Game Theory-Based Channel Allocation in Cognitive Radio Networks

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Game Theory-Based Channel Allocation in
Cognitive Radio Networks
Vani Shrivastav, Sanjay K. Dhurandher
CAITFS, Division of Information Technology
NSIT, University of Delhi, Delhi, India
E-mails: {shriv40, dhurandher}@gmail.com
Isaac Woungang
Department of Computer Science
Ryerson University, Toronto, ON., Canada
E-mail: woungang@scs.ryerson.ca
Vinesh Kumar
SC & SS, Jawaharlal Nehru University
Delhi, India
E-mail: vineshteotia@gmail.com
Joel J.P.C. Rodrigues
Instituto de Telecomunicac¸ ˜
oes, University of Beira Interior, Covilh˜
a, Portugal &
King Saud University, Riyadh, Saudi Arabia
E-mail: joeljr@ieee.org
Abstract—Cognitive radio is an optimistic technology to
implement the concept of dynamic spectrum access and provide
a flexible way to share the spectrum among the primary and
secondary users. In this paper, a game theoretic-based model is
presented using the concept of Nash Equilibrium for spectrum
sharing. In this model, interference and number of radios on
each link are considered as parameters for designing the game.
An algorithm for channel allocation among the users is also
presented. From the simulation analysis, it is observed that the
system performs satisfactorily in terms of network utilization.
Also, the Taguichi method is applied and an analysis of variance
(ANOVA) is performed, proving that the design parameters
taken into consideration in our proposed method are impactful.
Index Terms - Cognitive radio networks, Signal to Interference
plus Noise Ratio, Game theory, Nash Equilibrium, primary user,
secondary user.
I. INTRODUCTION
The spectrum being a scarce resource, its usage is generally
characterized by the fixed spectrum assignment policy, which
has proved to be a huge failure due to the sporadic and
geographically varied inefficient usage. This has motivated the
need to develop new networking paradigms including cognitive
radio networks (CRNs) [1]. Efficiently utilizing the spectrum
means opportunistically accessing the licensed band without
interfering with the existing users. This may impose a range of
quality of service (QoS) challenges due to the wide availability
of the spectrum. But, cognitive radios (CRs) operate in the best
available channel [1], thus facilitating the opportunistic access
to the licensed spectrum. They also enable the usage of the
temporary unused spectrum band (called spectrum hole) or
white space [2].
In a CRN, the CR periodically scans the spectrum so that the
SU can use the idle channel to communicate after estimating
the co-channel interference. There are several other parameters
that play a major role in enabling the SU to choose the best
channels out of available channels for efficient communication.
This selection of channel is considered as fruitful when a
complete transmission among the SUs occurs without any
interference to the primary users (PU) [3], leading to the so-
called spectrum sharing [1].
In this paper, the focus is on designing a channel allocation
method that can improve the CRN utilization. It is assumed
that the cognitive user can acquire the information about the
co-channel interference by performing a channel overhearing.
The number of radios per channel is also considered as design
parameter. Based on these two factors, the SUs may change
their selected channels to achieve a better utilization. Through
simulations, it is shown that the evaluation of this utility
function by each SU each time enables a better solution
in terms of bandwidth allocation. It is also shown that the
proposed game theory-based channel allocation scheme can
achieve the Nash Equilibrium (NE). In a NE, no user can
maximize its utility by changing its strategy unilaterally.
The rest of the paper is organized as follows. Section II
discusses some related work. In Section III, the proposed chan-
nel allocation model is described. In Section IV, simulation
results are presented, followed in Section V by some statistical
analysis using the Taguchi method [4]. Section VI concludes
the paper.
II. REL ATED WORK
In the literature, various game theory-based channel allocation
schemes for CRNs have been proposed. Some are discussed
here. In [5], a policy-based channel selection in CRN is
proposed, where each node sends its local sensing information
to the base-station and the base-station updates the channel
band state according to the received information. The base-
station then selects one of the channels from the pool of free
ones and allocates the same. In this work, it is reported that
it is essential to acquire the right information at the proper
time intervals, otherwise, the scheme my lead to inefficient
allocation. In [6], a rank-based channel selection algorithm
(RCSA) is proposed, where the rank of the channel is defined
by evaluating various parameters such as total utilization time,
total free time, and number of arrivals. Based on these param-
eters, the channel with the highest rank is selected. However,
this algorithm does not cover all the complex scenarios and
may also lead to starvation after a period of time. In [7], a
stochastic channel selection algorithm is proposed, which is
based on learning automata. Each node maintains a probability
vector and an estimation vector for all channels; and the
channels are selected on the basis of this vector. In [8], a game
theory model is proposed to improve the throughput of the
CRN while solving the channel allocation problem considering
the co-channel interference and few other factors. However,
this study only focuses on the interference present among the
nodes due to their respective locations and distances. In [9],
978-1-5090-1328-9/16/$31.00 ©2016 IEEE

a game theoretic model for channel allocation is proposed,
where each secondary user knows about the pay-off values
and strategies of each other. Under the considered bounded
rationality, each secondary user is expected to gradually and
iteratively adjust its strategy based on the previous observation.
