Radio spectrum is a precious resource and characterized by fixed allocation policy. However, a large portion of the allocated radio spectrum is underutilized. Conversely, the rapid development of ubiquitous wireless technologies increases the demand for radio spectrum. Cognitive Radio (CR) methodologies have been introduced as a promising approach in detecting the white spaces, allowing the unlicensed users to use the licensed spectrum thus realizing Dynamic Spectrum Access (DSA) in an effective manner. This paper proposes a generalized framework for DSA between the licensed (primary) and unlicensed (secondary) users based on Continuous Time Markov Chain (CTMC) model. We present a spectrum access scheme in the presence of sensing errors based on CTMC which aims to attain optimum spectrum access probabilities for the secondary users. The primary user occupancy is identified by spectrum sensing algorithms and the sensing errors are captured in the form of false alarm and misdetection. Simulation results show the effectiveness of the proposed spectrum access scheme in terms of the throughput attained by the secondary users, throughput optimization using optimum access probabilities, probability of interference with increasing number of secondary users. The efficacy of the algorithm is analyzed for both imperfect spectrum sensing and perfect spectrum sensing.
1. Introduction
R
adio spectrum is a precious, limited and scarce resource which is completely regulated by authorized bodies like Federal Communication Commission (FCC) and Ofcom. CR technology is proposed as a novel solution
[1]
for the conflicts between the spectrum scarcity in unlicensed band and low spectrum utilization in licensed band. Unlicensed users equipped with CRs may in future be able to sense and opportunistically utilize a licensed spectrum when the corresponding licensed user is not utilizing it. In the existing DSA/CR terminology, licensed users are called the primary users and unlicensed users the secondary users
[2]
. The key idea behind the DSA is to maximize the efficiency of the spectrum while ensuring the interference caused to the primary users is kept at a tolerable level. The secondary users are allowed to share the licensed spectrum only when the primary users have not occupied. This spectrum occupancy awareness can be achieved by spectrum sensing algorithms such as energy detection, matched filtering and feature detection
[3]
. Upon identifying the free spectrum, the secondary users can use it for their own communication without causing interference to the primary users. This approach of CR is called Hierarchical Access Model
[4]
. In addition, Spectrum Underlay is another approach of CR which aims at operating below the noise floor of primary users by using Ultra Wide Band techniques.
Standards like WiFi (IEEE 802.11), WiMAX (IEEE 802.16) and Zigbee (IEEE 802.15.4) include CR techniques to some extend in the form of coexistence, power control and dynamic selection of frequencies
[5]
. From the standardization perspectives of CR, the first milestone in the development of CR is the IEEE 802.22 WRAN standard, which proposes a CR based physical and MAC layer for the use of TV bands by the CR users on a noninterfering basis
[5]
. CR and DSA architectures and concepts are further developed by SCC41 / P1900 standards group
[6]
.
The spectrum sharing among the primary and secondary users can be either in the form of cooperation or in the form of coexistence. The coexistence model of spectrum sharing enforces that the secondary user is responsible for the intricacies of spectrum sharing and no changes in the primary system is needed. In this paper, we adopt the opportunistic use of spectrum holes among the different forms of coexistence. Cooperation among the primary and secondary users need some form of interaction between them. For example, the primary user can demand payment from the secondary user and offer spectrum for their use.
The application of CR technology to DSA has created interest in developing spectrum access algorithms and policies for making efficient use of idle spectrum. In this context, there are several contributions which modeled the primary user  secondary user interactions using Markov models for dynamic spectrum sharing
[7

12]
. In
[7
,
8]
, the authors proposed a centralized scheme for dynamic spectrum access using CTMC model of primary user  secondary user interaction. They proposed a primary prioritized Markovian access framework based on CTMC and evaluated the optimum access probabilities for the secondary users to maximize their throughput. Their contribution does not include the errors arising from spectrum sensing. The authors of
[9]
proposed a spectrum access scheme using CTMC with optimal channel reservation for secondary users. In
[10]
the authors evaluated the performance of opportunistic spectrum access using a two dimensional Markov model for a military environment. In
[11]
, a framework based on Discrete Time Markov Chain for spectrum channelization between primarysecondary spectrum sharing was proposed. Their work included errors resulting from spectrum sensing for the performance evaluation and extended in
[12]
for flexible spectrum channelization schemes. A simple spectrum allocation algorithm based on 4D Markov chain model was presented in
[13]
for heterogeneous networks.
