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Opportunistic channel selection approach under collision probability constraint in cognitive radio systems
Computer Communications 32 (2009) 1914–1922
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Opportunistic channel selection approach under collision probability constraint in cognitive radio systems Qinghai Xiao a,b,*, Yunzhou Li a, Ming Zhao a, Shidong Zhou a, Jing Wang a a
State Key Laboratory on Microwave and Digital Communications, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China b School of Electronic Technology, Information Engineering University, Zhengzhou 450004, China
a r t i c l e
i n f o
Article history: Available online 25 July 2009 Keywords: Opportunistic channel selection Collision probability Collision tolerable level Collision rate Handoff rate
a b s t r a c t In this work, we consider a cognitive radio system with multiple primary channels and one secondary user, and then we introduce a channel-usage pattern model and some basic concepts in this system. Based on this system model and the basic concepts, we propose two opportunistic channel selection algorithms to optimize the throughput of the secondary user: minimum collision rate channel selection algorithm and minimum handoff rate channel selection algorithm. According to the two algorithms, we, respectively, present the channel selection scheme based on minimum collision rate algorithm (CSSMCRA) and the channel selection scheme based on minimum handoff rate algorithm (CSS-MHRA) under the constraint that the collision probability is bounded below collision tolerable level. Theoretical analysis and simulation results both show that, on one hand, both CSS-MCRA scheme and CSS-MHRA can follow the constraint of collision tolerable level; on the other hand, the performance of CSS-MCRA scheme is better than that of CSS-MHRA scheme if handoff latency is zero or very low, while the performance of CSS-MHRA scheme is better than that of CSS-MCRA scheme if handoff latency is long enough. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The electromagnetic spectrum is a precious and limited natural resource, the use of which is licensed by government agencies. The conventional spectrum management policies use fixed spectrum assignment to prevent mutual interference all the time. This has led to the artificial radio spectrum scarcity that most of the available radio spectrum has already been allocated to various services. The frequency allocation chart [1] in the United States indicates multiple allocations over all of the frequency bands. On the other hand, careful studies of the spectrum-usage pattern by Spectrum Policy Task Force (SPTF) have revealed that many portions of the allocated radio spectrum experience low utilization and they are either unoccupied or partially occupied for long periods of time [2]. Extensive measurements also indicate that many portions of licensed spectrum lies unused at any given time and location [3]. Even when a channel is actively used, the bursty arrivals of many applications result in abundant spectrum opportunities at the slot level.
* Corresponding author. Address: State Key Laboratory on Microwave and Digital Communications, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China. Tel.: +86 13683219321. E-mail address: [email protected] (Q. Xiao). 0140-3664/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2009.06.015
Growing demand and low utilization for the radio spectrum lead to the concept of secondary use, which forms the key rationale for opportunistic spectrum access (OSA) envisioned by the DARPA XG program [4]. The main idea is to exploit instantaneous spectrum availability by opening licensed spectrum to secondary users, and allow unused or underused portions of the radio spectrum owned by primary (licensed) users (PUs) to become temporarily available for secondary (unlicensed) users (SUs). Namely, it allows secondary users to identify available spectrum resources and communicate in a manner that limits the level of interference received by the primary users. The OSA system requires that the secondary user efficiently utilizes unoccupied spectrum holes while avoiding interference with primary users [5]. The spectrum-usage patterns of primary users vary over time, thus, the secondary user experiences dynamic spectrum hole and needs to intelligently adapt its channel usage. In conventional methods, the secondary user senses local channels through individual or cooperative sensing [6–10], and reconfigures its own access parameters according to the channel-usage patterns of primary users. This adaptation is based on the current observation of the spectrum usage by primary users. Once detecting a primary user’s occurrence on its current band in use, the secondary user pauses transmissions, starts to sense the channel and waits next opportunity to resume transmissions. The conventional methods can not schedule future transmissions without any prior information about future spectrum holes, and results in that the
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secondary user frequently collides with primary users. Primary users can suffer from short-term interference until they are discovered. Collisions occur when the secondary user can not predict the appearance of primary users, and can only react to current observations of primary users. In this paper, we propose two channel selection schemes based on spectrum holes prediction where the secondary user builds a predictive model of primary users’ channel usage and predicts near future spectrum availability based on past observations. There have been several prior works on dynamic spectrum access and sensing. The most relevant works are [11,12]. In [11], the authors proposed a proactive access scheme based on the characteristics of TV-broadcast and explored the feasibility of proactive access method. In [12], the authors extended this work to the exponential ON–OFF model. Our work discusses OSA problems based on spectrum holes prediction while primary user traffic model is general model (including without limitation, the exponential ON–OFF model). Moreover, [11] mainly focuses on maximizing throughput of the secondary user, and [12] mainly adopts proactive channel access approach to minimize disruptions to primary users, while our work focuses on channel selection scheme to maximize throughput of the secondary user on the basis of satisfying the constraint of collision tolerable level allowed by primary network. The remainder of this paper is organized as follows. The next section describes the system model and some basic concepts. A channel selection scheme based on minimum collision rate algorithm is proposed in Section 3. A channel selection scheme based on minimum handoff rate algorithm is proposed in Section 4. Performance analysis and corresponding simulation results are presented in Section 5. Our main conclusions are summarized in the final section.
er than s and the duration is an integral-number of s for convenience. In this paper, there exist the following basic assumptions: (A1) The system is stationary and ergodic. (A2) The secondary user performs perfect sensing, i.e., the false alarm and missing probability are zero. (A3) The secondary user only selects one channel every time. (A4) The arrival process of one primary user is Poisson process while the service time distribution is arbitrary. This assumption holds in many situations such as voice traffic, data session and data network. When there are multiple primary users in a channel, the system can be modeled as an M/G/ 1 queue with multiple inputs and it can be proved that the idle period is exponential distribution while the busy period is general distribution [13]. Therefore, we can assume that the idle period of the ith channel is exponential distribution and its expectation is 1=ln while its busy period is general distribution and its average value is 1=mn . The idle period distribution function of the nth channel can be given as
fn ðtÞ ¼ un eun t
for t P 0;
n ¼ 1; . . . ; N:
2.2. Channel utilization and throughput In the nth channel, channel utilization (CU) of the primary users is defined as the fraction of time in which the channel is occupied by the primary users, i.e., the channel is in ON (busy) state, denoted by gPU n . And under assumption (A1), (A4), it can be given as [14]
gPU n ¼ lim PM M!1
PM
i¼1 1=vn;i
i¼1 ð1=un;i
þ 1=vn;i Þ
¼ lim
M!1
M=vn un ¼ ; M=un þ M=vn un þ vn
2. System model and basic concepts In this section, we consider multi-channel usage pattern model in the system with multiple primary channels and one secondary user, and explain some basic concepts. 2.1. Multi-channel usage pattern model Consider a system with multiple primary channels and one secondary user. Primary users are the licensed users of these channels and thus have higher priority over the secondary user. A channel is called idle if it is unoccupied by one or more primary users, and busy otherwise (Fig. 1). The duration of idle period is the time interval starting at the release of the channel until the first packet arrival. Similarly, the duration of busy period is the time interval starting at the first packet arrival until the moment that the channel becomes idle. We regard one sensing time of the secondary user as one time slot, denoted by s, i.e., s ¼ 1 time slot. Assuming that the duration of every idle period or busy period is much great-
ð1Þ
ð2Þ where 1=vn;i and 1=un;i denote the duration of the ith busy period and the duration of the ith idle period of the nth channel, respectively. The definition of spectrum hole is given in [15]. We define spectrum holes utilization (idle period utilization) of the nth channel as
gSH n ¼ lim
T!1
Duration of spectrum holes utilized by SU in ½0; T : Duration of all spectrum holes in ½0; T ð3Þ
In multiple primary channels, we can define the throughput of the secondary user as the expected number time slots that the secondary user accesses some channels in a specified time period. Thus, under the assumption of stationarity and ergodicity, we can denote normalized throughput of the secondary user as
rt ¼ lim
T!1
Number of access in ½0; T : Number of time slots in ½0; T
ð4Þ
2.3. Collision probability and collision rate
Fig. 1. Multi-channel usage pattern model.