However, as reported by the authors themselves, the proposed
model may not work for CRNs that are not based on adaptive
modulation and coding techniques. In [10], a model based on
the auction of the bandwidth is proposed, where each SU bids
for the required bandwidth from the PU and the PU assigns
the same on the basis of the information received from the SU
without degrading its own performance. This bidding and non-
cooperative behaviour is solved by the Nash Equilibrium. In
[11], a cooperative spectrum sharing scheme among a PU and
multiple SUs is proposed, where each PU selects the proper
set of SUs to serve as cooperative relays for the transmission.
The selection strategy includes the selection of the SU that is
associated with the least channel access time left. However, in
this scheme, the PU focuses only on selecting a certain number
of SUs among which the one that fulfills its criteria of least
access time, leaving the rest of SUs in a starvation state.
The above-discussed game theory-based channel allocation
schemes for CRNs have been designed by considering var-
ious parameters such as power, distance between the users,
bandwidth, to name a few. Among these schemes, those that
considered distance between the users as parameter may lack
behind when it comes to finding the exact coordinates of
the user. Also, rank-based schemes may lead to starvation or
deadlock for the users. Finally, some of those models have
been designed assuming that there are some limited factors
that can affect the interference.
Unlike these models, the game theory-based scheme pro-
posed in this paper tries to aggregate the interference caused
in the link while enforcing the fact that each SU must get an
equal opportunity to access the band and transmit the data,
thereby ensuring no starvation. The proposed model considers
the interference and number of radios per link as effective
parameters. The coined algorithm based on the two parameters
is shown to facilitate an efficient selection of the channel while
maximizing the spectrum utilization.
III. PROP OSE D APPROACH
A. System Model
It is assumed that the frequency band is sub-divided into
channels. The pair of users communicate with each other
through a single hop. The number of channels is denoted by
C. Each channel in the channel set Cis bidirectional. The
CRN consists of Nlinks, each oh which has a cognitive pair,
namely, a transmitter Tx and a receiver Rx. It is also assumed
that C < N .
Under this assumption, it is obvious that some transceivers
will use the same channel. Thus, it is true that when a pair
of CRs use the same channel, there will be interference,
otherwise, there will be no interference. This interference
between pairs iand jis represented by an interference function
I(Si, Sj). Game theory aims at modelling the scenarios where
an individual decision-maker has to choose specific actions
that have mutual or possible conflicting consequences.
The game consists of a set P=P1, . . . , Pnof players, non-
empty strategy sets for each player (Pi)∈P, and a utility set
for each player. Let Sidenote the strategy selected by Pi. The
interference function is then obtained as:
I(Si, Sj) = 1ifSi=Sj
0ifSi6=Sjotherwise (1)
Each player tries to maximize its utility by changing its
strategies. Each player also behaves as a selfish player, thus,
it is necessary to bring the game to an equilibrium point
using the Nash Equilibrium [12]. A pay-off value (or utility)
is a measure of the outcome of the player idetermined by
the actions and strategies adopted by all the other players.
It reflects the desirability of an outcome to a player. When
the outcome is random, the pay-off is generated as the result
of the probabilities under consideration. The expected pay-off
incorporates the player’s attitude towards a risk.
The pay-off is denoted as the product of two strategies
i.e. interference function (Equation (1)) and the number of
cognitive radios on the channel jfor player i, i.e.
U(Si, Sj) = I(Si, Sj)×Σc
j=1Ncij (2)
where Ncij denotes number of cognitive radio pair on the
channel jfor player i. As per the Nash Equilibrium for each
player i, the following condition holds (Equation (3)):
U(S∗
i, S∗
j)≥Ui(Si
0
, S−i
∗) (3)
for every strategy (S0
i∈Si), where Siis the strategy of the
player iand Sis the strategy set.
