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Modeling of Opportunistic Spectrum Sharing with Sub-banding in Cognitive Radio Networks Samira Homayouni, Seyed Ali Ghorashi Abstract—Cognitive radio is a technology to solve the problem of spectrum under-utilization in some licensed bands. In this paper, we propose a model for opportunistic spectrum sharing in cognitive radio networks for a special case in which, two secondary users are allowed to coexist in a channel (sub-banding). The proposed model is such that, when all the channels are occupied by the primary and secondary users, then the secondary users’ channels can be divided into two sub-bands, and two secondary users may use a sub-band, simultaneously. The state equations of the system are derived based on two-dimensional Markov chain model. Next, the system performance is evaluated by some metrics such as blocking and dropping probability as well as channel utilization. Furthermore, the results for the cases of using and not using sub-banding for the secondary users have been compared. The results demonstrate that in a spectrum sharing system, channel sub-banding significantly reduces the blocking and dropping probabilities of the secondary users, with the cost of lower quality channels in comparison with state without using sub-bands. Index Terms— Dynamic spectrum access, cognitive radio, channel sub-banding, Markov chain, blocking and dropping probabilities.

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1 INTRODUCTION

D

ue to the growth of telecommunication services and increasing need for high data rate transmissions, users’ demand for scarce frequency spectrum resources has been increased. Traditional wireless networks use the stationary spectrum allocation methods for licensed user. Nowadays, due to the increase of demand for spectrum, this procedure faces spectrum shortage in certain bands. Although a large portion of the spectrum is already allocated, it has been used sporadically; at special times and locations, these bands are not used by the corresponding users. This causes a non-optimal use of available spectrum resources and the average utilization of spectrum has been reported very low, [1], [2]. Therefore, using dynamic spectrum access techniques has significantly improved the usage efficiency of scarce spectrum resources [3], [4], as well as cognitive radio networks [5], which have the ability to realize the environment for opportunistically and intelligently utilization of the spectrum. Several works has been done on the processes of sharing and having access to the radio spectrum in cognitive radio networks. Fundamental basis in these networks is the opportunistic spectrum access for secondary users. They can detect unused spectrum holes and use them by utilizing different spectrum sensing techniques without interfering with primary users [6]. In these systems, when a primary user appears in the secondary user channel, the ————————————————

• Samira Homayouni is with the Cognitive Telecommunications Research Group, Department of Electrical Engineering, Shahid Beheshti University G. C., Evin 198396113, Tehran, Iran. • Seyed Ali Ghorashi is Assistant Professor of the Department of Electrical Enginireeing, Cognitive Telecommuications Research Group, Shahid Beheshti University G. C.,Evin 1983963113, Tehran, Iran.

secondary user should stop its data transmission on this channel, and switches to any other available channels. If there is not any idle channel in the system, secondary users’ service will be forced to drop. A number of papers related to spectrum sharing have been investigated in the literature. Performance model of an opportunistic spectrum sharing scheme is proposed in [7]. Since in practical systems, spectrum sensing mechanism is associated with errors, the authors have generalized their model to the cases of unreliable spectrum sensing in [8] and [9]. Authors in [10] used the channel aggregation methods in cognitive radio networks in order to increase the spectral efficiency of the network. Using these methods, a secondary user can take advantage of several separate or adjacent parts of the spectrum to be used as a channel, simultaneously. In [11], two channel aggregation methods (fixed and variable) are studied. [10] and [11] indicate that channel aggregation for secondary users increases their throughput and makes more utilization of the spectrum. [12] suggests channel reservation methods for the primary and secondary users in order to prevent call dropping, and [13] introduces the use of backup channels for the secondary users. In this paper, unlike [12], and [13] that use additional range of resources such as queues or additional bandwidth, we introduce a way of dropping probability reduction by channel sub-banding for secondary users. Here, a method of dynamic spectrum access in cognitive radio networks is proposed, in which primary and secondary users are in the same spectrum band. The proposed scenario is such that, if all the channels are occupied by the primary and secondary users, then secondary users’

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JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 1, AUGUST 2011 2

the figure shown here, is only a simple scenario for better insight, and can be easily extended to other scenarios.

