Content uploaded by Abdorasoul Ghasemi
Author content
All content in this area was uploaded by Abdorasoul Ghasemi on Apr 12, 2014
Content may be subject to copyright.
IEICE TRANS. COMMUN., VOL.E92–B, NO.12 DECEMBER 2009
3693
PAPER
Special Section on Dynamic Spectrum Access
A Simple MAC Protocol for Cognitive Wireless Networks
Abdorasoul GHASEMI†a),Nonmember and S. Mohammad RAZAVIZADEH†b),Member
SUMMARY A simple distributed Medium Access Control (MAC) pro-
tocol for cognitive wireless networks is proposed. It is assumed that the
network is slotted, the spectrum is divided into a number of channels, and
the primary network statistical aggregate traffic model on each channel is
given by independent Bernoulli random variables. The objective of the
cognitive MAC is to maximize the exploitation of the channels idle time
slots. The cognitive users can achieve this aim by appropriate hopping be-
tween the channels at each decision stage. The proposed protocol is based
on the rule of least failures that is deployed by each user independently.
Using this rule, at each decision stage, a channel with the least number of
recorded collisions with the primary and other cognitive users is selected
for exploitation. The performance of the proposed protocol for multiple
cognitive users is investigated analytically and verified by simulation. It is
shown that as the number of users increases the user decision under this
protocol comes close to the optimum decision to maximize its own utiliza-
tion. In addition, to improve opportunity utilization in the case of a large
number of cognitive users, an extension to the proposed MAC protocol is
presented and evaluated by simulation.
key words: medium access control (MAC), opportunistic spectrum access,
spectrum utilization
1. Introduction
There exists an increased research effort in wireless commu-
nications and networking for the optimal or efficient use of
scarce and costly network resources in recent years. By de-
ploying new physical transmission techniques as well as re-
vised and cross layer protocols, considerable improvement
in network resource management and specially in the net-
work spectrum utilization is achieved.
On the other hand, measurements of the FCC show that
much of the costly spectrum is idle or unutilized at any given
time and location [1]. Therefore, it seems that a revised ap-
proach to spectrum management and utilization is also re-
quired, i.e., the current licensed spectrum allocation and uti-
lization is inefficient. The cognitive radio concept, proposed
by Mitola [2], in its general meaning, shapes the structure
of the networks where the nodes are empowered to sense
the environment and opportunistically exploit the licensed
networks spectrum white spaces. Hence, the cognitive or
secondary user should infer the spectrum status and adapts
its transmission time and parameters accordingly. Then, his
decision is based on the history of spectrum sensing and pre-
Manuscript received April 16, 2009.
Manuscript revised July 15, 2009.
†The authors are with the Communication Technology Insti-
tute, Iran Telecommunication Research Center (ITRC), Tehran
14399-55471, Iran.
a) E-mail: arghasemi@itrc.ac.ir
b) E-mail: smrazavi@itrc.ac.ir
DOI: 10.1587/transcom.E92.B.3693
vious transmission results.
This idea results in some unique and new challenges in
the architecture design as well as all layers of the protocol
stack. In these networks, the basic assumption is the ability
to sense the spectrum perceptively and correctly for utiliza-
tion. Therefore, the main characteristic of these networks is
the tight coupling between the physical (PHY) layer opera-
tion and other layers.
In this paper, we focus on the cognitive MAC layer as-
suming simple model of spectrum sensing and transmission
at the PHY layer. The objective of the cognitive MAC is to
maximize the exploitation of the channels idle time slots by
the cognitive users.
The cognitive MAC involves with two problems of ex-
ploration and exploitation [3], [4]. The former deals with
perceptively selecting channels to be sensed at the begin-
ning of each sensing slot by cognitive user. The exploration
outcomes are used to infer the stochastic traffic model in-
formation of the primary network on each channel which is
subsequently used for better decisions in exploitation. That
is the aim of exploration is not to utilize an opportunity in-
stantly. In the exploitation, the cognitive user aims to se-
lect the best channel, i.e., channel which is more likely to
be idle, and instantaneous utilization at each decision step.
Spending more time for channels exploration leads to mak-
ing better decisions at upcoming slots in the cost of miss-
ing the instantaneous utilization opportunities. As a con-
sequence, there exists a tradeoffbetween the time that is as-
signed for channels exploration and the channel exploitation
at the MAC layer.