Because the secondary user performs perfect sensing, collisions happen only when primary users reoccur and occupy the same channel while the secondary user is transmitting on the channel. Collision probability (CP) is the probability of the secondary transmission colliding with the primary transmission. In this paper, we assume that the duration of one collision period is regarded as one time slot for convenience, i.e., one collision period is also equal to ss . Thus, under the assumption of stationarity and ergodicity, we can define collision probability of the nth channel as
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pcn ¼ lim
T!1
Number of collisions in ½0; T : Number of busy time slots of PU in ½0; T
ð5Þ
Collision tolerable level (CTL) of the nth channel is defined as the maximum probability of collision allowed by the primary users, denoted by 1n .The wireless communication systems, which provide with different services in different networks, can tolerate different collision types and collision probability. For example, voice service is real-time but it can tolerate a few packet losses. Whereas, data service can not lose packet but it may tolerate a little time delay. Therefore, almost all of different services can tolerate a few collisions in despite of the difference of collision types. In our work, we do not place emphasis on studying the differences of collision types, but we only assume that the primary users can accept collision tolerable level 1n . Collision tolerable level is also collision probability constraint of the cognitive radio system. Thus, the system must satisfy:
0 6 pcn 6 1n :
ð6Þ
Otherwise, too many collisions will affect the primary users’ transmission. It is a difficult key problem how to identify collision. Due to performing perfect sensing, collisions occur only when primary users reoccur and occupy the channel while the secondary user is transmitting. Because the secondary user can not sense the channel when transmitting, the secondary user can but regard transmission failure as collision. Though there exist many other factors such as channel fading, environment interference, that result in transmission failure, these do not increase collision probability, and only decrease spectrum holes utilization and secondary user’s throughput. In this work, for convenience of analysis, we assume that transmission failure only arise from collision, i.e., reoccurrence of the primary user. However, in a practical system, there surely exists the problem that other non-collision transmission failures lead to decrease spectrum holes utilization and secondary user’s throughput. But owing to sensing immediately after collision happens and performing perfect sensing, the secondary user wastes at most one time slot at every time when a non-collision transmission failure occurs. Therefore, under the assumption that transmission failure only arises from collision, we can only obtain maximal theoretical upper bound of spectrum holes utilization under the constraint of collision tolerable level. If the secondary user can exactly identify collision with primary users, we can understand that there exists at most one collision period at the beginning of every busy period. And the secondary user adopts this strategy where it keeps transmitting until primary users reoccur and collision happens if it senses the channel idle. Obviously, on the basis of the access strategy, every channel has the maximum collision probability (MCP), and we denote the maximum collision probability of the nth channel as PCn;max . Under the assumption of stationarity and ergodicity, we can obtain the following expression on average:
Pcn;max ¼ lim PM M!1
M
i¼1 1=vn;i
¼ lim
M!1
M ¼ vn ; M=vn
ð7Þ
where 1=vn;i is the duration of the i th busy period of the nth channel. We can see from (7) that the maximum collision probability is equal to the reciprocal of average value of the busy period. In one primary channel, we can evaluate the performance using collision probability. However, in multiple primary channels, it is difficult to define the collision probability. Thus, to evaluate the performance, we propose the collision rate. We define collision rate as the number of collisions that happen when primary users reoccur and occupy the channel while the secondary user is transmitting in a specified time period. Thus, under
the assumption of stationarity and ergodicity, we can denote collision rate as
rc ¼ lim
T!1
Number of collisions in ½0; T : Number of time slots in ½0; T
ð8Þ
2.4. Channel handoff rate In one primary channel, there does not exist channel handoff. However, in multiple primary channels, it is key problem how to switch from one channel to another. Thus, to evaluate the performance, we propose the channel handoff rate. We define channel handoff rate as the expected number of handoffs occurring between different channels in a specified time period. Thus, under the assumption of stationarity and ergodicity, we can denote channel handoff rate as
rh ¼ lim
T!1
Number of handoffs in ½0; T : Number of time slots in ½0; T
ð9Þ
Here, a handoff is made between different channels. That is, the handoff can be a general handoff between different channels in the same cell, and it can also be horizontal handoff in homogeneous wireless networks, and vertical handoff in heterogeneous wireless networks.
3. Minimum collision rate algorithm Our aim is to maximize the throughput of the secondary user under the constraint of collision tolerable level of every primary channel. In the case of one secondary user and one primary channel, it is easily understood that maximizing the throughput of the secondary user is equivalence to maximizing spectrum holes utilization of the primary channel. However, in the case of one secondary user and multiple primary channels, maximizing spectrum holes utilization of one certain primary channel can not always result in maximizing the throughput of the secondary user. To maximize the throughput of the secondary user, we propose two channel selection schemes in this section and in the next section, respectively. An intuitive idea is that at every time slot, the secondary user selects and accesses the channel, of which collision probability is less than that of all other channels. On the basis of this idea, we present a channel selection scheme based on minimum collision rate algorithm. 3.1. Minimum collision rate algorithm The main idea of minimum collision rate algorithm is that at every time slot, the secondary user selects the channel which carries minimum collision probability. We are now ready to formally state the optimization problem as follows. Given that the idle period distribution of every primary channel is fixed, select one channel to minimize collision probability at every time slot, subject to the constraint that the collision probability is bounded below collision tolerable level of every primary channel. That is, we can formulate the optimization problem as:
CHs ¼ arg min
n¼1;2;...;N
n o PCn;t
;
ð10Þ
s:t: PCn 6 1n where CHs is the sequence number of the selected channel, and P Cn;t is the collision probability of the nth channel in the tth time slot of current spectrum holes if the secondary user accesses the nth channel in this time slot, that is, PCn;t is the probability that the tth time slot of the nth channel becomes busy under the condition that
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all the first t 1 time slots are idle. PCn is the cumulative collision probability of the secondary user accessing the nth channel in the first t time slots. In the case that the idle period is exponential distribution, the solution of this optimization problem can be given by Proposition 1. Algorithm 1. (CSS-MCRA algorithm) Initialize: N a certain channel number For i ¼ 1 to N busytimei 0; idletimei 0; 1i a certain value Pci 0; collnumi 0; ui an arbitrary; transnumi vi an arbitrary; End for Repeat forever: For i ¼ 1 to N If current channel is the ith channel R ðidletime þ1Þs Pci þ ðidletimeiiþ1Þs fi ðtÞdt; Pci
0;
If P ci > 1i Select channel using (11); Switch to the selected channel; Elseif the ith channel is idle idletimei idletimei þ 1; transnumi transnumi þ 1; Else Store busytimei and idletimei ; Estimate ui ; vi using Maximum Likelihood Estimation; collnumi collnumi þ 1; busytimei 1; idletimei 0; Pci 0; Select channel using (11); Switch to the selected channel; End if Else Sense the ith channel; If the ith channel is idle idletimei idletimei þ 1; Else If idletimei > 0==idle period to busy period Store busytimei and idletimei ; busytimei 0; idletimei 0; P ci 0; Estimate ui ; vi using Maximum Likelihood Estimation; End if busytimei busytimei þ 1; End if // the ith channel is idle End if // current channel is the ith channel End for
Proposition 1. If the idle period is exponential distribution, the solution of optimization problem (11) can be obtained: The selected channel is
CHs ¼ arg min
n¼1;2;...;N
un ;
ð11Þ
where
( un
¼
un
if
1 if
Pcn < 1n Pcn
< 1n
:
ð12Þ
Proof. See Appendix A. h From proposition 1, we can see that the secondary user selects the channel with greatest average duration of idle period all the while under the constraint of collision tolerable level, and this conclusion is consistent with intuitive conclusion.
