A Cooperative Relay Scheme for Secondary Communication in Cognitive Radio Networks.

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A Cooperative Relay Scheme for Secondary
Communication in Cognitive Radio Networks
Xiaowen Gong, Wei Yuan, Wei Liu, Wenqing Cheng, Shu Wang
Department of Electronics and Information Engineering
Huazhong University of Science and Technology, Wuhan 430074, P.R.China
xwgong87@gmail.com
Abstract—In cognitive radio networks, secondary users (SUs)
opportunistically exploit the spectrum unutilized by primary
users (PUs). In this paper, we study the secondary communi-
cation where secondary transmitters and receivers have different
available spectrum. Considering the spectrum diversity and the
space distance between different PUs, we introduce cognitive
relay node into the secondary communication and propose a
novel Cooperative Relay Scheme (CRS) to increase the SINR
at secondary receivers. A novel Opportunistic Sharing Scheme
(OSS) is also proposed for the secondary transmitters to share
the spectrum of relay nodes. We model it with a non-cooperative
game, and study the performance of competition of SUs. The
Nash equilibrium and Pareto efficiency of this game is presented.
Simulations show that CRS can increase SINR at secondary
receivers under proper configurations.
I. INTRODUCTION
Cognitive radio is recently considered as a promising tech-
nology to improve spectrum utilization in wireless communica-
tion. Secondary users (SUs) detect spectrum holes [1] in their
radio environment for secondary communication. In cognitive
radio networks, each primary user (PU) uses licensed spectrum
within a geographic area [2]. However, PUs are not utilizing
the spectrum fully, which leave the spectrum too much space
idle. Such underutilization of spectrum gives SUs opportunity
to access the idle spectrum for secondary communication.
Since each PU acts independently, the spectrum utilization
is stationary in the entire area of one PU, but it varies for
different PUs, namely the spectrum availability for SUs varies
in different areas of PUs. Research works discussing secondary
communication are mainly under the assumption that transmit-
ters and receivers have the same available spectrum, or only
the common part of their available spectrum is utilized [2] and
[3].
In this paper, we study the secondary communication where
transmitters and receivers are located in different areas of
PUs with different available spectrum. We focus on how to
exploit the different part of their available spectrum so as to
increase spectrum utilization. This is a challenging issue that
has seldom been studied. We use power control as an efficient
way to improve spectrum reuse. SUs limit their transmit power
so as to coexist with PUs in the same spectrum [2]. A general
scheme of power control is discussed, where the transmitter
controls its power to satisfy the interference power constraint
(IPC) [6] [10] predefined by the PU. However, the SINR
obtained in this scheme is low due to the tight constraint of
the IPC.
Cooperative communication exploits the spatial diversity
inherent in multi-user systems by allowing users relay each
other’s data to the destination [4]. We carefully note that our
focused transmitter and receiver not only have difference in
available spectrum, but also have distance in space. In order
to make efficient use of such diversity in both spectrum and
space, we propose a novel cooperative relay scheme (CRS).
We introduce a cooperative node to relay the data from the
transmitter to the receiver with different available spectrum.
This novel scheme is proved to increase the SINR considerably
compared to the general scheme. To the best of our knowledge,
we are the first to combine power control and cooperative
communication in studying secondary communication.
Besides spectrum sharing between PUs and SUs, there also
exists spectrum sharing among SUs. Thus a general scenario of
the proposed CRS is studied. A general scheme of secondary
spectrum sharing critically reduces the SINR. To make the best
use of CRS, we present a novel opportunistic sharing scheme
(OSS), with which SUs obtain the maximized SINR while
compete for the limited bandwidth of the shared spectrum.
Considering the selfish but rational nature of each SU, we
formulate the problem as a non-cooperative game. We define
the bandwidth and the channel capacity of a SU as its strategy
and utility function respectively. Then we study our game by
analyzing its properties including Nash equilibrium and Pareto
efficiency.
The main contributions of this paper are concluded as
follows:
1) A novel cooperative relay scheme is proposed to improve
spectrum utilization and increase the SINR of secondary
communication.
2) A novel opportunistic sharing scheme is presented to
secondary spectrum sharing on relay nodes, and studied
through a game theoretical approach.
The rest of this paper is organized as follows. In section II,
we propose our cooperative relay scheme. In section III, we
study the secondary spectrum sharing issse. Numerical results
are presented in section IV, and this paper is concluded in
section V.