CR networks of the future may consist of primary and secondary users belonging to multiple networks operated by different service providers. This led to the distributed access coordination solutions as opposed to the centralized ones. To this end, there are several distributed schemes proposed in the literature. In
[14]
, a distributed algorithm for learning and cognitive medium access using a Multi Armed Bandit model was proposed based on the assumption of an independently and identically distributed (iid) distribution of primary user transmissions. In
[15]
, a game theoretic framework and no regret learning algorithm was proposed for distributed adaptive channel allocation. Another distributed approach to optimize the efficiency of spectrum allocation using a local bargaining mechanism was proposed in
[16]
. Thus in the literature, there are several centralized and distributed DSA schemes showing successful enhanced performance to increase the spectrum efficiency. Distributed DSA using a Markovian model was proposed in
[17

18]
both for perfect sensing and imperfect sensing. The throughput performance for one primary and two secondary users using a Distributed Primary prioritized Markovian Access (DPMA) algorithm was calculated. They did not consider a generalized scenario for performance evaluation and they assumed the spectrum sensing error parameters such as probability of detection and probability of false alarm. A detailed comparison of the existing models with the proposed is shown in
Table.1
.
Comparison of the proposed and the existing models
Comparison of the proposed and the existing models
In this paper, the spectrum access pattern using CTMC has been extended for a generalized scenario in which the spectrum sensing errors are incorporated from energy detection based spectrum sensing. The use of the proposed CTMC model for both centralized and distributed spectrum access approaches have been justified and the expected results based on the CTMC model are presented. The main objective of the CTMC based spectrum access algorithm is to optimize the throughput for multiple secondary users operating in the licensed spectrum of a single primary user. A detailed study on the use of access probabilities for the secondary users to achieve maximum throughput optimization is carried out. The performance of the algorithm is analyzed both for primary and secondary users in terms of throughput, access probability variations and interference.
Further this paper is organized as below: in Section 2 the System Model is discussed; in Section 3, Energy detection for spectrum sensing is explained; Section 4 describes the CTMC model for spectrum access; Simulation results and analysis are presented in Section 5; Section 6 is the conclusion of the paper.
2. System Model
We consider a primarysecondary system consisting of a primary network with one primary user and a CR network composed of
N
secondary users, each secondary user being equipped with a rudimentary CR system. The CR system model is either centralized or distributed depending on the architecture. The system model for the distributed CR system and centralized CR system with the proposed spectrum access scheme are shown in
Fig. 1
and
Fig. 2
respectively.
CR System with Distributed DSA
CR System with Centralized DSA
In the distributed approach
[16]
, the CR system employs a spectrum sensing algorithm at the physical layer. The spectrum sensing algorithm is responsible for the primary channel occupancy detection. The results of the spectrum sensing algorithm are reported to the MAC layer at the end of every sensing. The MAC layer is incorporated with the spectrum access algorithm based on CTMC model of primary user – secondary user interactions. Initially, if the spectrum is found to be free, the secondary user accesses the spectrum with a probability
α
and other secondary users trying to access the spectrum at the same time can cause interference to the existing user. The concurrent occurrence of secondary users is less likely in a CTMC based model. Nevertheless, the interference can be controlled by a proper access probability assignment. The access probability values are calculated by the secondary users on their own based on the sensing outcome and the instantaneous interference encountered by the secondary user such that their throughput is maximized. In such a distributed scheme, the CR system should necessarily have an interference measurement unit to measure the interference experienced by the secondary user with other secondary users.
In the centralized scheme
[7]
, each secondary user individually senses the primary spectrum and reports the results to the central base station via the common control channel. The fusion center in the CR base station is responsible for providing the access probabilities to the secondary users based on the sensing results and the service requests of the secondary users. The fusion center calculates the access probability such that the throughput attained by the secondary user is maximized.
The proposed model can be applied for any kind of spectrum access approach. In either case, the computation of access probabilities is very important and the actual method of computing the access probabilities is described in sec 4. Thus, we present the performance of the CTMC model which offers a wide range of applicability with high degree of practicality.