3.2. Channel selection scheme based on minimum collision rate algorithm (CSS-MCRA) According to Proposition 1, we present the channel selection scheme based on minimum collision rate algorithm (CSS-MCRA) (Algorithm 1) in the case that the idle period is exponential distribution. In Algorithm 1, transnumi ; collnumi are the number of successful transmission, the number of colliding with primary users of the ith channel, respectively; and busytimei ; idletimei are the elapsed time of one busy period, the elapsed time of the idle period of the ith channel, respectively. Now we analyze the channel handoff of the CSS-MCRA scheme. In the CSS-MCRA scheme, channel handoff happens in two cases: one is that collision occurs, and the other is that the collision probability of another channel is less than that of current channel. Since the occurrence of collision is random, we mainly analyze the latter case. According to the characteristic of exponential distribution, we can easily obtain the following conclusions: (1) ui > uj when accessing the ith channel, the secondary user must switch to the jth channel when the jth channel begins a new spectrum hole; (2) ui 6 uj when accessing the ith channel, the secondary user must switch to another jth channel if only current spectrum hole of the jth channel lasts for a period of time. That is to say, when the cumulative collision probability of current channel is less than collision tolerable level, the secondary user may switch to another channel. Thus, the CSS-MCRA scheme may result in higher handoff rate.
4. Minimum handoff rate algorithm From the previous section, we know that the CSS-MCRA scheme may lead to higher handoff rate, and it is not optimal if handoff latency is long. To solve this problem, we present another channel selection scheme based on minimum handoff rate algorithm in this section. 4.1. Expected available transmission time The main idea of minimum handoff rate algorithm is to decrease the number of channel handoff as much as possible. That is, the secondary user occupies one channel as long as possible, i.e., when making a decision every time, the secondary user selects one channel that has maximum expected available transmission time. Expected available transmission time can be defined as expected time interval starting when the secondary user accessing one channel until collision happens or cumulative collision probability of this channel is not less than its collision tolerable level. Under the assumption of stationarity and ergodicity, expected available transmission time of the nth channel can be given as
En ðxn ; T n Þ ¼
Z
xn þT n
xn
ðt xn Þfn ðtÞdt þ T n
Z
1
fn ðtÞdt;
ð13Þ
xn þT n
where fn ðtÞ is the probability density function of the idle period, and xn ; T n are current idle time slot, available transmission time of the nth channel, respectively. The first part of the right side of Eq. (13) represents the transmission time expectation that the idle period terminate in the time interval ½xn ; xn þ T n Þ and the second part of the right side of Eq. (13) represents the transmission time expectation that the idle period does not terminate in the time interval ½xn ; xn þ T n Þ.
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4.2. Problem formulation In the minimum handoff rate algorithm, when making a decision every time, the secondary user should select one channel with maximum expected available transmission time. We are now ready to formally state the optimization problem as follows. Given that the idle period distribution of every primary channel is fixed, select one channel to maximize expected available transmission time, subject to the constraint that the collision probability of every primary channel is bounded below its collision tolerable level. That is to say, we can formulate the optimization problem as:
If the ith channel is idle idletimei idletimei þ 1; Else If idletimei > 0==idle period to busy period Store busytimei and idletimei ; busytimei 0; idletimei 0; Pci 0; Estimate ui ; vi using Maximum Likelihood Estimation; End if busytimei busytimei þ 1; End if // the ith channel is idle End if // current channel is the ith channel End for
CHs ¼ arg max fEn ðxn ; T n Þg n¼1;2;...;N
ð14Þ
;
s:t: P Cn 6 1n
where CHs is the sequence number of the selected channel, and T n ; P Cn and 1n are available transmission time, cumulative collision probability and collision tolerable level of the nth channel, respectively. According to (13) and (14), we can obtain the optimization problem as follows:
CHs ¼ arg max
Z
n¼1;2;...;N
s:t:
PCn;max
Z
xn þT n
ðt xn Þfn ðtÞdt þ T n
xn
Z
1
fn ðtÞdt
xn þT n
xn þT n
xn
ð15Þ
fn ðtÞdt 6 1n :
1=un lnðeun xn 1n =vn Þ xn 1
1n < Pcn;max ; 1n P Pcn;max
ð16Þ
Algorithm 2. CSS-MHRA algorithm Initialize: N a certain channel number For i ¼ 1 to N busytimei 0; idletimei 0; 1i a certain value; P ci 0; collnumi 0; ui an arbitrary; transnumi vi an arbitrary; End for Repeat forever: For i ¼ 1 to N If current channel is the ith channel R ðidletime þ1Þs P ci þ ðidletimeiiÞs fi ðtÞdt; Pci
En ðxn ; T n Þ ¼
1n =un vn
1n < Pcn;max
eun xn =un
1n P Pcn;max
;
0;
If P ci > 1i Select channel using (18); Switch to the selected channel; Elseif the ith channel is idle idletimei idletimei þ 1; transnumi transnumi þ 1; Else Store busytimei and idletimei ; Estimate ui ; vi using Maximum Likelihood Estimation; collnumi collnumi þ 1; busytimei 1; idletimei 0; P ci 0; Select channel using (18); Switch to the selected channel; End if Else Sense the ith channel;
ð17Þ
and the selected channel is n¼1;2;...;N
Proposition 2. If the idle period is exponential distribution, the solution of optimization problem (15) is described as follows: The available transmission time is
Tn ¼
(
CHs ¼ arg max fEn ðxn ; T n Þg:
In the case that the idle period is exponential distribution, the solution of optimization problem (15) can be obtained by Proposition 2.
(
where xn is the duration from the first time slot of current spectrum hole to current time slot. The expected available transmission time is
ð18Þ
Proof. See Appendix B. h 4.3. Channel selection scheme based on minimum handoff rate algorithm (CSS-MHRA) According to Proposition 2, we present the channel selection scheme based on minimum handoff rate algorithm (CSS-MHRA) (Algorithm 2) in the case that the idle period is exponential distribution. All variables of Algorithm 2 are the same with Algorithm 1.