Fig.1. General model of spectrum sharing with channel sub-banding.

channels are divided into two sub-bands, and two secondary users can use a sub-band, simultaneously. We evaluate system performance of the proposed method in terms of various metrics such as blocking probability, dropping probability and total channel utilization. The proposed models in [7]-[9] are specific models in which the number of primary and secondary users in system are equal. In contrast, our proposed model is a general model that can easily be extended to different scenarios. The reminder of the paper is organized as follows. Section 2 explains the system model and its assumptions in detail. Section 3 develops Markovian model and channel allocation process of system. In section 4 different measurement metrics of interest are derived. Section 5 represents the analytical and simulation results and discussions, and illustrates the system performance with respect to the different metrics. Finally, the paper is concluded in section 6.

2 MODEL AND ASSUMPTIONS 2.1 System Model Consider a cognitive radio network consists of primary and secondary users (PUs and SUs) who operate at the same spectrum bands, and spectrum holes are used by SUs opportunistically. PUs have the priority to access the spectrum bands. Therefore, their activities should not be affected by the SUs’ transmissions. Suppose that the PUs and SUs are both operate on an infra-structured network. A simple diagram of a network is shown in Fig.1. The primary system Access Point (AP1), manages all the N channels in a given service area. Also, we assume that the SUs are equipped with cognitive radio equipment’s so that they have the capability to detect the PUs’ activities, i.e. they can recognize the presence of the PU in the band and their departure from special bands. Furthermore, the SUs’ access to channels is assumed to be controlled by a secondary access points (AP2). When a PU appears on a given SUs channel, the SUs should stop their transmission on the channel, and set their parameters, i.e. they have to reduce their power transmission or vacate the channel and attempt to access other available bands. Note that,

2.2 Spectrum Sharing with Sub-banding In this section we propose a new opportunistic spectrum sharing scheme in cognitive radio networks in which, if all channels are occupied by PUs and/or SUs, then the SUs’ channels are divided into two sub-channels. In this way, two SUs can use a channel simultaneously, if the channel is not occupied by the PUs. Obviously, the data transmission rate will be reduced by half. However, in many scenarios, to have a lower data rate communication link between many nodes (with a low dropping probability) is much more beneficial than having a few high data rate links between some selected nodes while experiencing a high level of dropping probability for SUs. A typical scenario is shown in Fig.1, where, the SUs have the capability of detection channel status without causing interference with PUs. Therefore, when an ongoing SU detects the presence of a PU in its current channel, SU releases its channel to PU. By considering the spectrum hand over, SU switches to one of other idle channels if it is possible. If all the channels are occupied by other PUs and there is no SU in system, the PU achieves the channel with a priority in accessing the channel and the ongoing SU will be dropped. If at that time, all channels are busy, and there is at least another SU in the system, the SU channel is divided to two sub-bands, and both SUs use the same channel simultaneously with a lower data rate. A PU’s request will be blocked only if all the channels are occupied by other PUs. When a SUs’ request arrives to the system and all of the channels are busy, and also all the SUs’ sub-bands have been occupied, the SU’s request will be blocked. But, if there is at least one SU in the system, the channel is divided to two sub-bands and the new SU coexists with ongoing SU in the same channel. When the PU’s request arrives to sub-bands which are used by SUs (e.g. A and B), and if there are at least two other SUs (e.g. C and D) in a system that their channels are not divided to sub-bands yet, each of the two SUs (A and B) joins the other SU channels (C and D) and PU occupies the initial channel. If there is only one SU in the system (e.g. A), which uses non-divided channel, one of the ongoing SUs (B and C) coexists with the SUs’ channel (A), and the other SU is dropped. If there is no subbanded channel of other SUs, then the two ongoing SUs will be dropped.

3 PERFORMANCE ANALYSIS AND CHANNEL ALLOCATION PROCESS In this section, we analyze the performance of the

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JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 1, AUGUST 2011 3