In [3] using dynamic programming, a recursive struc-
ture for the optimal medium access control of a cognitive
user is derived. Also, to avoid the computational complex-
ity, an asymptotic optimal strategy with low complexity is
developed. In [4] the opportunistic spectrum access prob-
lem is analyzed in the framework of partially observable
Markov decision process. A decentralized cognitive MAC
is suggested to optimize the performance of the cognitive
users while limiting the interference for the primary users.
The channel selection problem for spectrum agile user
is formulated as a multiarmed bandit problem in [5]. The
optimal policy for channel selection is then derived by com-
puting the Gittins indices. Since the computation of these
indices is complex in general, approximate values are com-
puted by truncating the state space to find an appropriate
finite state Markov chain. For the primary network traffic
modeling, a simple model is adopted which is also vali-
Copyright c
2009 The Institute of Electronics, Information and Communication Engineers
3694
IEICE TRANS. COMMUN., VOL.E92–B, NO.12 DECEMBER 2009
dated by experimental measurements of an IEEE 802.11b
network. The developed algorithm is based on the number
of failures and successes on each channel to estimate the
channels Bernoulli traffic parameter and to select the best
channel at each decision step. In addition, exploring the
channels continuously, this algorithm can track the channels
traffic variations and consequently select the best channel
over time as in [5]. We note that the primary network traffic
on the channels could change over time and the cognitive
MAC is responsible to track these variations. The achiev-
able gain by spectrum agility is also discussed in [6] in terms
of two performance criteria, i.e., spectrum utilization and
spectrum access blocking. Furthermore, a framework con-
sists of three building blocks namely “spectrum opportunity
discovery, spectrum opportunity management, and spectrum
usage coordination” is proposed and evaluated via simula-
tions.
In this paper, applying the results of Kelly on the the-
ory of multiarmed bandit problem in [7], we develop and
analyze a simple MAC protocol for the cognitive users. The
proposed scheme requires uncomplicated computations and
stores a simple state vector. In the case of a single cognitive
user, it could track the best channel as in [5] without com-
puting the Gittins indices. In the case of multiple cognitive
users, the protocol can be deployed by each user indepen-
dently. It is shown that as the number of users increases,
their distributed decisions follow the optimal trend to maxi-
mize each user utilization while the fairness is also guaran-
teed. In addition, an extension to this protocol is presented
and evaluated by simulations that achieves better utilization
in the case of large number of cognitive users.
The rest of this paper is organized as follows. The sys-
tem model and problem statement are presented in Sect. 2.
In Sect. 3, the algorithm based on the rule of least failures is
presented and its optimality for the case of a single cognitive
user is discussed and evaluated by simulation. The multi-
ple user cognitive MAC protocol, its performance study and
simulation are presented in Sect. 4. In Sect. 5, an extension
to the protocol is proposed that leads to better utilization
when the number of cognitive users is large. Section 6 con-
cludes the paper.
2. System Model and Problem Statement
We assume that the spectrum assigned to the primary
network consists of Nnon-overlapping channels, N=
{1,2,...,N}. It is also assumed that the system is time slot-
ted. The channels usage in different time slots depends on
the primary users aggregate traffic in practice. We use a sta-
tistical model to describe this traffic. Since the objective of
the cognitive MAC is the exploitation of the remaining white
spaces, the adopted statistical model is a key parameter in
the system model that affects the cognitive MAC analysis
and evaluation. It is assumed that channel jis busy or black
in each time slot with probability of qj. Therefore, the num-
ber of white spaces or idle time slots between any two black
spaces has a geometric distribution with mean (1 −qj)/qj.
This model is used in [3], [5], where in [5] its consistency
with the experimental measurements for the trafficofnet-
works using IEEE 802.11b standard is verified.
The cognitive network consists of Musers. It is as-
sumed that each user could sense one channel in a time slot
and its possible transmission is synchronized with the pri-
mary network. At the beginning of each decision slot, the
cognitive user decides on selecting a channel to sense. The
selected channel could be idle or busy. If the channel is idle,
the cognitive user transmits a packet and furthermore up-
dates his history for this channel state. The state of other
channels does not change in this case. Therefore, the state
of channel jreflects the number of encountered failed and
successful transmissions on it and can be used for the esti-
mation of its traffic parameter, i.e., qj. Hence, the sequence
of selected channels determines the rewarded gain from the
spectrum which depends on the decision strategy of the user.