5. Performance analysis and simulation results In this section, we present numerical and simulation results to evaluate and compare the performance of the CSS-MHRA scheme and the CSS-MCRA scheme. To compare with their performances, we introduce two channel selection schemes: random channel selection scheme (RCSS) and channel selection scheme based on maximum mean idle period (CSS-MMIP). The RCSS scheme means that at every time slot, the secondary user randomly selects one channel to see whether the channel is idle and it accesses this channel at the next time slot if the channel is idle, otherwise it continues to select randomly another channel until it finds one available idle channel. Without any prior information of idle periods of primary channels, the RCSS scheme adopts reactive approach to select opportunistic channel. The CSS-MMIP scheme means that at every time slot, the secondary user selects the channel with maximal mean idle period. Without considering the constraint of collision tolerable level, the CSS-MMIP scheme adopts predictive approach to select opportunistic channel. Therefore, according to Proposition 1, we can easily obtain that without the constraint of collision tolerable level, the CSS-MCRA scheme is identical to the CSS-MMIP scheme. In simulation, we generate the channel-usage patterns for five independent channels using exponential distribution random number generator in MATLAB and the following parameters: the expectation values of idle period for the five channels 1=u1 ¼ 10; 1=u2 ¼ 20; 1=u3 ¼ 50; 1=u4 ¼ 65 and 1=u5 ¼ 100, respectively; and all of the expectation values of busy period 1=vi ¼ 20 ði ¼ 1; 2; 3; 4; 5Þ.
Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
1919
1n ¼ 0:02 (n = 1, 2, 3, 4,
Fig. 2. Performance comparison (collision tolerable level 1n ¼ 0:01 (n = 1, 2, 3, 4, 5)).
Fig. 3. Performance comparison (collision tolerable level 5)).
In Fig. 2, we study and compare the performances of the CSSMCRA scheme, the CSS-MHRA scheme, the RCSS scheme and the CSS-MMIP scheme in the case that collision tolerable levels of all
five channels are 0.01, i.e., 1i ¼ 0:01ði ¼ 1; 2; 3; 4; 5Þ. In plot (a), after the channel-usage estimates converge, handoff rate of CSS-MCRA scheme is greater than that of CSS-MHRA scheme,
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mates converge, if switching latency is zero or very short, the throughput of CSS-MCRA scheme is greater than that of CSSMHRA scheme, but they are less than that of CSS-MMIP scheme and the throughput of CSS-MMIP scheme is close to that of RCSS scheme. However, after the channel-usage estimates converge, if switching latency is long, the throughput of CSS-MCRA scheme is less than that of CSS-MHRA scheme and they are greater than that of RCSS scheme, but they are less than that of CSS-MMIP scheme. In plot (c), after the channel-usage estimates converge, collision rate of CSS-MCRA scheme is greater than that of CSS-MHRA scheme, but they are less than that of CSS-MMIP scheme and collision rate of CSS-MMIP scheme is less than RCSS scheme. We study and compare the performances of the CSS-MCRA scheme, the CSS-MHRA scheme, the RCSS scheme and the MMIP scheme in the case that collision tolerable levels of all five channels are 0.02 in Fig. 3, respectively. We also can obtain the same conclusions with Fig. 2. In Fig. 4, we study and compare every primary channel performance of the CSS-MCRA scheme, the CSS-MHRA scheme, the RCSS scheme and the MMIP scheme in the case that collision tolerable levels of all five channels are 0.01. In plot (a), the channel utilization of the CSS-MCRA scheme is close to that of CSS-MHRA, but they are less than that of the RCSS. Moreover, the channel utilization of the CSS-MMIP scheme is unbalanced, and the channel utilization of the 5th channel is very greater than that of the other channels. In plot (b), collision probability maximal value for every channel of the CSS-MCRA scheme and the CSS-MHRA scheme are close to its collision tolerable level, 1n ¼ 0:01ðn ¼ 1; 2; 3; 4; 5Þ, but collision probability maximal value for every channel of the RCSS scheme is greater than its collision tolerable level. Moreover, collision probability maximal value of the CSS-MMIP scheme is unbalanced: collision probability maximal value of the 4th channel is greater than its collision tolerable level, and collision probability maximal value of the 5th channel is very much greater than its collision tolerable level, while collision probabilities of the other channels are very much less than collision tolerable level. In plot (c), collision probability mean value for every channel of the CSSMCRA scheme and the CSS-MHRA scheme are less than its collision tolerable level, 1n ¼ 0:01ðn ¼ 1; 2; 3; 4; 5Þ, but collision probability mean value for every channel of the RCSS scheme is greater than its collision tolerable level. Moreover, collision probability mean value of the CSS-MMIP scheme is unbalanced: collision probability mean value of the 4th channel is greater than its collision tolerable level, and collision probability mean value of the 5th channel is very much greater than its collision tolerable level, while collision probabilities of the other channels are very much less than collision tolerable level. From the above analysis and simulation results, we can obtain the following results:
Fig. 4. Performance comparison (collision tolerable level 5)).
1n ¼ 0:01 (n = 1, 2, 3, 4,
but they are less than that of RCSS scheme and greater than that of CSS-MMIP scheme. In plot (b), after the channel-usage esti-
(1) The performances of CSS-MCRA scheme and CSS-MHRA scheme are always better than that of the RCSS scheme. (2) The performance of the CSS-MCRA is better than that of the CSS-MHRA scheme if switching latency is zero or very short, while the performance of the CSS-MHRA is better than that of the CSS-MCRA scheme if switching latency is long. (3) Though the performance of CSS-MMPP scheme, such as throughput, handoff rate and collision rate etc, is always better than that of the CSS-MCRA scheme and the CSS-MHRA scheme, the CSS-MMIP scheme always selects the same channel every time and this results in that collision probability of this channel is very much higher than its collision tolerable level and spectrum holes utilizations of other channels are very low.
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6. Conclusion
CHs ¼ arg min fun g if Pcn 6 1n
In this study, we consider a cognitive radio system with multiple primary channels and one secondary user. On the basis of this model, we present two opportunistic channel selection algorithms: minimum collision rate algorithm (MCRA) and minimum handoff rate algorithm (MHRA), and, respectively, propose two opportunistic channel selection schemes: channel selection scheme based on minimum collision rate algorithm (CSS-MCRA) and channel selection scheme based on minimum handoff rate algorithm (CSSMHRA). Analysis and numerical results both show that The RCSS scheme and CSS-MMIP scheme cannot satisfy the constraint of collision tolerable level of every primary channel. Compared to this, the CSS-MCRA scheme and CSS-MHRA scheme can optimize the throughput of the secondary user under the constraint of collision tolerable level of every primary channel. Moreover, under the constraint of collision tolerable level, the CSS-MCRA scheme is better than the CSS-MHRA if switching latency is zero or very small, while the CSS-MHRA scheme is better than the CSS-MCRA scheme if switching latency is long enough. In practical systems, there exist many cases that the idle period is not exponential distribution. Though we only investigate the case that the idle period follows exponential distribution, we can also adopt similar method to analyze the case that the idle period follows other distributions, such as Pareto distribution, Weibull distribution and obtain their analytical solutions. Though we only consider a single user scenario in this study, the secondary users can utilize this work result in multi-user case. In multi-user cooperative case, the secondary users can utilize this work result and adopt a cooperation protocol to effectively access the idle channel. In multi-user competitive case, the secondary users can utilize this work result and adopt a competition mechanism to maximize channel utilization, minimize collision and achieve an optimal state such as Nash equilibrium. Studying effective cooperation protocol and competition mechanism will be the future important works.