II. COOPERATIVE RELAY SCHEME
A. System Model
We focus on the communication among the secondary users
with different available spectrum. One simple scenario is
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indicated in Fig.1. There are two PUs Ua and Ub with the
effective communication areas denoted by a and b. Two SUs
s and d are located in a and b respectively. The whole channel
set is represented by I, while the subset of I available to s and
d are denoted as Iaand Ib. The idle channel set in a but busy
in b is denoted as Ia−b= Ia− Ib, and the channel set idle in
b but busy in a is Ib−a. We assume that none of the sets is
empty, and the SUs can sense the spectrum and distribute their
Channel State Information (CSI) of the sets to each other.
ba
m
n
a b
I?
a b
I?
b a
I?
a b
I?
b a
I?
r
Cooperative Relay Scheme
Non-Cooperative Scheme
Power Interference
b B
a B
s
d
b
U
a
U
Fig. 1.
nication
Typical scenario of cooperative relay scheme in secondary commu-
The general principle of cognitive radio is that, SUs are
allowed to communicate without interference to PUs. Most
of current researches in spectrum sharing [2] [3] follow this
principle and study the system under the constraint of Inter-
ference Power Constraint (IPC) to PUs. However, if SUs are
geographically distributed with various available spectrum, the
direct deployment of this principle may not be a good choice.
Take the secondary communication from s to d as an example.
s can only use the channels in Ia−b, and must control its
power to satisfy the IPC in b. It is obvious that the spectrum
bandwidth of sender s will be smaller and the SINR of receiver
d will be lower.
B. Cooperative Relay Scheme
Motivated by the recent progresses in cooperative commu-
nication [4], we introduce relay nodes to exploit the spatial
diversity in secondary communication. In our proposed Co-
operative Relay Scheme (CRS), the data from source SUs
will be forwarded to the geographically distributed destination
SUs. For the convenience in comparison, we name the directly
secondary communication scheme described above as Non-
Cooperative Scheme (NCS).
As shown in Fig.1, a cognitive relay node r is located be-
tween the areas of a and b. Take the secondary communication
from s to d as an example, CRS will have following steps:
• s transmits data to r with Ia−bunder the IPC constraint
in a;
• r receives data from s with Ia−b;
• r forwards data to d with Ib−aunder the IPC constraint
in b;
• d receives data from r with Ib−a.
Compared to NCS, the cooperative relay node r in CRS will
improve the received SINR at d. Since r is closer to s than d,
r receives a higher power from s than d. After the working
channels are switched from Ia−bto Ib−a, the forward power
of r is constrained by the IPC in b, and no longer constrained
by the IPC in a. Then if r is closer to b than to a, the received
power at d is not tightly constrained as before. In conclusion,
the proposed CRS not only improves spectrum utilization via
spacial cooperation, but also increases the SINR.
C. Performance Analysis
In order to investigate the general performance of proposed
CRS, we adopt a framework to formulate the power control
issues in CRS. As shown in Fig.1, two measurement points m
and n are deployed to monitor the interference power on the
busy channels in b and a respectively. m(or n) is located on
the boundary of b (or a) with the shortest distance to a (or b).
For simplism, we assume r, m and n are located in one line.
In this way, they can detect the strongest interference power
at their respective locations. This framework is also adopted
in our previous work [6], where interference power threshold
(IPT) is the highest interference power tolerable for a PU. As
long as the IPTs set on m and n are not violated, the IPC is
satisfied in the entire areas of a and b.
Following assumptions and notations are adopted for anal-
ysis: The noises at r and d are white noises adding the
interferences from the PUs and other SUs that access the same
channels. We assume that the noise power is the same at r and
d in NCS and CRS, and denote it as σ2. The transmit power
of node j is denoted as pj and the link gain between node j
and node k is denoted as hjk. The IPTs set on n and m are
Taand Tb.
At first, we consider the case of NCS. The IPT in b and the
SINR at d can be given as:
pshsm≤ Tb
(1)
SINR =pshsd
σ2
≤Tbhsd
σ2hsm
(2)
Then, we consider the case of CRS. The received SINR from
s to d will be the smaller one in the two phrases of cooperative
relaying. An Effective SINR (SINRe) is defined to describe
the SINR in CRS. It is the minimum of the received SINR at
r and d.