Focusing on the utility function, the Nash Equilibrium can be
achieved by using the following matrix and the well-defined
”Dominant Strategy Rule” and ”Thumb Rule” [13]. According
Player 2
Player 1
0 1
0 (0×Ncij ),(0×Ncij ) (0×Ncij ),(1×Ncij )
1 (1×Ncij ),(0×Ncij ) (1×Ncij ),(1×Ncij )
to the above matrix, each player tries to use the channel
with the minimum or no interference. The following algorithm
describes how our proposed channel allocation model for
CRNs works: Referring to the above matrix, only the cell
Algorithm 1: GAME()
1: Create array of available channels AvailableChannelhi
2: Create array for storing the interference value for each
available channel ChannelI nterf erencehi
3: Create array that stores the number of radios that each
secondary user has Numberradioshi
4: Create array that stores the Utility calculated for each
available channel Utilityhi
5: while (End of the AvailableC hannelhi )do
6: if (ChannelInterf erencehi == 0) then
7: Allocate the Channel
8: else
9: (Utilityhi =
ChannelInterf erencehi × N umberradioshi)
10: end if
11: end while
12: Sort the Utiltityhi
13: The channels will now be allocated on the basis of
increasing order of Utility
14: end

that has a low value of interference get selected despite the
number of radios. According to the above algorithm, after
the calculation of the utility/pay-off value of each player,
the channel that has the minimum value of interference. is
allocated.
IV. PERFORMANCE EVALUATI ON
A. Simulation Parameters
The simulation of the proposed algorithm is performed us-
ing OMNET++ in the INET environment [14]. The network
utilization, measured in terms of number of times a channel
is utilized by a user, is evaluated, considering a network
with various different number of users (both primary and
secondary). More precisely, we have used four sets of users
with 5, 10, 15 and 20 PUs respectively, representing four
scenarios. The simulation time for each of these sets of users is
10000 seconds. As the number of PUs vary, so is the number of
licensed channels that can be allocated to the SUs. In running
our proposed algorithm, the number of iterations refers to the
number of times that the algorithm runs and the best available
channel gets allocated to the SUs.
B. Simulation Results
In Fig. 1, it can be observed that there is an effective increase
of 28.7 % in the utilization when any number of randomly
selected channels out of five gets allocated to the SU. This is
attributed to the fact that the interference among the channels
is less due to less number of channels. It is also observed that
as the network gets dense, the interference among the channel
increases and the overall utilization decreases.
Fig. 1. Variation in the utilization as the number of users varies.
Again, Fig. 2 shows an increase of 9.09% in the overall
utilization of the network with the introduction of the SUs.
It is also observed that with the increase in the density of
the network, there is an increase in the interference among
the channels; and as per our proposed algorithm, only those
available channels that have lesser interference get allocated.
Fig. 2. Variation in the utilization as the number of iterations varies in set
with 5 PU’s and 4 SUs.
Similarly, in Fig. 3, it is observed that there is an increase of
5% in the overall utilization.
Fig. 3. Variation in the utilization as the number of iterations varies in set
with 10 PU’s and 4 SUs
In Fig. 4, it can be observed that the utilization of the network
is increased by 4.6%, confirming the fact that as per our
proposed algorithm, only those available channels that have
lesser interference get allocated. Indeed, when the density of
the network increases, the interference among the channels
also increases, leading to some extend to a decrease in chan-
nels allocation, which in turns affect the channel utilization
adversely. From all the above results, it can be inferred that
there is more channel utilization when the number of available
channels is less since the same channel is being utilized over
and over again.
Fig. 4. Variation in the utilization as the number of iterations varies in set
with 15 PU’s and 4 SUs.

Fig. 5. Variation in the utilization as the number of iterations varies in set
with 20 PU’s and 4 SUs.
In Fig. 5, it can be observed that the utilization of the network
is increased by 17.5%. The overall utilization of the network
is maximum when there are more number of users and the
interference is low.
V. SENSITIVITY ANALYSI S
The main objective of this section is to study the impact
of the four individual factors, namely, interference, radios,
number of users, and data rate, on the network utilization.
This is motivated by the fact that from a practical perspective,
practitioners wiling to use our proposed model will be more
concerned about understanding the priority factors that they
must focus on when designing or controlling their systems.
The main objective is to provide a quick insight of the relative
contribution of the priority factors on the performance of the
system.
Keeping this in mind, we have explored the use of Taguchi
method [4] to guide our simulation study. This method pro-
vides a means to study a number of design factors at different
levels simultaneously. It should be noted that our above
simulation study has motivated a ”what-if” analysis for the
changes made in the aforementioned factors and their effect
on the system performance.