The objective is to maximize the exploitation of the
spectrum white spaces by applying an optimal policy. This
policy uses the past observations which are summarized in
the current state. Let the attained reward in each time slot is
denoted by R(t), where R(t)=1 is for successful transmis-
sion upon selecting an idle channel and R(t)=0isforbusy
one. The objective is to maximize
E⎡
⎢
⎢
⎢
⎢
⎢
⎣
∞
t=0
βtR(t)⎤
⎥
⎥
⎥
⎥
⎥
⎦(1)
over all possible channel selection policies where β∈(0,1)
is a discount factor. This problem is referred to multiarmed
bandit problem and the best decision at each stage could
be found by computing the Gittins indices [8]. Assume an
uncertain system which returns different rewards for each
possible excitation according to a probability distribution.
Multiarmed bandit problem is a model for an agent that
aims to attain new knowledge of this system and simulta-
neously optimize its decision based on the current knowl-
edge. The agent should make a tradeoffbetween explor-
ing the system by new excitations to attain more knowledge
about these probability distributions and instantaneous ex-
ploitation based on current knowledge. The optimal de-
cision should yield the maximum reward over all possible
ending time.
The Gittins indices are an ordered set and can be com-
puted according to the current state of the channels. The
main problem is that computing the Gittins indices are com-
plex in general. Hence, other algorithms have been proposed
to find optimal or suboptimal solutions with less complexity
by adding new assumptions to the problem [7], [8]. In this
paper, according to the structure of the defined problem, we
deploy one of these algorithms for the case of single cog-
nitive user and then extend the results to multiple cognitive
users.
GHASEMI and RAZAVIZADEH: A SIMPLE MAC PROTOCOL FOR COGNITIVE WIRELESS NETWORKS
3695
Algorithm 1 The MAC Protocol Based on the Least Failure
Rule
Initialization: Set S0
j=F0
j=0for j∈N
for t=1,2,... do
ν=least f ailure(St−1,Ft−1)
sense channel ν
if busy then
Ft
ν=Ft−1
ν+1
else
St
ν=St−1
ν+1
exploit channel ν
end if
end for
3. Single Cognitive User Case
3.1 The Least Failure Rule
In [7], Kelly shows that as the discount factor approaches
one, the simple least failure rule tends to be the optimal pol-
icy. This rule states that at each stage the cognitive user
should select the channel which has incurred the least num-
ber of failures and in the case that this rule returns more than
one solution, the channel with the largest number of suc-
cesses should be selected. Therefore, it is just required that
the user maintains the number of incurred successes and fail-
ures on each channel and decides based on the above simple
rule.
We first discuss about the reasonability of the assump-
tion β→1 for the cognitive MAC problem. In multiarmed
bandit problem, βis used as a discount factor indicating the
preference of the nearer time horizon rewards against the
farther ones. The rationale behind this is the exploitation
of the opportunities over all possible terminating time. The
assumption of β→1 neglects this preference. This assump-
tion is reasonable if we assume that the spectrum opportu-
nities are not vanished, the cognitive users always have data
to transmit, and they could tolerate transmission delay.
3.2 Single Cognitive User MAC Algorithm
Let St
j,Ft
jbe the number of incurred successful and failed
accesses to channel jtill the time slot t.Thestateofall
channels are shown by the vectors St=(St
1,...,St
N),Ft=
(Ft
1,...,Ft
N). Algorithm 1 is used by the cognitive user for
spectrum exploitation.
In this algorithm, the lea st f ailure function returns
the best channel according to the rule of least failures. It
should be noted that after exploiting channel j,Sjis in-
cremented while Fjand the state of other channel do not
change. Therefore, this channel would be the best channel
in forthcoming time slots for exploitation till a failure is in-
curred on it.
3.3 The Achievable Utilization
The cognitive user utilization of the channels white spaces
is the percentage of successful access to the total number
of access. The following result is stated in [7], where we
represent its proof by a simple reasoning for completeness.
Lemma 1: Using the least failure rule the maximum
achievable utilization by the cognitive user after a long pe-
riod is given by:
Uopt =lim
T→∞ E⎡
⎢
⎢
⎢
⎢
⎢
⎣
1
T
T
t=1
R(t)|q1,q2,...,qN⎤
⎥
⎥
⎥
⎥
⎥
⎦
=⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
N
j=1
1
qj
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
−1N
j=1
1−qj
qj
(2)
≤max(1 −q1,1−q2,...,1−qN)(3)
Proof: Letattimet,jbe the best channel under this rule.