Moreover, the secondary user can not select the nth channel if the cumulative collision probability of the nth channel Pcn is not less than the collision probability level of the nth channel 1n . Otherwise, the secondary user may override the constraint of collision tolerable level of the nth channel. Therefore, we can obtain that the selected channel is
ðn ¼ 1; 2; . . . ; NÞ:
n¼1;2;...;N
CHs ¼ arg min fun g;
ðI4Þ
n¼1;2;...;N
where
( un
¼
if
Pcn 6 1n
1 if
Pcn > 1n
nn
:
ðI5Þ
Appendix B. Proof of Proposition 2 Assume that xn is the duration from the first time slot of current spectrum hole to current time slot. Now, we analyze the following two cases: (1)
1n P Pcn;max
Now the secondary user can start to transmit at current time slot (i.e., the xn th time slot) in current spectrum hole, and keep transmitting until collision occurs. That is to say, available transmission access time is limitless in this spectrum hole, i.e.,
T an ¼ 1:
ðII1Þ
The available transmission time expectation can be obtained
En ðxn ; T n Þmax ¼ En ðxn ; 1Þ ¼ ¼
Z
Z
1
ðt xn Þfn ðtÞdt
xn
1
un teun t dt xn
Z
xn
Acknowledgements (2) This work is partially supported by the National Basic Research Program of China (No. 2007CB310608), the National High Technology Research and Development (863) Program of China (No. 2007AA01Z2B6), the National Natural Science Foundation of China (No. 90204001) and the Tsinghua-Fujitsu Joint Research Program.
ðI3Þ
1
un eun t dt ¼
xn
1 un xn e : un
ðII2Þ
1n < Pcn;max
According to (15), we can obtain:
R x þT PCn ¼ P Cn;max xnn n fn ðtÞdt 6 1n R xn þT n ) v n xn un eun t dt 6 1n
ðII3Þ
) eun xn eun ðxn þT n Þ 6 1n =vn Appendix A. Proof of Proposition 1
) T n 6 lnð1 1n eun xn =vn Þ=un :
We first analyze this case that P cn 6 1n ðn ¼ 1; 2; . . . ; NÞ. Assume that PIn;t is the probability that the tth time slot of the nth channel is still idle under the condition that all the first t 1 time slots are idle. We have
Pcn;t ¼ 1 P In;t :
ðI1Þ
We can compute conditional probability
PIn;t
R ts
Thus, we can obtain:
T an ¼ maxfT n g ¼ 1=un ln ðeun xn 1n =vn Þ xn :
The available transmission time expectation can be given as:
En ðxn ; T n Þ ¼
R ts
1 0 fn ðxÞdx 1 0 un eun x dx ¼ ¼ eun ts =eun ðt1Þs ¼ eun s ¼ R ðt1Þs R ðt1Þs 1 0 fn ðxÞdx 1 0 un eui x dx
¼
Z
xn þT n
Thus,
þ Tn un s
¼1e
ðI2Þ
: P cn;t
From (I2), it is easily seen that decreases monotonically as un decreases. Therefore, Pcn;t is minimal as un is minimal, i.e., we can obtain that the selected channel is
ðt xn Þfn ðtÞdt þ T n
xn Z xn þT n xn
Pcn;t
ðII4Þ
Z
un teun t dt xn
Z
Z
1
fn ðtÞdt
xn þT n xn þT n
un eun t dt
xn 1
un eun t dt
xn þT n
1 un xn 1 e T n eun ðxn þT n Þ eun ðxn þT n Þ þ T n eun ðxn þT n Þ un un 1 1 1 ¼ eun xn eun ðxn þT n Þ 6 n : ðII5Þ un un un vn
¼
1922
Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
Thus, it can easily obtained that
En ðxn ; T n Þmax ¼ 1n =ðun vn Þ if T n ¼
T an :
[4] [5]
In summary, the available transmission time is
( Tn ¼
1=un lnðe
un xn
c n < P n;max c n P P n;max
1n =vn Þ xn
1 1
1
;
the expected available transmission time is
( En ðxn ; T n Þ ¼
1n =un vn un xn
e
=un
1 1
c n < P n;max c n P P n;max
[7] [8]
;
and the selected channel is
CHs ¼ arg max fEn ðxn ; T n Þg:
[6]
[9]
[10]
n¼1;2;...;N
[11] [12]
References [1] United State Frequency Allocation Chart. Available from:
[13] [14]
[15]
Spectrum Company. Available from:
Contents lists available at ScienceDirect
Computer Communications journal homepage: www.elsevier.com/locate/comcom
Opportunistic channel selection approach under collision probability constraint in cognitive radio systems Qinghai Xiao a,b,*, Yunzhou Li a, Ming Zhao a, Shidong Zhou a, Jing Wang a a
State Key Laboratory on Microwave and Digital Communications, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China b School of Electronic Technology, Information Engineering University, Zhengzhou 450004, China
a r t i c l e
i n f o
Article history: Available online 25 July 2009 Keywords: Opportunistic channel selection Collision probability Collision tolerable level Collision rate Handoff rate
a b s t r a c t In this work, we consider a cognitive radio system with multiple primary channels and one secondary user, and then we introduce a channel-usage pattern model and some basic concepts in this system. Based on this system model and the basic concepts, we propose two opportunistic channel selection algorithms to optimize the throughput of the secondary user: minimum collision rate channel selection algorithm and minimum handoff rate channel selection algorithm. According to the two algorithms, we, respectively, present the channel selection scheme based on minimum collision rate algorithm (CSSMCRA) and the channel selection scheme based on minimum handoff rate algorithm (CSS-MHRA) under the constraint that the collision probability is bounded below collision tolerable level. Theoretical analysis and simulation results both show that, on one hand, both CSS-MCRA scheme and CSS-MHRA can follow the constraint of collision tolerable level; on the other hand, the performance of CSS-MCRA scheme is better than that of CSS-MHRA scheme if handoff latency is zero or very low, while the performance of CSS-MHRA scheme is better than that of CSS-MCRA scheme if handoff latency is long enough. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The electromagnetic spectrum is a precious and limited natural resource, the use of which is licensed by government agencies. The conventional spectrum management policies use fixed spectrum assignment to prevent mutual interference all the time. This has led to the artificial radio spectrum scarcity that most of the available radio spectrum has already been allocated to various services. The frequency allocation chart [1] in the United States indicates multiple allocations over all of the frequency bands. On the other hand, careful studies of the spectrum-usage pattern by Spectrum Policy Task Force (SPTF) have revealed that many portions of the allocated radio spectrum experience low utilization and they are either unoccupied or partially occupied for long periods of time [2]. Extensive measurements also indicate that many portions of licensed spectrum lies unused at any given time and location [3]. Even when a channel is actively used, the bursty arrivals of many applications result in abundant spectrum opportunities at the slot level.