primary and secondary networks in the given service area in which the spectrum is shared. Assume that there are N channels to serve both primary and secondary traffic. All cells are statistically identical, so we analyze our model in a single cell. In each cell, the arrival times of PU and SU calls are independent Poisson processes with rates λ p and λs , respectively. The holding times (service duration) of both PU and SU calls follows an exponentially distributed with means 1 / h p and 1 / hs , respectively. The resident times of the PU and SU calls in the area under the service is exponentially distributed with mean 1 / rp and 1 / rs , respectively. We assume that the channel holding time is equal to the minimum holding time of calls and residence time in the given service area. Therefore, channel holding time for the PU and SU calls is exponentially distributed −1 −1 with means µ P = 1 / ( h p + r p )and µ S = 1 / ( h S + rS ), respectively [15]. For the sake of simplicity we assume that both PU and SU calls occupy only one channel per call. We define ( X1 (t ), X 2 (t)) as a 2-D Markov process with state spaces S = {( k1 , k 2 ) | 0 ≤ k1 ≤ N , 0 ≤ k 2 ≤ 2 N )} in which X 1 ( t ) and X 2 ( t ) are the number of channels that are used by PUs and SUs at time t, respectively.T kk1 1, k',2k 2 ,' is the transition rate from state ( k1 , k 2 ) to ( k1 ', k 2 '). We also define the indicator function of 1{ x} , which is 1 if x is true and is 0 in other cases. Channel allocation process by the primary access point is uniform; i. e. a PU selects a channel randomly with equal probability among the channels. Hence, the PU can randomly chooses an unused channel or a channel which is used by one or two SUs. The transition rate T kk1 1, k',2k 2 ' for the Markov model with sub-banding is obtained as follows:

T kk1 1, k+21 , k 2 = λ p 1{ 0 ≤ k 1 < N , 0 ≤ k 2 ≤ 2 ( N − ( i + 1 ))}

2N

N

∑ ∑ π (k , k 1

2

)I ( k1 , k2 ) = 1

(3)

k2 = 0 k1 = 0

By computing the steady state probabilities expressed above, we can obtain different metrics such as blocking probabilities for SUs and PUs, dropping probability for SUs, and channel utilization of the whole system.

4 PERFORMANCE METRICS In this section we describe different measures of interest, such as total channel utilization as well as blocking and dropping probabilities.

A. Blocking probability •

Blocking probability of SUs

The blocking of the SUs (with sub-bands) happens when all channels have been occupied by SUs and/or PUs, while an SU arrives in the system, and there is no available sub-band for new request, i.e. all channels of SUs have divided and occupied. Blocking probability of the SUs is denoted by PBSU that is given by: N

PBSU = ∑ π ( k1 , 2( N − k1 )) k1 = 0

(4)

For without sub-banding mode, blocking of the SUs happens when at the arrival of a SU, all channels are occupied by other SUs and/or PUs and there is no idle channel for a new request. PBSU in this case is given by: N

PBSU = ∑ π ( k1 , N − k1 )

T kk1 1, k−21 , k 2 = k 1 µ p 1{1 ≤ k 1 ≤ N , 0 ≤ k 2 ≤ 2 ( N − i )}

k1 = 0

T kk1 1, k, k2 2 + 1 = λ s 1{ 0 ≤ k 1 ≤ N − 1 , 0 ≤ k 2 ≤ 2 ( N − i ) − 1}

•

T kk1 1, k, k2 2 − 1 = k 2 µ s 1{ 0 ≤ k 1 ≤ N − 1 ,1 ≤ k 2 ≤ 2 ( N − i )} T kk1 1, k+21 , k 2 − 1 = λ p 1{ 0 ≤ k 1 < N , k 2 = 2 ( N − i ) − 1} T kk1 1, k+21 , k 2 − 2 = λ p 1{ 0 ≤ k 1 < N , k 2 = 2 ( N − i )} k + 1 , k −1

and

(1)

(5)

Blocking probability of PUs

A PU call request is blocked when upon an arrival of a primary call request, all the channels have been occupied by PUs and at that time there is no idle channel for a new primary call request. Blocking probability of the PUs is denoted by PBPU , and it does not depend on the channel sub-banding by SUs. Therefore it is obtained in both cases as:

k +1,k − 2

Two transitions rates T k 1 1, k 2 2 and T k 1 1, k 2 2 represent (6) the states in which one SU and two SUs are interrupted PBPU = π ( k1 = N , k 2 = 0) from the system, respectively. We define I ( k1 , k2 ) as a function that for 0 ≤ k1 ≤ N and B. Dropping probability 0 ≤ k 2 ≤ 2 N it is equal to 1, if 2 k1 + k 2 ≤ 2 N and I ( k1 , k2 ) = 0 Upon the arrival of a PU, if all channels have been ocotherwise. We denote π ( k1 , k 2 ) as the steady state probacupied by SUs and/or PUs, and also there is no idle bility for the state ( k1 , k 2 ) . Then, the balanced state equachannel for an ongoing SU or SUs to switch to, then the tion can be expressed as: user or users will be dropped. In this case all channels of (Tkk11, k+21,k2 + Tkk11,k−21, k2 + Tkk11, k+21, k2 −1 + Tkk11, k+21, k2 − 2 + Tkk11, k,k22 +1 + Tkk11, k,k22 −1 ) SUs have already divided and occupied. Also note that in such a case, at least one SU should be available in the sysI ( k1 , k2 ) π ( k1 , k 2 ) = Tkk11+,1,k2k2 I ( k1 +1,k2 )π ( k1 + 1, k 2 ) + Tkk11−,1,k2k2 I ( k1 −1, k2 ) tem. Dropping probability of the SUs is denoted by PDSU and can be written as follows:

π ( k1 − 1, k2 ) + Tkk , k,k +1 I ( k , k 1

1

2

2

I ( k1 , k2 −1)π ( k1 , k 2 − 1)

1

π ( k1 , k2 + 1) + Tkk , k,k −1 1

2 +1)

1

2

2

N

(2)

PDSU = ∑ π ( N − k 2 , k 2 ) k2 =1

(7)

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0.1

and

0.09

Analysis SU Analysis PU Simulation SU Simulation PU

PDSU = ∑ ∑ (Tkk11,k+21,k2 −1π (k1 , k2 ) + Tkk11,k+21,k2 −2π (k1 , k2 ))I ( k1 ,k2 ) k2 =1 k1 =0

(8)

for the cases of without and with sub-banding, respectively

C. Channel utilization probability The ratio of the average number of busy channels to the number of all channels is called total channel utilization. It is denoted by η and for the case of without subbanding it can be written as follows:

η=

1 N

N

N − k1

∑∑

(( k1 + k 2 )π ( k1 , k 2 ))I ( k1 ,k2 )

k1 = 0 k 2 = 0

(9)

SU and PU call blocking probabilities

2 N N −1 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 100

200

300 400 500 600 700 800 number of SUs ( number of PUs = 500)

900

1000

Fig. 2.Validation of PU and SU call blocking probabilities, in the case of channel sub-banding. 0.35

1 N 2( N − k1 ) η = [ ∑ ∑ (( k1 + k 2 )π ( k1 , k 2 ))I ( k1 ,k2 )1{0≤ k1 + k2 ≤ N } N k1 = 0 k2 = 0 N

+∑

2N

∑

( N π ( k1 , k 2 ))I ( k1 , k2 )1{k1 + k2 > N } ]

k1 = 0 k 2 = N − k1 +1

(10)

SU without sub-banding SU with sub-banding PU without sub-banding PU with sub-banding

0.3 S U and P U c all bloc k ing probabilities

In calculating this utilization, when a channel is used by two SUs, it is assumed that one channel is busy. For the case of with sub-banding η and can be written as follows:

0.25

0.2

0.15

0.1

0.05

5 NUMERICAL AND SIMULATION RESULTS

200

300

400 500 600 700 800 number of SUs ( number of PUs = 500)

900

1000

Fig. 3. SU and PU call blocking probabilities. 0.35 SU without sub-band SU with sub-band

0.3 S U D r o p in g p r o b a b ilit y

In this section, we present the numerical and simulation results to show the applicability and the performance of the proposed channel allocation method. In order to show the performance benefit of our proposed scheme, we also include the performance of an original system without sub-banding for comparison purposes. Also, we study the impact of channel sub-banding on blocking and dropping probabilities. To obtain numerical and simulation results, we consider a cellular system in which each cell has 10 channels available. We assume that the arrivals of both PU and SU calls follow a Poisson process with parameter λ p = λs = 1 call / hour , and the call time of users follows an exponential distribution with the mean of is 30 sec. We assume that the number of PUs per each cell is constant and it is equal to 500, while the number of SUs is variable to study the effect of users’ number on the performance of PUs. All the simulations are performed by MATLAB software. First, we validate the analysis of blocking probabilities by comparing the simulation and analytical results at the presence of sub-banding for both PUs and SUs. Notice that sub-banding has no effect on PUs blocking probability as indicated in Fig. 2 shows an exact compliance between simulation and analytical results of proposed

0 100

0.25 0.2

0.15 0.1

0.05 0 100

200

300

400 500 600 700 number of SUs ( numer of PUs = 500)

800

900

1000

Fig. 4. SU call dropping probability, in the case of using and not using channel sub-banding.