3. Energy Detection for Spectrum Sensing
In this section, we discuss the spectrum sensing mechanism performed by the CR system to identify the occupancy of the primary user. Spectrum sensing is performed periodically and it greatly depends on various aspects like channel conditions, hidden user problem, sensitivity of the sensing device, etc
[19]
. Consequently, the reliability of the sensing outcome may be limited. Spectrum sensing can be modeled as a binary hypothesis testing problem as,

H0: Primary user is idle

H1: Primary user is busy
When the primary user is present and the sensing algorithm selects
H_{0}
, it is a misdetection. Alternatively, when the primary user is not present and the sensing algorithm selects
H_{1}
, it is a false alarm. The performance of the sensing algorithm can be defined by the following probabilities: probability of false alarm
p_{f}
= Prob(
H_{0}
/
H_{1}
), probability of misdetection
p_{md}
= Prob(
H_{1}
/
H_{0}
) and the probability of detection
p_{d}
= Prob(
H_{1}
/
H_{1}
). The probabilities
p_{d}
and
p_{md}
are complementary, given by
p_{d}
= 1
p_{md}
. It is often desirable to have low
p_{f}
and high
p_{d}
. However, there always exists a tradeoff between the two values. Receiver Operating Characteristic (ROC) curves are useful in exploring the relationship between the two probabilities,
p_{d}
and
p_{f}
which is a measure of sensitivity and specificity of the spectrum sensing technique respectively
[19]
.
Energy detection is one of the most popular techniques employed for spectrum sensing. The energy detector, measures the energy received on the primary band over an interval of time and states the channel condition as occupied (
H_{1}
) if the signal energy is greater than a predefined threshold or unoccupied (
H_{0}
) otherwise
[19]
. The energy is computed using,
where
T_{i}(y)
is the test statistic (energy) computed at the
i
^{th}
sensing,
x_{i}(n)
is the signal observed on the primary band and
M
is the number of samples considered for energy detection over the particular interval of time. The decision is to distinguish between the two hypotheses using a predefined fixed threshold
λ
, given by,
Closed form solutions can be obtained for
p_{d}
and
p_{f}
[20]
where
based on the assumptions:

1. The primary user signals(t)is real Gaussian and the noisen(t)is Additive White Gaussian and real with zero mean and varianceσs2andσu2respectively.

2. The primary user signal and the noise are uncorrelated.
The decision threshold is calculated using,
where
p_{f(tar)}
is the target probability of false alarm.
Thus, the test statistic is compared with the decision threshold, the state of the channel is identified and the results are reported to the spectrum access algorithm.
In a centralized scheme, the sensing is performed by the individual secondary user and the results are reported to the CR base station. The base station is employed with fusion algorithms
[21]
and evaluates the state of the channel as busy or idle.
The CR base station fuses the binary decisions according to the logic rule
[21]
,
where
D_{i}
(i = 1,2,…N)
is the binary decision of local observation,
n
is an integer threshold which represents ‘
n
out of
N
’ voting rule. If
n
=1, the voting rule is the OR rule and
n=N
corresponds to the AND rule. Apart from this, few other fusion rules
[22]
are ChairVarshney (CV), Likelihood Ratio Test based on Channel Statistics (LRTCS), Equal Gain Combining (EGC), maximum ratio combining (MRC) can also be used.
In a distributed scheme, the CR system independently sense the channel condition and arrive at a decision or the secondary users in the CR network can exchange their sensing outcome via a common control channel and use any of the fusion rules to arrive at a final decision.
The sensing outcome in either case is reported to the spectrum access algorithm and the access probability values are calculated. The CTMC model for the spectrum access of secondary users, using which the access probability are calculated is described in the following section.
Cooperative sensing schemes are often vulnerable to Byzantine attacks in which malicious users send false decisions to the fusion centre so as to degrade the sensing performance. This necessitates the exclusion of potential attackers from participating in sensing. Many attacker detection and exclusion schemes are proposed in the literature
[23

27]
. Solutions for Byzantine attacks have been obtained in the optimal sense using minmax approach, game theory, based on Markovian model with conditional frequency check statistics and by using Hidden Markov Models. Our model assumes that all the secondary users are genuine users. Decision fusion in the presence of malicious users will degrade the performance of the system. The existence of Byzantine attacks for our model deserves further study and will be extended as future work.
4. CTMC Model for Spectrum Access
In this section, the CTMC model for DSA involving one primary user and multiple secondary users is studied.
Fig. 3
shows the CTMC state transition diagram for DSA with one primary user
P
and one secondary user
A
. Similarly, the CTMC state transition diagram for DSA with one primary user
P
and two secondary users
A
and
B
is shown in
Fig. 4
[16]
, which can also be extended to
N
number of secondary users. A system with single primary user (
P
) and two secondary users (
A
and
B
) is considered for illustration. The primarysecondary spectrum sharing is modeled as CTMC based on the assumptions of Poisson arrival of service requests (
λ
) and exponentially distributed service rates (
μ
). The arrival rates of the users
P
,
A
and
B
are denoted by
λ_{P}
,
λ_{A}
and
λ_{B}
respectively. Similarly the service rates for
P
,
A
and
B
are denoted by
μ_{P}
,
μ_{A}
and
μ_{B}
.
