusion

In this paper, we developed the distributed relay beam-

forming for an underlay bidirectional cognitive network

which consists of two transceivers and K relay nodes

between them all equipped with single-antenna in the

presence of primary network. For effective use of spec-

trum, MABC two-way relaying which needs two time

slots to swap two symbols between the two transceivers

proposed for cognitive networks. We study SINR balanc-

ing technique where the smaller of the two transceiver

SINRs is maximized while keeping the interference

power below interference temperature. We herein have

shown that this approach leads to a closed-form solution.

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