* Corresponding author. Address: State Key Laboratory on Microwave and Digital Communications, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China. Tel.: +86 13683219321. E-mail address: [email protected] (Q. Xiao). 0140-3664/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2009.06.015
Growing demand and low utilization for the radio spectrum lead to the concept of secondary use, which forms the key rationale for opportunistic spectrum access (OSA) envisioned by the DARPA XG program [4]. The main idea is to exploit instantaneous spectrum availability by opening licensed spectrum to secondary users, and allow unused or underused portions of the radio spectrum owned by primary (licensed) users (PUs) to become temporarily available for secondary (unlicensed) users (SUs). Namely, it allows secondary users to identify available spectrum resources and communicate in a manner that limits the level of interference received by the primary users. The OSA system requires that the secondary user efficiently utilizes unoccupied spectrum holes while avoiding interference with primary users [5]. The spectrum-usage patterns of primary users vary over time, thus, the secondary user experiences dynamic spectrum hole and needs to intelligently adapt its channel usage. In conventional methods, the secondary user senses local channels through individual or cooperative sensing [6–10], and reconfigures its own access parameters according to the channel-usage patterns of primary users. This adaptation is based on the current observation of the spectrum usage by primary users. Once detecting a primary user’s occurrence on its current band in use, the secondary user pauses transmissions, starts to sense the channel and waits next opportunity to resume transmissions. The conventional methods can not schedule future transmissions without any prior information about future spectrum holes, and results in that the
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Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
secondary user frequently collides with primary users. Primary users can suffer from short-term interference until they are discovered. Collisions occur when the secondary user can not predict the appearance of primary users, and can only react to current observations of primary users. In this paper, we propose two channel selection schemes based on spectrum holes prediction where the secondary user builds a predictive model of primary users’ channel usage and predicts near future spectrum availability based on past observations. There have been several prior works on dynamic spectrum access and sensing. The most relevant works are [11,12]. In [11], the authors proposed a proactive access scheme based on the characteristics of TV-broadcast and explored the feasibility of proactive access method. In [12], the authors extended this work to the exponential ON–OFF model. Our work discusses OSA problems based on spectrum holes prediction while primary user traffic model is general model (including without limitation, the exponential ON–OFF model). Moreover, [11] mainly focuses on maximizing throughput of the secondary user, and [12] mainly adopts proactive channel access approach to minimize disruptions to primary users, while our work focuses on channel selection scheme to maximize throughput of the secondary user on the basis of satisfying the constraint of collision tolerable level allowed by primary network. The remainder of this paper is organized as follows. The next section describes the system model and some basic concepts. A channel selection scheme based on minimum collision rate algorithm is proposed in Section 3. A channel selection scheme based on minimum handoff rate algorithm is proposed in Section 4. Performance analysis and corresponding simulation results are presented in Section 5. Our main conclusions are summarized in the final section.
er than s and the duration is an integral-number of s for convenience. In this paper, there exist the following basic assumptions: (A1) The system is stationary and ergodic. (A2) The secondary user performs perfect sensing, i.e., the false alarm and missing probability are zero. (A3) The secondary user only selects one channel every time. (A4) The arrival process of one primary user is Poisson process while the service time distribution is arbitrary. This assumption holds in many situations such as voice traffic, data session and data network. When there are multiple primary users in a channel, the system can be modeled as an M/G/ 1 queue with multiple inputs and it can be proved that the idle period is exponential distribution while the busy period is general distribution [13]. Therefore, we can assume that the idle period of the ith channel is exponential distribution and its expectation is 1=ln while its busy period is general distribution and its average value is 1=mn . The idle period distribution function of the nth channel can be given as
fn ðtÞ ¼ un eun t
for t P 0;
n ¼ 1; . . . ; N:
2.2. Channel utilization and throughput In the nth channel, channel utilization (CU) of the primary users is defined as the fraction of time in which the channel is occupied by the primary users, i.e., the channel is in ON (busy) state, denoted by gPU n . And under assumption (A1), (A4), it can be given as [14]
gPU n ¼ lim PM M!1
PM
i¼1 1=vn;i
i¼1 ð1=un;i
þ 1=vn;i Þ
¼ lim
M!1
M=vn un ¼ ; M=un þ M=vn un þ vn
2. System model and basic concepts In this section, we consider multi-channel usage pattern model in the system with multiple primary channels and one secondary user, and explain some basic concepts. 2.1. Multi-channel usage pattern model Consider a system with multiple primary channels and one secondary user. Primary users are the licensed users of these channels and thus have higher priority over the secondary user. A channel is called idle if it is unoccupied by one or more primary users, and busy otherwise (Fig. 1). The duration of idle period is the time interval starting at the release of the channel until the first packet arrival. Similarly, the duration of busy period is the time interval starting at the first packet arrival until the moment that the channel becomes idle. We regard one sensing time of the secondary user as one time slot, denoted by s, i.e., s ¼ 1 time slot. Assuming that the duration of every idle period or busy period is much great-
ð1Þ
ð2Þ where 1=vn;i and 1=un;i denote the duration of the ith busy period and the duration of the ith idle period of the nth channel, respectively. The definition of spectrum hole is given in [15]. We define spectrum holes utilization (idle period utilization) of the nth channel as
gSH n ¼ lim
T!1
Duration of spectrum holes utilized by SU in ½0; T : Duration of all spectrum holes in ½0; T ð3Þ
In multiple primary channels, we can define the throughput of the secondary user as the expected number time slots that the secondary user accesses some channels in a specified time period. Thus, under the assumption of stationarity and ergodicity, we can denote normalized throughput of the secondary user as
rt ¼ lim
T!1
Number of access in ½0; T : Number of time slots in ½0; T
ð4Þ
2.3. Collision probability and collision rate
Fig. 1. Multi-channel usage pattern model.
Because the secondary user performs perfect sensing, collisions happen only when primary users reoccur and occupy the same channel while the secondary user is transmitting on the channel. Collision probability (CP) is the probability of the secondary transmission colliding with the primary transmission. In this paper, we assume that the duration of one collision period is regarded as one time slot for convenience, i.e., one collision period is also equal to ss . Thus, under the assumption of stationarity and ergodicity, we can define collision probability of the nth channel as
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Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
pcn ¼ lim
T!1
Number of collisions in ½0; T : Number of busy time slots of PU in ½0; T
ð5Þ
Collision tolerable level (CTL) of the nth channel is defined as the maximum probability of collision allowed by the primary users, denoted by 1n .The wireless communication systems, which provide with different services in different networks, can tolerate different collision types and collision probability. For example, voice service is real-time but it can tolerate a few packet losses. Whereas, data service can not lose packet but it may tolerate a little time delay. Therefore, almost all of different services can tolerate a few collisions in despite of the difference of collision types. In our work, we do not place emphasis on studying the differences of collision types, but we only assume that the primary users can accept collision tolerable level 1n . Collision tolerable level is also collision probability constraint of the cognitive radio system. Thus, the system must satisfy:
0 6 pcn 6 1n :
ð6Þ
Otherwise, too many collisions will affect the primary users’ transmission. It is a difficult key problem how to identify collision. Due to performing perfect sensing, collisions occur only when primary users reoccur and occupy the channel while the secondary user is transmitting. Because the secondary user can not sense the channel when transmitting, the secondary user can but regard transmission failure as collision. Though there exist many other factors such as channel fading, environment interference, that result in transmission failure, these do not increase collision probability, and only decrease spectrum holes utilization and secondary user’s throughput. In this work, for convenience of analysis, we assume that transmission failure only arise from collision, i.e., reoccurrence of the primary user. However, in a practical system, there surely exists the problem that other non-collision transmission failures lead to decrease spectrum holes utilization and secondary user’s throughput. But owing to sensing immediately after collision happens and performing perfect sensing, the secondary user wastes at most one time slot at every time when a non-collision transmission failure occurs. Therefore, under the assumption that transmission failure only arises from collision, we can only obtain maximal theoretical upper bound of spectrum holes utilization under the constraint of collision tolerable level. If the secondary user can exactly identify collision with primary users, we can understand that there exists at most one collision period at the beginning of every busy period. And the secondary user adopts this strategy where it keeps transmitting until primary users reoccur and collision happens if it senses the channel idle. Obviously, on the basis of the access strategy, every channel has the maximum collision probability (MCP), and we denote the maximum collision probability of the nth channel as PCn;max . Under the assumption of stationarity and ergodicity, we can obtain the following expression on average:
Pcn;max ¼ lim PM M!1
M
i¼1 1=vn;i
¼ lim
M!1
M ¼ vn ; M=vn
ð7Þ
where 1=vn;i is the duration of the i th busy period of the nth channel. We can see from (7) that the maximum collision probability is equal to the reciprocal of average value of the busy period. In one primary channel, we can evaluate the performance using collision probability. However, in multiple primary channels, it is difficult to define the collision probability. Thus, to evaluate the performance, we propose the collision rate. We define collision rate as the number of collisions that happen when primary users reoccur and occupy the channel while the secondary user is transmitting in a specified time period. Thus, under
the assumption of stationarity and ergodicity, we can denote collision rate as
rc ¼ lim
T!1
Number of collisions in ½0; T : Number of time slots in ½0; T
ð8Þ
2.4. Channel handoff rate In one primary channel, there does not exist channel handoff. However, in multiple primary channels, it is key problem how to switch from one channel to another. Thus, to evaluate the performance, we propose the channel handoff rate. We define channel handoff rate as the expected number of handoffs occurring between different channels in a specified time period. Thus, under the assumption of stationarity and ergodicity, we can denote channel handoff rate as
rh ¼ lim
T!1
Number of handoffs in ½0; T : Number of time slots in ½0; T
ð9Þ
Here, a handoff is made between different channels. That is, the handoff can be a general handoff between different channels in the same cell, and it can also be horizontal handoff in homogeneous wireless networks, and vertical handoff in heterogeneous wireless networks.