CTMC State diagram for one primary and one secondary user
CTMC State diagram for one primary and two secondary users
The state transition diagram of
Fig. 4
is explained as follows.
S_{0}
is defined as the idle state of the spectrum. If the secondary user
A
(or
B
) tries to access the spectrum, it first senses the spectrum. If the spectrum is found idle with no false alarm, the CTMC transits from
S_{0}
to
S_{A}
(or
S_{B}
) at a rate of (1
p_{f}
)
α_{A}
λ_{A}
(or (1
p_{f}
)
α_{B}
λ_{B}
), where
α_{i}
, is the access probability of the secondary user
i
,
i∈{A,B}
. To guarantee the spectrum access opportunity for the secondary user, the probability of false alarm
p_{f}
should be maintained low. If secondary user
A
(or
B
) completes its service before any request from secondary user
B
(or
A
), the CTMC transits to
S_{0}
with a rate of
μ_{A}
(or
μ_{B}
). Otherwise, the state transition will be
S_{AB}
with a rate of
α_{B}
λ_{B}
(or
α_{A}
λ_{A}
) where both secondary users share the spectrum. However, primary user may appear anytime during either
A
’s or
B
’s service or when both share the spectrum. If the secondary users identify the arrival of primary user, the CTMC transits to state
S_{P}
with a rate of (1
p_{md}
)
λ_{P}
. When the secondary users misdetect the arrival of primary, the CTMC transits to
S_{PA}
,
S_{PB}
or
S_{PAB}
correspondingly with a rate of
p_{md}λ_{P}
. The above three states represent the possibilities in which the primary user gets interfered with the secondary user’s communication and does not contribute to throughput. The probability that the CTMC is in these states should be avoided to protect the primary user from interference. This is possible only if the probability of misdetection
p_{md}
is very low. The spectrum sensing algorithm employed in the physical layer should be efficient enough to reduce the misdetection probability. Thus the probability of false alarm reduces the spectrum access opportunities to the secondary user and the probability of misdetection cause interference to the primary users. The description of the CTMC states is shown in
Table 2
.
State description of the CTMC
State description of the CTMC
The CTMC introduced for one and two users can also be extended to multiple secondary users. For
N
number of secondary users, then the total number of states in CTMC is 2
^{N+1}
. If
S
= [1,2,….
N
], the overall state space can be expressed as,
where state (1,[0,…,0]) denotes the state where the primary user is operating in the spectrum alone and the state {(0,
φ_{S}
)} represents that only the secondary users are in service. Similarly, the state {(1,
φ_{S}
)} represents that both the primary and secondary users interfere due to imperfect sensing.
For the generalized CTMC model, the state diagram can be represented as an
N
+1 dimensional hypercube. Each vertex of the hypercube represent a particular state in {(
φ_{P}
,
φ_{S}
)}, the edges are bidirectional which represent the user’s beginning or end of transition. The state probabilities can be obtained by solving the set of linear equations given in
Table 3
.
Algorithm to solve the state probability for CTMC with imperfect sensing
Algorithm to solve the state probability for CTMC with imperfect sensing
For each secondary user, the number of states in which it is in service is 2
^{N1}
, out of which there are
2^{N2}
states do not contribute to throughput and represent the interference with the primary user. If
N
increases, the contention for spectrum also increase and each user share less spectrum on an average. For
N
=2, the state probabilities are denoted by,
Each probability in p can be viewed as the ratio of allocation time to that particular state to the entire reference time
[7]
. The throughput of a particular secondary user can be evaluated by taking the product of the particular state probability that the secondary user is in service and the capacity achieved by the secondary user when operating in that band. The analytical solution to determine the state probability for one primary and one secondary user is derived in Appendix.
If
R_{P}
,
R_{A}
,
R_{B}
are denoted as the maximum achievable capacity values of primary user
P
, secondary users
A
and
B
respectively, the average throughput per user can be expressed as,
where
R_{A’}
and
R_{B’}
are the capacities of the secondary users
A
and
B
when they coexist. The capacity values
R_{i}
and
R_{i’}
can be evaluated by
[7]
,
where
W
is the communication bandwidth,
P_{t}
is the transmission power of the secondary user,
N_{0}
is the Additive White Gaussian Noise (AWGN) power and
G_{ij}
is the channel gain of
i
^{th}
transmitter to
j
^{th}
receiver.
