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
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
C
opyright © 2012 SciRes. IJCNS

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

H


ag

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

A

di

A


 A
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

=T
transceiver and the relays by
12nn
nkn
f
fff
=T ff f

f
=T 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

1
1112 22ppp
PsPsPs

 xfff υ
1
(1.1)
where x is the
K

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

1
p


2
p
s
,
s
represent the infor-
mation symbols transmitted by PU transmitter in the first
and second time slot respectively. v is the
K
1

com-
plex vector of the relay noises with covariance matrix
2

I
*
w
.
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
** *
12
,,,
k
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
T
T
yn
PsP sP


fWx
fW ff (1.3)


12ppp
s nfυ
22 2
2111222
T
T
yn
PsPsP


fWx
fW ff (1.4)
Using



=T diagba
T
diagab , we rewrite (3 ) and (4)
as

11111
1
H
pp
yP s
Ps


wFf
wFf
2122
111
HH
H
p
P s
n
wFf
wFυ (1.5)

21211
1
H
pp
yP s
Ps


wFf
wFf
2222
222
HH
H
p
P s
n
wFf
wFυ

H


(1.6)
where , 11 , diagwW diagFf


diagFf
22
.
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
1
2122 1
desiredsignal interference
H
HH
pp
yy Ps
PsP


wFf
wFf wFf

   11
noise
H
p
s nwFυ
 (1.7)
and similarly

222 222
1
12112
desiredsignal interference
H
HH
pp
yy Ps
PsP


wFf
wFf wFf

   22
noise
H
p
s nwFυ
 (1.8)
The received signal at the primary receiver can be ex-
pressed as







2
2
1112 2 2
2
noise
desiredsignal
1112
interferencefromsecondaryne
1
self interference
T
ppppp p
T
ppp p
pp
ppp p
HH
1
22
twork
p p
H
p
pp
s n
s


fυ
f wGυ

H
pp pp
yPhs n
Phs
PsP sP
Phs n
PsP
Ps






gWx
gW
ff
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


12
max min,
I
th
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
m
mm
s
min
P
SINR m
PP

 (1.11)




1
*
2122221
2
21221 2
1
2
2
HHH
s
HHH
HH
H
PEP ss
PEE s
P
P





wFf fFw
wFffFw
whhw
wAw

12 21
=hFf Ff
(1.12)
H
Ahh
 
. where ,





*
1
11
21 1
2
1
11
1
2
HHH
ipppp
HHH
ppp p
HH
PEP ss
PEE s
P




wFf fFw
wFffFw
wkkw

1
(1.13)
where
p
KFf.




1
2
11 1
2
11
22
1
HHH
n
HHH
H
PE En
E





wFυυ Fw
wF υυ Fw
wDw
111
(1.14)
H
DFF
2
2
2
1
22
2
H
s
HH
ip
H
n
PP
PP
P
, similarly where









wAw
wLLw
wDw
2
where
p
LFf222
H
DFF
, .

2
122 1
2
22
1
2
2
H
HHH
p
H
HH
p
H
H
P
SINR P
P
P
P






wAw
wDw wkkw
wAw
wDkkw
wAw
wBw
(1.15)
and similarly

S. H. SAFAVI, M. ARDEBILIPOUR 681

1
1222
1
22
2
1
2
H
H
H
H
H
P
SINR
P
P






wA
wDw
wA
wD
wAw
wCw
HH
H
p
H
p
P
P
w
wLLw
w
LLw
21
22
(1.16)
where
H
p
H
p
P
P


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
11
22
2
11
2
1
1
HHH
Ipp
HHH
pp
HHH
pp
HH
ppppp
HH H
HH H
pp
H
PEPss
EP ss
E
EP ss
PEsP
PEs







wGffGw
wGffGw
wGυυ Gw
wGffGw
wUUw wY
wZZw wG
wQw




2
2
2 2
11
H
H
H H
pp
Es
E


Yw
υυ Gw


1
2
p
p
(1.17)
where
p
p





UGf
YGf
ZGf
2
and
12
H
HH H
p
pp
 Z GG
12
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
2
2
H
H
Hth
P
I
 

wAw
wBw
wQw
max
.. St
(1.20)
to solve (20), let us write the weight vector w as
1
2
1
th
H
I 

wQ w
ww







(1.21)
then we can rewrite the optimization problem as
2
2
2
max
.. 1,
H
H
th
PI
I
StI I
 

wAw
wBw
w





(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.
2
2
2
max
.. 1
H
th H
th
PI
I
St
 

wAw
wBw
w






1
2
th
I 

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
.


1
2
max th
I 

wBIA
 
 (1.24)
as a result, the beamforming weight vector can be written
as


12 max
1
1212 21212
th
th
I
I




 


wQ
QBQIQAQ (1.25)
and the maximum achievable SINR can be expressed as


max 2
1
1212 21212
max
th
th
SINRP I
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
ff
and 2) . As can be seen from this figur e ,
22
==0dB 
22
12
==3d
ff
 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) .
22
12
==0 dB
ff
σσ 22
12
==3 dB
ff
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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