3. Minimum collision rate algorithm Our aim is to maximize the throughput of the secondary user under the constraint of collision tolerable level of every primary channel. In the case of one secondary user and one primary channel, it is easily understood that maximizing the throughput of the secondary user is equivalence to maximizing spectrum holes utilization of the primary channel. However, in the case of one secondary user and multiple primary channels, maximizing spectrum holes utilization of one certain primary channel can not always result in maximizing the throughput of the secondary user. To maximize the throughput of the secondary user, we propose two channel selection schemes in this section and in the next section, respectively. An intuitive idea is that at every time slot, the secondary user selects and accesses the channel, of which collision probability is less than that of all other channels. On the basis of this idea, we present a channel selection scheme based on minimum collision rate algorithm. 3.1. Minimum collision rate algorithm The main idea of minimum collision rate algorithm is that at every time slot, the secondary user selects the channel which carries minimum collision probability. We are now ready to formally state the optimization problem as follows. Given that the idle period distribution of every primary channel is fixed, select one channel to minimize collision probability at every time slot, subject to the constraint that the collision probability is bounded below collision tolerable level of every primary channel. That is, we can formulate the optimization problem as:
CHs ¼ arg min
n¼1;2;...;N
n o PCn;t
;
ð10Þ
s:t: PCn 6 1n where CHs is the sequence number of the selected channel, and P Cn;t is the collision probability of the nth channel in the tth time slot of current spectrum holes if the secondary user accesses the nth channel in this time slot, that is, PCn;t is the probability that the tth time slot of the nth channel becomes busy under the condition that
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Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
all the first t 1 time slots are idle. PCn is the cumulative collision probability of the secondary user accessing the nth channel in the first t time slots. In the case that the idle period is exponential distribution, the solution of this optimization problem can be given by Proposition 1. Algorithm 1. (CSS-MCRA algorithm) Initialize: N a certain channel number For i ¼ 1 to N busytimei 0; idletimei 0; 1i a certain value Pci 0; collnumi 0; ui an arbitrary; transnumi vi an arbitrary; End for Repeat forever: For i ¼ 1 to N If current channel is the ith channel R ðidletime þ1Þs Pci þ ðidletimeiiþ1Þs fi ðtÞdt; Pci
0;
If P ci > 1i Select channel using (11); Switch to the selected channel; Elseif the ith channel is idle idletimei idletimei þ 1; transnumi transnumi þ 1; Else Store busytimei and idletimei ; Estimate ui ; vi using Maximum Likelihood Estimation; collnumi collnumi þ 1; busytimei 1; idletimei 0; Pci 0; Select channel using (11); Switch to the selected channel; End if Else Sense the ith channel; If the ith channel is idle idletimei idletimei þ 1; Else If idletimei > 0==idle period to busy period Store busytimei and idletimei ; busytimei 0; idletimei 0; P ci 0; Estimate ui ; vi using Maximum Likelihood Estimation; End if busytimei busytimei þ 1; End if // the ith channel is idle End if // current channel is the ith channel End for
Proposition 1. If the idle period is exponential distribution, the solution of optimization problem (11) can be obtained: The selected channel is
CHs ¼ arg min
n¼1;2;...;N
un ;
ð11Þ
where
( un
¼
un
if
1 if
Pcn < 1n Pcn
< 1n
:
ð12Þ
Proof. See Appendix A. h From proposition 1, we can see that the secondary user selects the channel with greatest average duration of idle period all the while under the constraint of collision tolerable level, and this conclusion is consistent with intuitive conclusion.
3.2. Channel selection scheme based on minimum collision rate algorithm (CSS-MCRA) According to Proposition 1, we present the channel selection scheme based on minimum collision rate algorithm (CSS-MCRA) (Algorithm 1) in the case that the idle period is exponential distribution. In Algorithm 1, transnumi ; collnumi are the number of successful transmission, the number of colliding with primary users of the ith channel, respectively; and busytimei ; idletimei are the elapsed time of one busy period, the elapsed time of the idle period of the ith channel, respectively. Now we analyze the channel handoff of the CSS-MCRA scheme. In the CSS-MCRA scheme, channel handoff happens in two cases: one is that collision occurs, and the other is that the collision probability of another channel is less than that of current channel. Since the occurrence of collision is random, we mainly analyze the latter case. According to the characteristic of exponential distribution, we can easily obtain the following conclusions: (1) ui > uj when accessing the ith channel, the secondary user must switch to the jth channel when the jth channel begins a new spectrum hole; (2) ui 6 uj when accessing the ith channel, the secondary user must switch to another jth channel if only current spectrum hole of the jth channel lasts for a period of time. That is to say, when the cumulative collision probability of current channel is less than collision tolerable level, the secondary user may switch to another channel. Thus, the CSS-MCRA scheme may result in higher handoff rate.
4. Minimum handoff rate algorithm From the previous section, we know that the CSS-MCRA scheme may lead to higher handoff rate, and it is not optimal if handoff latency is long. To solve this problem, we present another channel selection scheme based on minimum handoff rate algorithm in this section. 4.1. Expected available transmission time The main idea of minimum handoff rate algorithm is to decrease the number of channel handoff as much as possible. That is, the secondary user occupies one channel as long as possible, i.e., when making a decision every time, the secondary user selects one channel that has maximum expected available transmission time. Expected available transmission time can be defined as expected time interval starting when the secondary user accessing one channel until collision happens or cumulative collision probability of this channel is not less than its collision tolerable level. Under the assumption of stationarity and ergodicity, expected available transmission time of the nth channel can be given as
En ðxn ; T n Þ ¼
Z
xn þT n
xn
ðt xn Þfn ðtÞdt þ T n
Z
1
fn ðtÞdt;
ð13Þ
xn þT n
where fn ðtÞ is the probability density function of the idle period, and xn ; T n are current idle time slot, available transmission time of the nth channel, respectively. The first part of the right side of Eq. (13) represents the transmission time expectation that the idle period terminate in the time interval ½xn ; xn þ T n Þ and the second part of the right side of Eq. (13) represents the transmission time expectation that the idle period does not terminate in the time interval ½xn ; xn þ T n Þ.