ROC Curve of Energy detector
Symmetric distribution of CR
Each user’s throughput Vs Arrival Rate λ_{A} (Symmetric interference)
Asymmetric distribution of CR
Each user’s throughput Vs Arrival Rate λ_{A} (Asymmetric interference)
Overall Throughput Vs Arrival Rate λ_{A} (Symmetric interference)
Throughput Vs No. of secondary users
In a centralized approach, the fusion centre calculates the access probabilities such that the throughput achieved by the secondary users is maximized. For a two user scenario, we formulate this as an optimization problem where the goal is to determine the access probability of the secondary users
α_{A}
and
α_{B}
such that the system performance is maximized as given by,
where
p_{j}
and
p_{kj}
are the state probability values obtained using algorithm given in
Table 3
. As the closed form expression for
α_{j}
is difficult to obtain, their values can be numerically solved as shown in
Fig 12
. In a distributed scheme, one heuristic technique
[18]
to obtain the access probability which is expected to maximize the throughput is by using the idle probability
p_{0}
as the access probability from the perspective of that secondary user.
Throughput performance with access probabilities
As the number of secondary users (
N
) increase, the numbers of states grow exponentially. But this approach of assigning access probabilities to the users eliminates the need for power control to manage the interference
[8]
. In a dynamically changing spectrum environment, when global optimization approaches are used for power control to manage interference, for changing number of secondary users, the network needs to reoptimize the power allocation completely. This results in high complexity and overhead when there are frequency service requests. Hence the proposed approach considerably reduces the complexity involved in interference management with access probability assignment and maximizes the average throughput in the long run.
5. Simulation Results and Analysis
In this section, the performance of CTMC based spectrum access algorithm for secondary users is analyzed. Initially, the ROC performance of the energy detector is analyzed for the extraction of
p_{d}
and
p_{f}
values. Secondly, the throughput for two secondary users is studied. The overall throughput performance of the secondary users is compared with a CRCSMA based random access scheme. We also compare the performance of the proposed scheme with access probability assignment against the case with no access control. The overall performance gains achieved by the secondary users are clearly identified. The analysis is also extended for multiple secondary users. In addition, the maximum throughput is explored numerically using the optimum access probabilities. Finally, the collision probability analysis is performed based on the access probability.
 5.1 Performance of the Energy Detector
The performance of the energy detector between
p_{f}
and
p_{d}
are evaluated using ROC curves. The decision threshold is obtained based on
p_{f}
. The number of samples
M
considered for the analysis of energy detection is varied from 500 to 5000. The state of the channel (
H_{0}
/
H_{1}
) is determined by comparing the decision threshold with the calculated energy. The detection probability
p_{d}
is obtained both analytically and by Monte Carlo simulations. From
Fig. 5
, it is observed that the probability of detection increases as the number of samples increases for a fixed probability of false alarm.
The probability of detection
p_{d}
and probability of misdetection
p_{md}
are obtained for false alarm probabilities
p_{f}
of 0.01, 0.05 and 0.1. The number of samples
M
considered for the analysis is varied from 500 to 5000 as shown in
Table 4
. It is clearly evident from the table that when the probability of false alarm increases, probability of misdetection decreases and vice versa. Since the probability of misdetection should be less to protect the primary user from interference with the secondary users, further analysis is carried out using
p_{f}
= 0.1 and
p_{md}
= 0.001.
ROC values extracted fromFig. 5
ROC values extracted from Fig. 5
 5.2 Secondary User Throughput Analysis
For this analysis, one primary and two secondary users are considered. The parameters considered for the analysis are shown in
Table 5
.
Simulation Parameters
In case one, symmetric interference between the secondary users
A
and
B
is assumed. The transmitter and receiver location of the secondary users are shown in
Fig. 6
. The throughput performance of secondary users
A
and
B
for perfect sensing (
p_{f}
= 0 and
p_{md}
= 0) and imperfect sensing (
p_{f}
= 0.1 and
p_{md}
= 0.001) are shown in
Fig.7
. From (12) and (13), for the locations stated above, it is clear that
R_{A}
=
R_{B}
>
R_{A’}
=
R_{B’}
. Thus, when
λ_{A}
< 85s
^{1}
, the throughput of the secondary user
A
is less than the throughput of the secondary user
B
. This is because the secondary user
A
has limited access to the spectrum than secondary user
B
till
λ_{A}
=85s
^{1}
. When
λ_{A}
=
λ_{B}
, the throughput of both the users are identical as they experience similar channel conditions and service requests. When
λ_{A}
> 85s
^{1}
, the throughput of secondary user
B
is reduced. Under perfect sensing, the throughput is better for secondary users
A
and
B
without affecting the throughput of the primary user. For the parameters considered as shown in
Table 5
, the primary user occupancy is 45.95% under perfect sensing. For imperfect sensing, the throughput of the primary user is slightly reduced to 45.89%, since low value is considered for misdetection probability.