The average achieved utilization on this channel is 1−qj
qj
while the cognitive user encounters a failure on it. Hence, it
tries this channel 1−qj
qj+1=1
qjtimes. It then switches to the
new best channel according to the least failure rule. There-
fore, all channels are scanned to encounter a failure on them
and then we return to exploit channel jagain after N
j=1
1
qj
time slots. Scanning the channels in round robin manner,
the maximum average achievable utilization is given by (2).
To find (3) we note that the utilization is a weighted average
of 1 −qjand hence is less than their maximum value.
We should note that the cognitive user does not have
prior knowledge about the channels traffic parameters.
Therefore, it is not surprising that that the maximum average
utilization is less than 1 −qmin, i.e., when the cognitive user
locks on the best channel. We could think that the difference
between these two values, i.e., (1−qmin )−Uopt as the cost of
learning and tracking the channels traffic status if their pa-
rameters are not known or is varying in time. If the primary
network traffic on channels is not varying in time or its vari-
ation is slow, the cognitive user could estimate the channels
traffic parameters and lock on the best channel. Specifically,
after enough observation, qjcould be estimated according
to [5]:
qj=Fj
Sj+Fj+1(4)
The following property is also constructive.
Lemma 2: Applying the least failure rule, the average
probability of selecting channel jis given by:
pj=1/qj
N
j=11/qj
(5)
Proof: The algorithm based on least failure rule exploits
the channels white spaces in a round robin fashion such that
after any long period of time, i.e., T, the number of failures
on each channel is almost equal. Therefore, after Tslots we
should have:
(Tpj)qj=F0∀j∈N
3696
IEICE TRANS. COMMUN., VOL.E92–B, NO.12 DECEMBER 2009
Fig. 1 The exploited time slots by the cognitive user in 100 consecutive time slots using least failure
rule.
Fig. 2 Channels utilization over time and maximum achievable
utilization.
where F0is a constant. This leads to pj=1/qj
T/F0.Since
jpj=1, we find (5). Also, F0=T
j1/qj=T
T0shows that
in average at each round, i.e., T0slots, we have one failure
on each channel.
3.4 Numerical Evaluation
The primary network spectrum is assumed to consist of
N=20 non overlapping channels. The parameters of ran-
dom variables describing the primary traffic on each chan-
nel, are selected randomly in the range [0.10.5] for 19 chan-
nels while for one arbitrarily selected channel, i.e., channel
10, we set q10 =0.05. Therefore, this channel is the least
busy channel. The algorithm operation on this channel is
tracked in the following simulation. In simulation, the pri-
mary network traffic on each channel, busy and idle time
slots, is determined by generating random uniform numbers
in the range [0 1] and comparing with its Bernoulli param-
eter. The cognitive user stores the number of perceived suc-
cesses and failures on each channels for his decisions. Also,
the percentage of perceived idle slots to the total simulation
time is considered as the cognitive user utilization. The uti-
lization of white spaces by cognitive user, using Algorithm
1, in 100 consecutive time slots is depicted in Fig. 1. As this
figure shows, the cognitive user switches from one channel
to another one when it encounters a failure on the current
channel.
In Fig. 2, the achieved utilization of the five less busy
channels specifically channel number 10 as well as the to-
tal achieved utilization over time is depicted. The steady
achieved utilization is Uopt =0.77 which is consistent with
(2). The achieved utilization by simulation on channel 10
is also consistent with the expected one and is equal to
p10(1 −q10 )=0.20 where p10 is computed using (5). Also,
compared with the steady available white space on the best
channel, 1 −qmin =0.95, the cost of learning is 0.18.
4. Multiple Cognitive Users Case
If the cognitive network consists of Musers, then a fraction
of opportunities is wasted due to the simultaneous secon-
daries transmissions on the channels. The secondary user
encounters this type of collision when he senses a channel
idle at the beginning of a time slot but at the end of that slot
he does not receive ACK from his receiver. Therefore, he
could discriminate these types of collisions from the colli-
sions with the primary users.
In the multiple user scenario the objective of the cog-
nitive MAC is to maximize the sum of cognitive users ex-
ploitations as well as providing the fairness among them. To
this end, their transmissions on channels should be sched-
uled such that each user could exploit the opportunities
while perceiving minimum interference from others.