The Taguchi method [4] is based on the technique of matrix
experiments [15], where an experimental design procedure is
used to standardize an array of experiments with respect to
a number of factors and their levels to be studied. In this
experimental design procedure, a special set of arrays called
orthogonal arrays (OAs) are used, which allow the study
of simultaneous effects of several procedure parameters in
an efficient manner, based on a suitable choice of the level
combinations of the input design variables for each experiment.
Typically, the experimental design procedure includes (1)
selecting a suitable OA, (2) assigning the above-mentioned
factors to the appropriate columns of the OA, and (3) deter-
mining the conditions for the individual experiments. It should
be mentioned that the results of the Taguchi experiments can be
analyzed and the contribution of each factor of an experiment
can be quantitatively derived by using the analysis of variance
(ANOVA) technique [4].
In this work, we have considered the L9OA, which is
meant for understanding the effect of the above-mentioned
four independent factors, namely, interference, radios, number
of users, and data rate, each having 3 factor level values [6].
Table I shows the different levels of factors studied using L9,
and only 9 experiments are required to study the effect of the
these four factors on each of the three levels. It should be
noted that as per the Taguchi method, it is suggested that the
percentage contribution of the pooled errors when conducting
the ANOVA analysis do not exceed 15% to 20%.
Fig. 6 shows the main effect of the above-mentioned four
factors i.e. interference level, number of radios, number of
users, and data rate, on the system performance. It can be
observed that the mean effect of the data rate is maximum
when compared to that of the other main factors. The data
rate, which has three levels, namely, 100, 150, and 200 has a
significant effect on the network utilization performance. It is
also observed that the next important contribution (but less than
that of the date rate) on the network utilization performance is
attributed to the number of users. Finally, the remaining factors
(i.e. interference and radios) does not vary significantly at the
three assumed levels.
As the network utilization has been considered as perfor-
mance measure, one can consider the objective of the Taguchi
experiments [4] to be ”the larger the better”. Considering this
objective, Fig. 6 reveals that the following setting: higher date
rate equals to 200, number of users equals to 25, number of
radios equals to 25, and interference equals to 0.1yields the
best condition to operate the system. It is worth mentioning
that the average utilization decreases at radio equals to 25 as
compared to radio equals to 1. This suggests that there may
be some interaction between the factors, which could influ-
ence the performance of other factors. The average utilization
performance decreases with increase the interference.
Fig. 6. Average performance of the considered factors.
Table II shows the factors, namely degree of freedom (df),
variance (V), variance ratio (F), pure sum of squares (S) and
percent contribution (P) after pooling the results. The value
of the F-test from the standard table for 2 degree of freedom
of the errors is 4.46 at 95% confidence interval (CI). From
Table II, it can be observed that most of the factors after the
pooling have a value of the variance ratio (F) more than 4.46
(95% CI), hence the percent contribution (P) shown in the
last column of the Table have some significance. From
the above analysis, it can be concluded that the data rate has
the highest percentage contribution (73.63%) in the network
utilization performance, followed by the number of users (with
a percentage contribution of 21.84%). The interference has a
contribution of 2.26% in the network utilization performance.
The effect of the number of radios has been pooled with error,

TABLE I. ORT HOGO NAL AR RAY L9 (F OR FOU R FACTO RS OF TH REE
LE VELS )
Column 1 2 3 4 Utilization
Factors
Exp. no. Interference Number of radios User sets Data-Rate
1 0.1 5 5 100 340
2 0.1 15 10 150 674
3 0.1 25 25 200 1048
4 0.5 5 10 200 894
5 0.5 15 25 100 518
6 0.5 25 5 150 524
7 0.9 5 25 150 752
8 0.9 15 5 200 728
9 0.9 25 10 100 464
TABLE II. ANOVA ANA LYSIS O F THE A SSUM ED FACTO RS.
Name of Factor df S V F S’ P(%)
Interference 2 11009 5504 5 8753 2.26
Number of Radios 2 2257 1128
Number of Users 2 89164 44582 40 86908 21.84
Data Rate 2 303321 151660 134 301065 73.63
Error 2 2257 1128 9025 2.27
Total 8 398060 49757 100.00
#Pooled factors
which means that the number of radios may not have much
effect on the the network utilization performance. However,
the number of radios may not have significant direct effect on
the network utilization as it can be observed that the average
utilization changes with the number of radios. This suggests
that the number of radios may have interaction with some
other factors, which needs to be studied in future. These results
have some significance since the value F is more than 4.46,
which corresponds to a 95% confidence level with 2 degree of
freedom of the pooled error.