In case two, asymmetric interference between the secondary users
A
and
B
is assumed. The transmitter and receiver location of the secondary users are shown in
Fig. 8
. In this scenario, from (12) and (13),
R_{A}
>
R_{B}
>
R_{A’}
>
R_{B’}
since the channel for secondary user
B
is inferior to secondary user
A
. Thus the average throughput of secondary user
B
is lesser than that of secondary user
A
as shown in
Fig. 9
. It is observed, similar to case one, the primary user spectrum occupancy is unaffected for perfect sensing and is 0.06% less for imperfect sensing. The average throughput performance of secondary users is tabulated in
Table 6
.
Throughput Performance of secondary usersAandB
Throughput Performance of secondary users A and B
In both cases one and two, the throughput performance of the spectrum access algorithm using the proposed CTMC model is analyzed for two secondary users without access control i.e., spectrum access probabilities are not assigned to the secondary users. The proposed scheme is also compared with the CSMA based random access scheme
[29]
in
Fig. 10
. For this comparison, a symmetric distribution of the transmitter receiver pair is assumed. A time slotted CSMA scheme is considered with the slot size of 5ms. We see that the overall throughput gain of the proposed is better than the CSMA for increasing arrival rates of secondary user
A
. This is because the secondary users are not allowed to utilize the spectrum simultaneously. However in the proposed scheme, secondary users can simultaneously share the spectrum and properly assigned access probabilities will enhance the overall performance gain. A similar performance can also be achieved in an asymmetric interference scenario. The access control probabilities provide control over the spectrum access and optimize the overall throughput of the secondary users. Thus, in the following section, the overall throughput for N secondary users is analyzed with and without access control and the use of access probabilities to the secondary users is justified.
 5.2 Spectrum Access among Multiple Secondary Users
Fig. 11
shows the overall throughput for increasing number of secondary users without access control for both perfect and imperfect sensing. The spectrum access among multiple secondary users should be controlled by properly assigning the access probabilities. This can be accomplished through centralized or distributed approach which depends on the secondary network architecture. As the number of user increases, the average throughput per user is highly reduced, since the contention for spectrum is intense and each user shares a little spectrum.
The overall throughput of secondary users with and without access control probabilities is compared as shown in
Fig.12
both for perfect and imperfect spectrum sensing. As the access probability is reduced, the secondary user throughput increases. From
Fig.13
, it can be observed that there exists a particular access probability for which the throughput is maximum. Hence, the access probability which maximizes the throughput is obtained numerically for the secondary users and assigned to them. It is also noted that the access probability which maximizes the throughput varies for increasing number of secondary users. With access control, the CTMC based spectrum access scheme achieves 12% to 42% higher throughput on an average. The throughput comparison for with and without access control is illustrated in
Table 7
.
Throughput Vs Access probability
Throughput comparison for with and without access control
Throughput comparison for with and without access control
From
Fig.14
, the collision probability, which is the probability that the primary user get interfered with the secondary users, is observed. The collision probability increases with the access probability of secondary user and increases with increasing number of secondary users.
Fig. 15
shows the variation of collision probability with increasing probability of misdetection for various access probability values. It is evident that the collision probability decreases with decrease in access probability.
Collision Probability Vs Access probability
Collision Probability Vs Probability of misdetection
5. Conclusions
In this paper, a flexible spectrum access scheme using CTMC suitable for centralized or distributed CR network is presented. The proposed model can support a wide range of implementation possibilities. Secondary users perceive the behavior of the spectrum occupancy as a CTMC model. The primary spectrum occupancy awareness is achieved by sensing techniques. Based on the statistics of the secondary users and the sensing results, access probabilities are assigned to the secondary users such that the throughput of the secondary users is maximized. The tradeoff between the secondary user throughput and the sensing accuracy is studied. The performance of the scheme with and without access probability control is compared. The throughput degradation with respect to the increasing number of secondary users is analyzed. The possible probability of collision is also analyzed for various access probabilities. Simulation results show that for the abovementioned situations, these access probabilities help the secondary user to increase their throughput and reduce the interference.