SINRe= min(SINRr,SINRd)
(3)
where SINRrand SINRdcan be given as:
SINRr=pshsr
σ2
≤Tbhsr
σ2hsm
(4)
SINRd=prhrd
σ2
≤Tahrd
σ2hrn
(5)
According to the simple path loss model in [6], link gain
is a strictly decreasing function of the distance between the
transmitter and the receiver, so following inequations are
satisfied in our scenario of Fig.1:
hsm> hsd,hsr> hsd,hrd> hrn
(6)
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We compare the performance of SINRr and SINRd by
relaxing the IPT conditions. The IPT condition at n is given as
prhrn≤ Ta. We assume the IPTs set on m and n are the same
(Ta= Tb) to simplify the problem (we will discuss it later).
When the transmit powers of s and r are maximized, namely
the equalities in IPT condition hold in (1). We can obtain
SINRr=Tbhsr
σ2hsm
>Tbhsd
σ2hsm
(7)
SINRd=Tahrd
σ2hrn
>Ta
σ2=Tb
σ2>Tbhsd
σ2hsm
(8)
Combining with (2) and (3), we can get
SINRe> SINR
(9)
which indicates that CRS outperforms NCS in the performance
of communication quality at received node.
D. Discussion
The performance of CRS is closely related to two issues,
the location of r and the IPT conditions of Taand Tb.
An appropriate selection of r guarantees a better perfor-
mance of CRS than NCS. The discussion of best location of
relay node is so complex and out of the scope of this paper.
Here we focus our study with the relay architecture as well as
the resource sharing issue. In the subsection above, we assume
that r is located on the line of m and n for simplism. In fact,
this assumption can be relaxed a little. As long as r located
between a and b and close to b, the inequations of (6) will
hold and a higher SINR of CRS than NCS is guaranteed. If
the distance between node i and j is denoted as Lij, then the
conditions are Lsd> Lsr and Lrn> Lrd. In section V, we
will show the influence of r’s location to effective SINR with
detailed numerical results.
The performance of CRS is also related to Taand Tb, either
of which is the constraint of effective SINR. If Ta is too
small compared to Tb, the advantage of CRS over NCS is
highly degraded. When Ta≥ Tbis satisfied, the advantage of
CRS over NCS is evident. We will show such influence with
numerical results in section IV.
III. COOPERATIVE RELAY SCHEME WITH SECONDARY
SPECTRUM SHARING
In section II, we study a typical scenario of the proposed
CRS, where only one pair of SUs uses CRS. In this section, we
extend our study to a general scenario of CRS. As shown in
Fig.2, there are N SUs S = {s1,s2,...,sN} in a transmitting
data to their intended SUs D = {d1,d2,...,dN} in b by using
CRS simultaneously. They share the idle channels in Ia−b
and Ib−a, and they cooperate with nodes R = {r1,r2,...,rN}
respectively. We assume that all the cooperative nodes are at
the same location to simplify the problem.
ba
m
n
R
Cooperative Relay Scheme
Power Interference
1s
1d
id
is
Ns
N
d
???
???
???
???
Fig. 2.General scenario of cooperative relay scheme
A. Deterministic Sharing scheme
In a general scheme of secondary spectrum sharing, which is
used in prevalent research works such as [2], [3], [6] and [10],
each SU accesses all the shared channels at the same time.
Since all the SUs choose the same set of channels to access,
we call it deterministic sharing scheme (DSS) for convenience.
We study the performance of CRS with this general scheme.
The IPT is not violated at m is given as
N
?
i=1
psihsim≤ Tb
(10)
Thus the SINR at riis
SINRri=
psihsiri
σ2+?N
j=1,j?=ipsjhsjri
(11)
The IPT is not violated at n is given as
N
?
i=1
pridihrin≤ Ta
(12)
Thus the SINR at diis
SINRdi=
prihridi
σ2+?N
j=1,j?=iprjhrjdi
(13)
When comparing (11) and (13) to (4) and (5) respectively,
we note that each node’s power is forced to critically decrease,
and nodes generate considerable interference to each other. As
a result, each SU’s SINR is critically reduced.
B. Opportunistic Sharing Scheme
SUs use CRS to increase the SINR, but the performance
of CRS is highly degraded with the general DSS. Therefore
we propose a novel opportunistic sharing scheme (OSS) to
make the best use of CRS. It is a distributed and opportunistic
scheme where each shared channel is accessed by at most one
SU.