In Alg. 1, a collision with a primary user triggers the
channel hopping. Intuitively, if we increase the hopping be-
tween the channels according to the secondaries collisions,
then the probability of simultaneous exploitation by two
cognitive users is decreased. On the other hand, we should
keep the fraction of times that each user exploiting chan-
nel jas in Alg. 1 to ensure the near maximum utilization of
available white spaces. By appropriate hopping between the
channels one hopes to achieve the total utilization MUopt
when Uopt is given by (2), i.e., when each user exploits
the opportunities without interfering for others. Since the
less busy channels are more visited by the cognitive users,
we expect to have more secondary collisions on these chan-
nel. Therefor, the main problem is on designing the hopping
sequence according to the incurred primary and secondary
collisions on each channel. Also, we note that the users de-
cisions should be make in a distributed fashion. We start
with the case of two cognitive users and then extend to the
GHASEMI and RAZAVIZADEH: A SIMPLE MAC PROTOCOL FOR COGNITIVE WIRELESS NETWORKS
3697
general case.
4.1 Two Cognitive Users
Assume that M=2,NM. We first discuss that taking
into account the secondaries collisions as failure in Alg. 1,
i.e., these collisions are also trigger channel hopping, a near
optimal and fair solution could be achieved. In other words,
the fraction of times that each user exploits channel jdose
not changed much compared with a single user scenario
while the fraction of secondaries collisions is limited. Let
Ft
j=Ft
1j+Ft
2j,whereFt
1j,Ft
2jare the number of incurred
failures on channel jby each user due to collisions with pri-
mary and the other secondary users respectively.
Also, assume that the channel selection process by each
user in the consecutive time slots is independent, i.e., at the
beginning of a time slot each cognitive user selects channel
jwith probability ˆpj,j=1,...,N. We note that according
to Alg. 1, the selected channel by each user at the beginning
of a time slot depends on his previous deploying channel
because he does not hop to a new channel until a failure
is incurred. However, the probability of finding a channel
idle in some consecutive time slots is not large. Also, this
assumption is a pessimistic assumption in our analysis and
as we will see in following the results based on is consistent
with simulation. Using this assumption after an enough long
time slots, T,wehave:
F1j=Tˆpjqj(6)
F2j=Tˆp2
j(7)
Where (7) is probability of selecting channel jby both users
simultaneously. According to the rule of least failure, the
incurred total number of failures on each channel should be
the same named ˆ
F0. Therefor, applying Alg. 1, we should
have:
ˆp2
j+qjˆpj−ˆ
F0/T=0,j=1,2,...,N(8)
The acceptable solution for ˆpjis: ˆpj=qj(1+4ˆ
F0/Tq
2
j−1)
2.
Let c=4ˆ
F0/T. Hence, c/4 is the ratio of incurred failed to
the total number of time slots on each channel. To com-
pare the results with one cognitive user scenario, noting that
1+c/qj2≤1+0.5c/qj2, we use the approximation:
1+c/qj21+0.5c/qj2ζ(c,qj),ζ(c,qj)<1(9)
where ζ(c,qj)<1 is used as a correction factor that come
close to one if c/qj21. Using (9), we have ˆpj=
1/qj
T/ˆ
F0ζ(c,qj). Applying jˆpj=1, we found:
ˆ
F0=T
j(1/qj)ζ(c,qj)(10)
ˆpj=(1/qj)ζ(c,qj)
j(1/qj)ζ(c,qj)(11)
Comparing with a single cognitive user case in the previous
section we conclude that:
1) If cis sufficiently small, e.g., when the number of chan-
nels is sufficiently large compared to the number of users,
such that ζ(c,qj)ζ(c)qj∈(0,1), according to (11) the
channels access probabilities does not change much, i.e.,
ˆpjpj, while the perceived number of failures increased
to ˆ
F0=F0
ζ(c).
2) In average, each cognitive user utilization on each chan-
nel and hence their total utilization are equal. Therefore, the
fairness is guaranteed. For numerical evaluation, Alg. 1 is
used by M=2 cognitive users independently considering
secondaries collisions as failure. The channel hopping of
the users and exploited time slots are depicted in Fig. 3. The
steady achieved utilization is U1=U2=0.74.