VI. CONCLUSION
This paper has proposed a game theoretic-based model for
channel allocation in cognitive radio networks. The proposed
scheme has been analyzed by using the concept of Nash
equilibrium where the interference is considered as the main
parameter for channel allocation. Simulation results have
shown that the network utilization is increased by about 17.5%.
An ANOVA analysis has also been conducted, showing that
the interference, data rate, and number of users, are the most
important factors that influence the network utilization. In
future, we plan to incorporate other additional design factors
such as power, bit error rate and investigate the network
utilization performance of the proposed scheme.
ACKNOWLEDGMENT
The work by the 3rd author was supported in part by the
Natural Sciences and Engineering Research Council of Canada
(NSERC) grant #RGPIN/293233-2011.
REFERENCES
[1] I. F. Akyildiz, W-Y. Lee, M. C. Vuran, S. Mohanty, ”Next genera-
tion/dynamic spectrum access/cognitive radio wireless networks: a sur-
vey”, Computer Networks, Vol. 50, No. 13, 2006, pp. 2127-2159,
[2] S. Haykin, ”Cognitive radio: brain-empowered wireless communica-
tions”, IEEE Journal on Selected Areas in Comm., Vol. 23, No. 2, 2005,
pp. 201-220.
[3] E. Tragos, S. Zeadally, A. G. Fragkiadakis, V. A. Siris, ”Spectrum
Assignment in Cognitive Radio Networks: A Comprehensive Survey”,
IEEE Comm. Surveys & Tutorials, Vol. 15, No. 3, 2013, pp. 1108-1135.
[4] T. P. Bagchi, ”Taguchi Methods Explained-Practical Steps to Robust
Design”, Prentice-Hall India, 1993, ISBN: 0-87692-808-4.
[5] D. Na, N.Hao, Y. Sang-Jo, ”Policy-based dynamic channel selection
architecture for cognitive radio networks”, Proc. of CHINACOM 2007,
Aug. 22-24, 2007, Shanghai, China, pp. 1190-1194.
[6] A. Ali, M. Sakhare, K. Hwang, D. Y. Suh, ”A Novel Channel Indexing-
based channel selection algorithm for cognitive radio networks”, Proc. of
IEEE Intl. Conference on ICT Convergence (ICTC), Oct. 14-16, 2013,
Jeju Island, Korea, pp. 682-687.
[7] Y. Song, Y. Fang, Y. Zhang, ”Stochastic channel selection in cognitive
radio networks”, Proc. of IEEE GLOBECOM 2007, Washington DC, Nov.
26-30, 2007, pp. 4878-4882
[8] J-P. Sheu, Z. X. Wu ; C. Ma, R. Jagadeesha, ”Interference-aware channel
allocation algorithm with game theoretic approach for cognitive radio
networks”, Proc. of 20th IEEE Intl. Conference on Parallel & Distributed
Systems (ICPADS), Hsinchu, Taiwan, Dec. 16-19, 2014, pp. 41-46.
[9] D. Niyato, E. Hossain, ”Competitive Spectrum Sharing in Cognitive
Radio Networks: A Dynamic Game Approach”, IEEE Trans. on Wireless
Communications, Vol. 7, No. 7, 2008, pp. 2651-2660.
[10] X. Wang, Z. Li, P. Xu, Y. Xu, X. Gao, H-H. Chen, ”Spectrum Sharing
in Cognitive Radio Networks - An Auction-based Approach”, IEEE Trans.
on Systems, Man & Cybernetics - Part B, Vol. 40, No. 3, June 2010, pp.
587-596.
[11] H. Wang, L. Gao, X. Gan, X. Wang, E. Hossain, ”Cooperative spectrum
sharing in cognitive radio networks: A game-theoretic approach”, Proc. of
ICC 2010, Cape Town, South Africa, May 23-27, 2010, pp. 1-5.
[12] A. B. MacKenzie, L. A. DaSilva, ”Game Theory for Wireless En-
gineers”, Synthesis Lectures on Communications, Morgan & Claypool,
2006, ISBN: 9781598290172, 86 pages
[13] J-J. Laffont, E. Maskin, ”Nash and dominant strategy implementation
in economic environments”, Journal of Mathematical Economics, Vol. 10,
No. 1, 1982, pp. 17-47.
[14] T. Chamberlain, ”Learning OMNeT++”, Packt Publishing, Sept. 2013,
102 pages, ISBN: 978-1-84969-715-6.
[15] M. S. Phadke, ”Quality Engineering using Robust Design”, 1st Ed.,
Prentice Hall International editions, 1989, ISBN: 9780137451678, 334
pages.