For each siand ri, it is given as:
• siopportunistically accesses the channels in Ia−bthat are
not accessed by any other sj;
• riopportunistically accesses the channels in Ib−athat are
not accessed by any other rj;
In Fig.3, we demonstrate OSS and DSS by indicating each
si’s transmission bandwidth and the detected power at m. We
denote the total spectrum bandwidth of the channels in Ia−b
and Ib−aas Wa−band Wb−arespectively.
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bT
bT
a b
W?
a b
W?
1s
2s
1
Ns
?
N s
1s
2s
1
Ns
?
N s
???
???
Opportunistic Sharing SchemeDeterministic Sharing Scheme
Detected
Power at m
Transmission
Bandwidth
00
Detected
Power at m
Transmission
Bandwidth
Fig. 3.Deterministic sharing scheme and opportunistic sharing scheme
We can see from Fig.3 that with OSS, each SU’s available
bandwidth decreases while its SINR equals that in the typical
scenario of CRS. Thus OSS can maximize the performance
of CRS in the general scenario. Note that Fig.3 is only used
for conceptional demonstration on our motivation, it may not
work in some wireless scenarios.
C. Game Model
With the proposed OSS, each SU’s SINR can be maximized
at the cost of bandwidth decrease. As a result, each SU has the
incentive to obtain larger bandwidth from the shared channels
to achieve higher throughput. On one hand, each SU wants
to access more channels or channels with larger bandwidth,
namely to selfishly maximize its own benefit; on the other
hand, each SU rationally avoids accessing the channels used
by others, namely to be affected by others’ actions. In a
word, each SU competes with other SUs to exploit the limited
bandwidth of the shared channels. Thus game theory is suitable
to investigate it.
We give the following notations:
• bsi: the transmit bandwidth of si;
• bri: the forward bandwidth of ri;
• cri: the channel capacity between siand ri;
• cdi: the channel capacity between riand di;
• csi: the channel capacity between siand di;
Let G = [S,{BS,BR},C] denotes a non-cooperative game,
where S = {s1,s2,...,sN} denotes the set of players. BS =
{bs1,bs2,...,bsN} and BR = {br1,br2,...,brN} denote the
strategy of players. C = {cs1,cs2,...,csN} denotes the utility
of players.
The total bandwidth of the shared channels is limited is
given as
N
?
and
N
?
With OSS, each SU’s SINR is maximized. According to (4)
and (5), we have
i=1
bsi≤ Wa−b
(14)
i=1
bri≤ Wb−a
(15)
SINRri=psihsiri
σ2
=Tbhsiri
σ2hsim,∀i ∈ N
(16)
and
SINRdi=prihri
σ2
=Tahridi
σ2hrin,∀i ∈ N
(17)
Thus we have
cri= bsilog(1 + SINRri) = bsilog(1 +Tbhsiri
σ2hsim)
(18)
and
cdi= brilog(1 + SINRdi) = brilog(1 +Tahridi
σ2hrin)
(19)
As referred in [5], the channel capacity between siand di
is determined by the minimum of the two hops, which is
csi= min(cri,cdi)
(20)
D. Nash Equilibrium
We use Nash equilibrium to analyze the stability of our
game. The outcome of a game is a Nash equilibrium if none
of the players has the incentive to change its strategy, which
is the best strategy for it given other player’s strategies [7].
Theorem 1: An outcome of the game is a Nash equilibrium
if and only if one of the following three conditions is satisfied.
N
?
N
?
i=1
bsi= Wa−band
N
?
N
?
i=1
bri< Wb−aand cri≤ cdi,∀i ∈ N
(21)
i=1
bsi< Wa−band
i=1
bri= Wb−aand cri≥ cdi,∀i ∈ N
(22)
N
?
i=1
bsi= Wa−band
N
?
i=1
bri= Wb−a
(23)
Proof: Let us prove (21). For any si who wants to uni-
laterally increase csi, it should increase cribecause of (20)
and cri≤ cdi. We also know from?N
can’t increase. The proofs of (22) and (23) are similar to that
of (21). In conditions other than (21), (22) and (23), there
must exist some sithat can increase bsior brito increase csi
without violating the IPT.
In a Nash equilibrium, none of the SUs can improve its
channel capacity by unilaterally changing its transmission
bandwidth. Therefore, a Nash equilibrium is a stable outcome
of the game.
We use Pareto efficiency to characterize the goodness of a
Nash equilibrium. The outcome of a game is Pareto-efficient
if no other outcome makes every player at least equally as
well off and at least one player strictly better off [7]. So a
Pareto-efficient outcome must be a Nash equilibrium.