4.2 MCognitive Users
Assuming Mcognitive users, the average perceived failures
due to the secondaries collision on channel jfrom the per-
spective of one cognitive user is given by:
F2j=Tˆpj[1 −(1 −ˆpj)M−1] (12)
That is if at least one user from the remaining M−1 ones ex-
ploits channel jsimultaneously. Again, adding with the fail-
ures due to collisions with primary users and equating a con-
stant number of failure, we should solve an equation of de-
gree Mto find ˆpj. To find how the algorithm performs when
the number of users increased, we can use the approximation
(1 −ˆpj)M−11−(M−1) ˆpjand hence Fj
2T(M−1) ˆpj2
to obtain:
(M−1) ˆp2
j+qjˆpj−ˆ
F0
T=0 (13)
This leads to the solution ˆpj=qj(1+4( M−1) ˆ
F0/Tq
2
j−1)
2(M−1) .Com-
pared with the case of M=2users,c=4(M−1) ˆ
F0/Tis
increased and hence ζ(c,qj) is decreased for each channel.
Also, using the pessimistic assumption of independent chan-
nel selection in consecutive time slots, an under estimate of
each user utilization is given by:
ˆ
U=
j
ˆpj(1 −qj)−(M−1)
j
ˆp2
j(14)
Compared with (2), the utilization degradation has two rea-
sons. The first one roots in the changes in the channel access
probabilities, i.e, because of ζ(c,qj). Specifically, according
to (9), if qj<qkthen ζ(c,qj)<ζ(c,qk). Since the sum
of all channels access probabilities is one in this case too,
we found that by using (11) the channel access probability
to the less busy channels is decreased while it is increased
for more busy channels compared to the ones in (5). Intu-
itively, adding a failure to the number of failures on a less
busy channel is more destructive compared to a more busy
channel. The second one is due to the simultaneous access
to the channels.
The former is the main reason of utility degradation
3698
IEICE TRANS. COMMUN., VOL.E92–B, NO.12 DECEMBER 2009
Fig. 3 The exploited time slots by M=2 cognitive users in 100 consecutive time slots using Alg. 1
independently.
when MNbecause considering the secondary collision
as failure for channel hopping, strongly decreases the prob-
ability of selecting the same channel in the near future time
slots. However, as the number of users increased, the latter
would be more important in utility degradation. Specifically,
as the number of users increased, the access probability to
channel jconverges to 1/Nregardless of qj. This fact can
be shown according to (9) and (11). From (9), we have:
ζ(c,qj)
qj
=2[ qj2+c−qj]
c(15)
Which shows that as cincrease, i.e., because of increases in
M, the value of ζ(c,qj)/qjwould be approximately indepen-
dent of qj. Now according to (11) we found that for a large
number of users ˆpj1
N,j=1,2,...,N.
Therefore, without any coordination between the users
in exploiting the channel, i.e., just hopping upon any pri-
mary and secondary collision a fair solution is achieved.
This behavior is also near the optimal one that any user
should be take to maximize its own utilization from the
white spaces. To see this consider the problem:
max ˆ
U=
j
ˆpj(1 −qj)−
j
(M−1) ˆp2
j(16)
s.t.
j
ˆpj=1 (17)
0≤ˆpj≤1 (18)
That is each user adjust the channels access probability,
pj,j=1,2,...,N, to maximize its own utilization. The
Lagrangian function of this concave optimization problem
is given by:
L(ˆp1,..., ˆpN,λ)=
jˆpj(1 −qj)−(M−1) ˆp2
j
+λ⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎣
j
ˆpj−1⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
(19)
where λis the Lagrange multiplier for constraint (17). Ap-
plying the KKT conditions [9], it is easy to show that the
optimal access probability to channel j,ˆp∗
j, is given by:
ˆp∗
j=1
N+(1 −qj)−1
Nj(1 −qj)
2(M−1) j=1,...,N(20)
Fig. 4 Utilization of each cognitive user.
This shows that given M, the access probability to the
less busy channels should be greater. Also, as the number of
users increased the optimal channel access probability tends
to 1/N. This is consistent with the users decisions deploying
Alg. 1. We should note that the users adjust their access
probabilities to channels in a distributed fashion while they
don’t have any prior knowledge about the traffic parameter
of the channels and the number of users.
For numerical evaluation, Alg. 1 is applied to the net-
work setting of Sect. 3.4 for different number of users, M.