BIO
K.Muthumeenakshi graduated with a B.E in Electronics and Communication Engineering from Bharathiar University in 1999. She received her M.E in Applied Electronics from Anna University, Chennai, India in 2004. At present, she is working as an Assistant professor in the Department of ECE, SSN College of Engineering, Chennai, Tamil Nadu. She is currently pursuing her PhD in Anna University, Chennai. Her area of research interests are spectrum sensing and dynamic spectrum access in cognitive radios.
S. Radha graduated with a B.E in Electronics and Communication Engineering from Madurai Kamaraj University, India in 1989. She obtained her M.E in Applied Electronics from Government College of Technology, Coimbatore, India and her PhD in the area of mobile ad hoc networks from Anna University, Chennai, India. At present, she is working as a Professor and Head of the Department of ECE, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam, India. She has published more than 50 papers in international and national journals and conferences. Her current areas of research include security and architecture issues of mobile ad hoc and sensor networks, spectrum sharing in cognitive radios. She received the ISTE  S.K.Mitra Memorial Award in October 2006 for the Best Research paper published in the IETE Journal of Research and the CTS  SSN Best Faculty Award  2007 and 2009 for the outstanding performance in the academic year 200607 and 200809.
Mitola III J.
,
Doctor of Technology Dissertation
2000
“Cognitive Radio: An Integrated Agent Architecture for Software Defined Radio”
Royal Institute of Technology (KTH)
Sweden
Doctor of Technology Dissertation
Akyildiz F.
,
Lee W.Y.
,
Mohanty. S.
2006
“Next generation / dynamic spectrum access / cognitive radio wireless networks: A survey”
Computer Networks Journal (Elsevier)
Article (CrossRef Link)
50
2127 
2159
DOI : 10.1016/j.comnet.2006.05.001
Tevfic Y.
,
Arslan H.
2009
“A survey of spectrum sensing algorithms for cognitive radio applications”
IEEE Communications Surveys & Tutorials
First Quarter, Article (CrossRef Link)
11
(1)
116 
130
DOI : 10.1109/SURV.2009.090109
Zhao Q.
,
Sadler B.M.
2007
“A survey of dynamic spectrum access”
IEEE Signal Processing Magazine
Article (CrossRef Link)
24
(3)
79 
89
DOI : 10.1109/MSP.2007.361604
Sherman M.
,
Mody A.N
,
Martinez. R
,
Rodriguez. C
,
Reddy. R
2008
“IEEE standards supporting cognitive radio and networks, dynamic spectrum access and coexistence”
IEEE Communications Magazine
Article (CrossRef Link)
46
(7)
72 
79
DOI : 10.1109/MCOM.2008.4557045
Standards Coordination Committee (SCC), 41
http://www.scc41.org
Wang B.
,
Ji Z.
,
Liu K. J. R.
2007
“Primaryprioritized Markov approach for dynamic spectrum access"
in Proc. of IEEE DySPAN 2007
Dublin, Ireland
Article (CrossRef Link)
507 
515
Wang B.
,
Ji Z.
,
Liu K. J. R.
,
Clancy T. C.
2009
"Primaryprioritized Markov approach for dynamic spectrum allocation"
IEEE Transactions on Wireless Communications
Article (CrossRef Link)
8
(4)
1854 
1865
DOI : 10.1109/TWC.2008.080031
Zhu X.
,
Shen L.
,
Yum T.S.P.
2007
“Analysis of cognitive radio spectrum access with optimal channel reservation”
IEEE communication letters
Article (CrossRef Link)
11
(4)
304 
306
DOI : 10.1109/LCOM.2007.348282
Tang S.
,
Mark Brain.L.
2008
“An analytical performance of Opportunistic Spectrum Access in a Military Environment”
in Proc of Wireless Communication and Networking Conference
Article (CrssRef Link)
2681 
2686
Gelabert X.
,
Sallent O.
,
PerezRomero J.
,
Agusti Ramon
2010
“Spectrum Sharing in cognitive radios with imperfect spectrum sensing: A discrete time markov model”
Computer Networks Journal (Elsevier)
Article (CrossRef Link)
54
2519 
2536
DOI : 10.1016/j.comnet.2010.04.005
Gelabert X.
,
Sallent O.
,
PerezRomero J.
,
Agusti Ramon
2011
“Flexible spectrum access for opportunistic secondary operation in cognitive radio networks”
IEEE transactions on communications
Article (CrossRef Link)
59
(10)
2659 
2664
DOI : 10.1109/TCOMM.2011.071111.110024
Ha Jeounglak
,
Kim Jinup
,
Kim SangHa
2010
“Performance Analysis of Dynamic Spectrum Allocation in Heterogeneous Wireless Networks”
ETRI Journal
Article (CrossRef Link)
32
(2)
DOI : 10.4218/etrij.10.1409.0032
Anandkumar A.