Theorem 2: A Nash equilibrium of the game is Pareto-
efficient if and only if the following condition is not satisfied.
i=1bsi= Wa−b that
bsireaches the limit and can’t increase. Therefore criand csi
N ?
∃i,j ∈ N that cri< cdiand crj> cdj
i=1bsi= Wa−band
N ?
i=1bri= Wb−aand
(24)
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Proof: Assume that (24) is satisfied. Then as long as
cri≤ cdiis guaranteed, si can decrease briwhile keeps
csiunchanged. Therefore, sj can increase brjunder the total
bandwidth limit, so csjis increased. In conditions other than
(24), any si has to increase bsior briso as to increase csi.
However, under the total bandwidth limit, there must exist
some sj to decrease bsjor brj, which results in decrease in
csj.
In a Pareto-efficient outcome, none of the SUs can increase
its channel capacity without decrease of any other SU’s chan-
nel capacity. Thus a Pareto-efficient outcome is a preferred
Nash equilibrium.
A Pareto-efficient outcome may not be social optimal. The
social optimal outcome is the optimal outcome for system
utility, which is the total utilities of all the players [8]. So
in our game it is given as
{BS,BR}social= argmax
N
?
i=1
csi
(25)
Therefore, the social optimal outcome of our game is
desirable in that it makes the most efficient use of the limited
spectrum to maximize the total channel capacity of all the SUs.
IV. NUMERICAL RESULTS
In this section, we present the numerical results to study
the performance of CRS. The simulation scenario is shown in
Fig.4. The area a and b are two circles with centers at (-150,
0) and (150, 0) and the same radius of 50. The measurement
points m and n are on the boundary of a and b at (-100, 0)
and (100, 0) respectively. Three secondary transmitters s1, s2
and s3 are located at (170, 30), (120, 25) and (155, -30); their
respective secondary receivers d1, d2 and d3 are located at
(-170, 30), (-140, -20) and (-110, -10). Meter is the unit of
distance here.
The noise power is σ2= 10−9W and the interference power
thresholds are Ta= Tb= 10−8W. The link gain is obtained
from the simple path model h = K/L4, where K is set to
be 10−6and L is the distance between the transmitter and the
receiver. We set Wa−b= Wb−a= 106Hz.
−200 −150−100 −500 50100150 200
−100
−50
0
50
100
X axis
Y axis
mnr
s1 d1
s2
d2
s3
d3
ab
Fig. 4.System model in simulation
−100 −80−60
X−coordinate of r
s2 − d2
−40−200
0
20
40
s1 − d1
Effective SINR
NCSCRS
−100 −80 −60
X−coordinate of r
s3 − d3
−40 −200
0
20
40
Effective SINR
NCSCRS
−100 −80−60
X−coordinate of r
−40−200
0
20
40
Effective SINR
NCS CRS
Fig. 5.Effective SINR with different locations of r
0 0.51 1.52
x 10
−8
0
20
40
s1 − d1
IPT at n
s2 − d2
Effective SINR
NCSCRS
0 0.51 1.52
x 10
−8
0
20
40
IPT at n
s3 − d3
Effective SINR
NCS CRS
0 0.51 1.52
x 10
−8
0
20
40
IPT at n
Effective SINR
NCS CRS
Fig. 6.Effective SINR with different IPTs at n
A. Effective SINR of CRS under different configurations
We first investigate the performance of CRS under different
configurations when each pair of SUs uses CRS alone. The
performance results of Effective SINR of CRS in various
location of relay node are shown in Fig.5, while those result
in various IPT conditions are shown in Fig.6.
Fig.5 shows the effective SINR at each secondary receiver
compared to that of NCS when r’s Y-coordinate is fixed at
0 and r’s X-coordinate changes from -100 to 0. When r is
approaching too close to m or n, the SINR decreases, even be
lower than that of NCS. When r is located in proper locations,
as specified by Lsd> Lsrand Lrn> Lrd, the SINR increase
from NCS to CRS is evident. Since the SUs have different
locations, their optimal locations of r are different.
Fig.6 shows the effective SINR at each secondary receiver
compared to that of NCS, when Tbis fixed at 10−8W and Ta
(IPT at n) increases from 0W to 2×10−8W. We fix r at (-50,
0). The effective SINR first increases linearly with Taand then
holds constant, which indicates that the constraint of effective
SINR changes from Tato Tb. The turning points of the three
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
978-1-4244-2324-8/08/$25.00 © 2008 IEEE.