The achieved users utilization by simulation and using the
estimated one in (14) are shown in Fig. 4. The difference be-
tween the estimated utilization and simulated one is due to
the deployed pessimistic assumption of independent chan-
nel selection by each cognitive user at the beginning of each
time slot as it is explained in Sect. 4.1. In fact using this
assumption the probability of secondaries collision is in-
creased and its effect on decreasing the utilization is over
estimated. However, the same trend is seen between the sim-
ulated and estimated utilization when the number of cogni-
tive users is increased. In Fig. 5 a typical user access prob-
ability to the best channel, i.e. channel number 10, is de-
picted. This figure shows that for small number of cognitive
users this channel is more visited while for large number of
users the access probability to this channel is decreased to
1/N=1/20 =0.05. That is as the number of cognitive users
increased, random channel selection is the best decision to
GHASEMI and RAZAVIZADEH: A SIMPLE MAC PROTOCOL FOR COGNITIVE WIRELESS NETWORKS
3699
Fig. 5 Average access probability to channel number 10 for different
number of cognitive users.
reduce the secondary collision. The difference between the
optimal access probability and simulated one to limit the
secondary collisions is due to the independence assumption
which is used in estimating the cognitive user utilization.
5. Extension to the Multiple Users Cognitive MAC
From Fig. 4, we found that as the number of cognitive users
increases most of the spectrum opportunities are wasted due
to their competition. In this case, an appropriate decision
by each user is to exploit a fixed channel in consecutive
time slots to reduce the probability of collision with other
users. To find the winner of each channel, the competing
users transmissions on that channel are deferred randomly
according to the perceived number of secondaries collisions
on it. That is, the number of failure and hence their transmis-
sions delays on that channel, are increased in an exponential
backoffmanner. The winner of that channel is one who has
the minimum backoffand is encouraged to exploit that chan-
nel in forthcoming time slots. The encouragement is done
by decrementing its perceived secondaries collision on that
channel upon a successful transmission on it. Therefore,
the winner of channel jwould encounter a small backoffon
channel jand large backoffon other channels. The result
is that as the number of users increased each user tends to
exploit a fixed channel. Algorithm 2 shows this strategy for
decision making.
In this algorithm, function ceil(x) returns the smallest
integer not less than x,rand returns a random number in the
range (0,1), and Wmax is a constant for the maximum allow-
able backofffor each channel. In the case of small number
of users, Alg. 2 behaves like Alg. 1 because the probability
of secondary collision on channel jand hence F2jis low.
Also, it is obvious that by limiting the maximum backoffon
each channel, Wmax , this algorithm come close to Alg. 1.
We should note that the users utilization in Alg. 1 are
almost equal. However, their achieved utilization when us-
ing Alg. 2 depend on the selected channel for exploiting. In
other words, Alg. 1 leads to equal and fair utilization even in
short scale periods. To investigate the fairness degradation
Fig. 6 Average achieved utilization by using Alg. 2 for different number
of cognitive users.
Algorithm 2 Multiple Cognitive Users MAC Protocol
Each cognitive user follows these steps independently
Initialization: Set Wmax and S0
j=F0
j=F0
2j=0for j∈N
for t=1,2,... do
ν=least f ailure(St−1,Ft−1)
sense channel ν
if busy then
Ft
ν=Ft−1
ν+1
else
St
ν=St−1
ν+1
exploit channel ν
if exploitation is successful then
Ft
2ν=max{0,Ft−1
2ν−1}
else
Ft
2ν=Ft−1
2ν+1
W=2Ft
2ν−1
B=min{Wmax ,ceil(W∗rand)}
Ft
ν=Ft−1
ν+B
end if
end if
end for
in Alg. 2 we can use the Jain’s fairness index as a measure
given by [10]:
f=M
j=1Uj2
MM
j=1Uj2(21)
where Uj,j=1,2,...,Mis the achieved utilization by user
j.
For numerical evaluation, Alg. 2 is deployed by M
cognitive users independently for the network setting of
Sect. 3.4 and different values of Wmax. The average achieved
utilization are depicted in Fig. 6. This figure shows that by
limiting the number of secondaries collisions on the chan-
nels by deferring their exploitation on channels randomly
the achievable utilization is increased. This is more high-
lighted when the number of cognitive users is large, i.e.
M>8, when the secondaries collisions are the main reason
of utility degradation. Also, using larger values for max-
imum backoffwindow better protection against competing
simultaneous access can be provided. It is also interesting
3700
IEICE TRANS. COMMUN., VOL.E92–B, NO.12 DECEMBER 2009
to note that Alg. 2 outperforms Alg. 1 even for moderate
number of users. On the other hand, the fairness index is
more decreased using larger value for backoffwindow. For
example, using Wmax =256 the fairness index decreases
from f=1to f=0.95 for M=16,17,18,19,20 users.