,
Michael N.
,
Tang A. K.
,
Swami A.
2011
“Distributed algorithms for learning and cognitive medium access with logarithmic regret”
IEEE Journal on Selected Areas in Communications
Article (CrossRef Link)
29
(4)
731 
745
DOI : 10.1109/JSAC.2011.110406
Nie N.
,
Comaniciu C.
2006
“Adaptive channel allocation spectrum etiquette for cognitive radio networks”
Mobile Networks and Applications
Article (CrossRef Link)
11
779 
797
DOI : 10.1007/s110360060049y
Cao L.
,
Zheng H.
2005
“Distributed spectrum allocation via local bargaining”
in Proc. of IEEE SECON 2005
Santa Clara, CA
Article (CrossRef Link)
475 
486
Muthumeenakshi K.
,
Radha S.
2013
“Distributed Cognitive Radio Spectrum Access with Imperfect Sensing Using CTMC”
International Journal of Distributed Sensor Networks
Article ID 257801, Article (CrossRef Link)
2013
11 
DOI : 10.1155/2013/257801
Surendran. R
,
Muthumeenakshi. K
,
Radha. S
2011
“A distributed algorithm for dynamic spectrum access using primaryprioritised markov model”
in Proc. of IEEE International conference on Process Automation, Control and Computing
Article (CrossRef Link)
1 
5
LópezBenítez M.
,
Casadevall F.
2012
“Improved energy detection spectrum sensing for cognitive radio”
IET Communications
Article (CrossRef Link)
6
(8)
785 
796
DOI : 10.1049/ietcom.2010.0571
Liang YingChang
,
Zeng Yonghong
,
Peh E.C.Y.
,
Hoang Anh Tuan
2008
“SensingThroughput Tradeoff for Cognitive Radio Networks”
IEEE Transactions on Wireless Communications
Article (CrossRef Link)
7
(4)
1326 
1337
DOI : 10.1109/TWC.2008.060869
Zhang Wei
,
Mallik Ranjan K.
,
Letaief Khaled Ben
2009
“Optimization of Cooperative Spectrum Sensing with Energy Detection in Cognitive Radio Networks”
IEEE Transactions in Wireless Communications
Article (Cross Ref)
8
(12)
Lee Jeong Woo
2013
“Cooperative Spectrum Sensing Scheme over Imperfect Feedback Channels”
IEEE Communications Letters
Article (CrossRef Link)
17
(6)
1192 
1195
DOI : 10.1109/LCOMM.2013.050313.130531
Rawat A.S.
,
Anand P.
,
Chen H.
,
Varshney P.K.
2011
“Collaborative spectrum sensing in the presence of Byzantine attacks in cognitive radio networks”
IEEE Transactions on Signal Processing
Article (CrossRef Link)
59
(2)
DOI : 10.1109/TSP.2010.2091277
Li H.
,
Han Z.
2010
“Catch me if you can: An abnormality detection approach for collaborative spectrum sensing in cognitive radio networks”
IEEE Transactions on Wireless Communication
Article (CrossRef Link)
9
(11)
Vempaty A.
,
Ozdemir O.
,
Agrawal K.
,
Chen H.
,
Varshney P.
2013
“Localization in wireless sensor networks: Byzantines and mitigation techniques”
IEEE Transactions on Signal Processing
Article (CrossRef Link)
61
(6)
DOI : 10.1109/TSP.2012.2236325
He X.
,
Dai H.
,
Ning P.
2013
“HMMBased Malicious User Detection for Robust Collaborative Spectrum Sensing”
IEEE Journal on Selected Areas in Communications
Article (CrossRef Link)
31
(11)
He X.
,
Dai H.
,
Ning P.
2013
“A Byzantine Attack Defender in Cognitive Radio Networks: The Conditional Frequency Check”
IEEE Transactions on Wireless Communication
Article (CrossRef Link)
12
(5)
DOI : 10.1109/TWC.2013.031313.121551
McHenry M. A.
2005
“NSF spectrum occupancy measurements project summary”
http://www.sharedspectrum.com/inc/content/measurements/nsf/NSF_Project_Summary.pdf
“Performance analysis of CSMA in an unslotted cognitive radio network with licensed channels and unlicensed channels”
EURASIP Journal on Wireless Communications and Networking 2012
Article (CrossRef Link)
2012
(12)