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0.95 0.9

total channel utilization

0.85 0.8 0.75 0.7 0.65 0.6

channel utilization without sub-band channel utilization with sub-band

0.55 0.5 0.45 100

200

300 400 500 600 700 800 Number of SUs (number of PUs =500)

900

1000

tem. But in the second case, as there is no idle channel in the system in this case, SU1 shares the spectral band with SU2 that may lead to a less utilization for individual users. After SU1's servicing is finished, SU2 continues receiving service till its service time finishes or a PU enters to the system. Therefore, the probability of busy channel increases and the utilization is higher in this case, particularly when there are more service requests and the average of busy channels to the total channels is large. Sub-banding the channels leads to a less individual utilization (throughput) for single users because, the data transmission rate will be reduced by half. In manyapplications, if the overhead header length is large in comparison with the frame length, this method loses its performance. This is a trade off, so we can say that this method efficiency decreases when the lengths of header in frame increases. This is the price paid for increasing the number of users.

Fig. 5. Channel utilization, in the case of using and not using channel subbanding.

6 CONCLUSION

schemes for both PUs and SUs and for different SU numbers. In Fig. 3, blocking probability for SUs and PUs is shown for two cases, with and without sub-banding, as a function of SUs number. We observe that the increase of SUs’ population in both cases have no effect on PUs blocking probability. This shows that in an ideal cognitive radio system, the SUs’ activities have no influence on PUs’ performance. The SUs blocking probability for the case of no sub-banding is more than the case of using subbanding. The reason is that, while all channels are busy, by dividing the channels to sub-bands, the number of available channels for incoming SU calls increases and the blocking probability of the SUs’ decreases, consequently. In Fig. 4, the dropping probabilities of the SUs for different populations of SUs, for two cases of using and not using sub-banding, are compared. According to this figure, if there are sub-bands, dropping probabilities of the SUs decreases, considerably. The reason is, when SUs are going to be dropped by arriving new PU calls, the channels of other SUs are divided into two bands, and two SUs use the same channel, simultaneously without dropping the ongoing SU calls. This decrease in dropping probability of SUs is the main advantage of sub-banding based proposed cognitive network. Fig. 5 compares the channel utilization for the two cases of without and with channel sub-banding. As you can see from the figure, channel utilization increases as the traffic increases for both cases. This is due to the fact that the probability of busy channel increases as the number of secondary users grows up. Furthermore, channel utilization is higher in the case of sub-banding, and when the traffic is high this difference is more. This can be explained as follows. Suppose a typical example that all channels are allocated to PUs and one channel is allocated to a SU, called SU1. As SU1 is receiving service, SU2 request for service arrives at the system. In the first case, this request fails since there is no free channel in the sys-

In this paper we formulated an opportunistic spectrum sharing model in cognitive radio networks under a special case which based on the channel sub-banding; two secondary users coexist in a channel. The proposed scenario is such that, if all the channels are allocated to the primary and secondary users, then secondary users’ channels are divided into two sub-bands, and two secondary users can use the same sub-band, simultaneously. The results for the case of using and not using subbanding for the secondary users are compared. Finally, it has been observed that in a cognitive network, channel sub-banding significantly reduces the blocking and dropping probabilities of the secondary users, with the cost of lower quality channels or lower individual throughput for single users than the case without sub-banding, off course.

ACKNOWLEDGMENT This work is supported by Iranian Education and Research Institute for Information and Communication Technology (ERICT), under the grant number 500/8974.

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Samira Homayouni is a M.Sc. student in Cognitive Telecommunications Research Group, at the Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran. Her research is focusedon Cognitive Radio Networks, opportunistic spectrum access, dynamic spectrum sharing and queuing theory. Seyed Ali Ghorashi Received his B.Sc. and M.Sc. Degrees in electrical engineering from the university of Tehran, Iran, in 1992 and1995, respectively. Then, he joined SANA Pro. Inc., where he worked on modeling and simulation of OFDM based wireless LAN systems and interference cancellation methods in WCDMA systems. Since2000, he worked as a research associate at King’s College London on “Capacity enhancement methods in Multi-leyer WCDMA systems”sponsored by Mobile VCE. In 2003 he received his PHD at King’s College and since then he worked at King’s College as a research fellow. In 2006 he joined Samsung Electronics (UK) Ltd as a senior researcher and now he is a faculty member of Cognitive Telecommunications Research Group, Department of Electrical Engineering, Shahid Beheshti University G.C., at Tehran, Iran, working on wireless communication.