This index for smaller values of Wmax would be closer to
one because the algorithm is more like to Alg. 1, e.g., for
Wmax =32 this index is about f=0.999. Therefore,
we could make tradeoffbetween increasing the sum of the
achieved utilization and the users fairness.
6. Conclusion
A simple MAC protocol for cognitive wireless networks is
presented. The objective is to opportunistically exploit the
spectrum white spaces by multiple cognitive users. Each
user maintains the history of the number of success and fail-
ures on each channel. Failure at a time slot on a channel is
happened if it was occupied by a primary or exploited by an-
other cognitive user simultaneously. The protocol is based
on the rule of least failures. That is at each decision stage,
the cognitive user hop to the channel which has incurred
the least number of failures. The properties of the protocol
for multiple cognitive users is investigated and its perfor-
mance is shown analytically and verified by simulations. It
is shown that the users utilizations are almost equal and de-
pend on the traffic statistics of the primary network and the
number of competing users. Using the independent channel
access assumption, an estimate of the achievable utilization
by each user is derived. It is shown that for a large number
of cognitive users, their distributed decisions using the pro-
posed algorithm come close to best decision to maximize
each user’s utilization rate.
References
[1] Q. Zhao and B.M. Sadler, “A survey of dynamic spectrum access,”
IEEE Signal Process. Mag., vol.24, no.3, pp.79–89, May 2007.
[2] J. Mitola, “Cognitive radio,” Licentiate Proposal, KTH, Stockholm,
Sweden, 1998.
[3] L. Lai, H. El Gamal, H. Jiang, and H.V. Poor, “Optimal medium ac-
cess protocols for cognitive radio networks,” Proc. IEEE Intl. Sym-
posium on Modeling and Optimization in Mobile, Ad Hoc, and
Wireless Networks,WiOPT2008, pp.328–334, March 2008.
[4] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized cogni-
tive MAC for opportunistic spectrum access in ad hoc networks: A
POMDP framework,” IEEE J. Sel. Areas Commun., vol.25, no.3,
pp.589–600, April 2007.
[5] A. Motamedi and A. Bahai, “Optimal channel selection for
spectrum-agile low-power wireless packet switched networks in un-
licensed band,” EURASIP Journal on Wireless Communications and
Networking, vol.2008, pp.1–10, Jan. 2008.
[6] C. Chou, S. Shankar, H. Kin, and K. Shin, “What and how much
to gain by spectrum agility?,” IEEE J. Sel. Areas Commun., vol.25,
no.3, pp.576–588, April 2007.
[7] F.P. Kelly, “Multi-armed bandits with discount factor near one: The
Bernoulli case,” Annals of Statistics, vol.9, no.5, 987–1001, 1981.
[8] V. Anantharam, P. Varaiya, and J. Walrand, “Asymptotically effi-
cient allocation rules for the multiarmed bandit problem with multi-
ple playspart I: I.I.D. rewards,” IEEE Trans. Autom. Control, vol.32,
no.11, pp.977–982, Nov. 1987.
[9] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge
University Press, 2004.
[10] L. Peterson and B. Davie, Computer Networks: A System Approach,
4th ed., Morgan Kaufmann, 2007.
Abdorasoul Ghasemi received his B.Sc.
degree (with honors) from Isfahan University
of Technology, Isfahan, Iran and his M.Sc. and
Ph.D. degrees from Amirkabir University of
Technology, Tehran, Iran, all in Electrical En-
gineering in 2001, 2003 and 2008, respectively.
He is currently working with Iran Telecommu-
nications Research Center (ITRC), Tehran, Iran
as a research associate. His research interests in-
clude Communication Networks, Network Pro-
tocols, and Signal Processing for Wireless Com-
munication Networks.
S. Mohammad Razavizadeh received his
B.Sc., M.Sc. and Ph.D. degrees, all in Electrical
Engineering from Iran University of Science and
Technology (IUST), Tehran, Iran in 1997, 2000
and 2006, respectively. From June 2004 to April
2005, he was a visiting scholar with Coding &
Signal Transmission (CST) Laboratory, Univer-
sity of Waterloo, ON, Canada. In May 2005, he
joined Iran Telecommunications Research cen-
ter (ITRC), Tehran, Iran, as a research assistant
where he is currently working as a research as-
sistant professor. His research interests are in the area of wireless commu-
nication systems including multi-antenna systems, cognitive radio, coop-
erative communications, mobile cellular systems and signal processing for
wireless communications.