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Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
4.2. Problem formulation In the minimum handoff rate algorithm, when making a decision every time, the secondary user should select one channel with maximum expected available transmission time. We are now ready to formally state the optimization problem as follows. Given that the idle period distribution of every primary channel is fixed, select one channel to maximize expected available transmission time, subject to the constraint that the collision probability of every primary channel is bounded below its collision tolerable level. That is to say, we can formulate the optimization problem as:
If the ith channel is idle idletimei idletimei þ 1; Else If idletimei > 0==idle period to busy period Store busytimei and idletimei ; busytimei 0; idletimei 0; Pci 0; Estimate ui ; vi using Maximum Likelihood Estimation; End if busytimei busytimei þ 1; End if // the ith channel is idle End if // current channel is the ith channel End for
CHs ¼ arg max fEn ðxn ; T n Þg n¼1;2;...;N
ð14Þ
;
s:t: P Cn 6 1n
where CHs is the sequence number of the selected channel, and T n ; P Cn and 1n are available transmission time, cumulative collision probability and collision tolerable level of the nth channel, respectively. According to (13) and (14), we can obtain the optimization problem as follows:
CHs ¼ arg max
Z
n¼1;2;...;N
s:t:
PCn;max
Z
xn þT n
ðt xn Þfn ðtÞdt þ T n
xn
Z
1
fn ðtÞdt
xn þT n
xn þT n
xn
ð15Þ
fn ðtÞdt 6 1n :
1=un lnðeun xn 1n =vn Þ xn 1
1n < Pcn;max ; 1n P Pcn;max
ð16Þ
Algorithm 2. CSS-MHRA algorithm Initialize: N a certain channel number For i ¼ 1 to N busytimei 0; idletimei 0; 1i a certain value; P ci 0; collnumi 0; ui an arbitrary; transnumi vi an arbitrary; End for Repeat forever: For i ¼ 1 to N If current channel is the ith channel R ðidletime þ1Þs P ci þ ðidletimeiiÞs fi ðtÞdt; Pci
En ðxn ; T n Þ ¼
1n =un vn
1n < Pcn;max
eun xn =un
1n P Pcn;max
;
0;
If P ci > 1i Select channel using (18); Switch to the selected channel; Elseif the ith channel is idle idletimei idletimei þ 1; transnumi transnumi þ 1; Else Store busytimei and idletimei ; Estimate ui ; vi using Maximum Likelihood Estimation; collnumi collnumi þ 1; busytimei 1; idletimei 0; P ci 0; Select channel using (18); Switch to the selected channel; End if Else Sense the ith channel;
ð17Þ
and the selected channel is n¼1;2;...;N
Proposition 2. If the idle period is exponential distribution, the solution of optimization problem (15) is described as follows: The available transmission time is
Tn ¼
(
CHs ¼ arg max fEn ðxn ; T n Þg:
In the case that the idle period is exponential distribution, the solution of optimization problem (15) can be obtained by Proposition 2.
(
where xn is the duration from the first time slot of current spectrum hole to current time slot. The expected available transmission time is
ð18Þ
Proof. See Appendix B. h 4.3. Channel selection scheme based on minimum handoff rate algorithm (CSS-MHRA) According to Proposition 2, we present the channel selection scheme based on minimum handoff rate algorithm (CSS-MHRA) (Algorithm 2) in the case that the idle period is exponential distribution. All variables of Algorithm 2 are the same with Algorithm 1.
5. Performance analysis and simulation results In this section, we present numerical and simulation results to evaluate and compare the performance of the CSS-MHRA scheme and the CSS-MCRA scheme. To compare with their performances, we introduce two channel selection schemes: random channel selection scheme (RCSS) and channel selection scheme based on maximum mean idle period (CSS-MMIP). The RCSS scheme means that at every time slot, the secondary user randomly selects one channel to see whether the channel is idle and it accesses this channel at the next time slot if the channel is idle, otherwise it continues to select randomly another channel until it finds one available idle channel. Without any prior information of idle periods of primary channels, the RCSS scheme adopts reactive approach to select opportunistic channel. The CSS-MMIP scheme means that at every time slot, the secondary user selects the channel with maximal mean idle period. Without considering the constraint of collision tolerable level, the CSS-MMIP scheme adopts predictive approach to select opportunistic channel. Therefore, according to Proposition 1, we can easily obtain that without the constraint of collision tolerable level, the CSS-MCRA scheme is identical to the CSS-MMIP scheme. In simulation, we generate the channel-usage patterns for five independent channels using exponential distribution random number generator in MATLAB and the following parameters: the expectation values of idle period for the five channels 1=u1 ¼ 10; 1=u2 ¼ 20; 1=u3 ¼ 50; 1=u4 ¼ 65 and 1=u5 ¼ 100, respectively; and all of the expectation values of busy period 1=vi ¼ 20 ði ¼ 1; 2; 3; 4; 5Þ.
Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
1919
1n ¼ 0:02 (n = 1, 2, 3, 4,
Fig. 2. Performance comparison (collision tolerable level 1n ¼ 0:01 (n = 1, 2, 3, 4, 5)).
Fig. 3. Performance comparison (collision tolerable level 5)).
In Fig. 2, we study and compare the performances of the CSSMCRA scheme, the CSS-MHRA scheme, the RCSS scheme and the CSS-MMIP scheme in the case that collision tolerable levels of all
five channels are 0.01, i.e., 1i ¼ 0:01ði ¼ 1; 2; 3; 4; 5Þ. In plot (a), after the channel-usage estimates converge, handoff rate of CSS-MCRA scheme is greater than that of CSS-MHRA scheme,
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mates converge, if switching latency is zero or very short, the throughput of CSS-MCRA scheme is greater than that of CSSMHRA scheme, but they are less than that of CSS-MMIP scheme and the throughput of CSS-MMIP scheme is close to that of RCSS scheme. However, after the channel-usage estimates converge, if switching latency is long, the throughput of CSS-MCRA scheme is less than that of CSS-MHRA scheme and they are greater than that of RCSS scheme, but they are less than that of CSS-MMIP scheme. In plot (c), after the channel-usage estimates converge, collision rate of CSS-MCRA scheme is greater than that of CSS-MHRA scheme, but they are less than that of CSS-MMIP scheme and collision rate of CSS-MMIP scheme is less than RCSS scheme. We study and compare the performances of the CSS-MCRA scheme, the CSS-MHRA scheme, the RCSS scheme and the MMIP scheme in the case that collision tolerable levels of all five channels are 0.02 in Fig. 3, respectively. We also can obtain the same conclusions with Fig. 2. In Fig. 4, we study and compare every primary channel performance of the CSS-MCRA scheme, the CSS-MHRA scheme, the RCSS scheme and the MMIP scheme in the case that collision tolerable levels of all five channels are 0.01. In plot (a), the channel utilization of the CSS-MCRA scheme is close to that of CSS-MHRA, but they are less than that of the RCSS. Moreover, the channel utilization of the CSS-MMIP scheme is unbalanced, and the channel utilization of the 5th channel is very greater than that of the other channels. In plot (b), collision probability maximal value for every channel of the CSS-MCRA scheme and the CSS-MHRA scheme are close to its collision tolerable level, 1n ¼ 0:01ðn ¼ 1; 2; 3; 4; 5Þ, but collision probability maximal value for every channel of the RCSS scheme is greater than its collision tolerable level. Moreover, collision probability maximal value of the CSS-MMIP scheme is unbalanced: collision probability maximal value of the 4th channel is greater than its collision tolerable level, and collision probability maximal value of the 5th channel is very much greater than its collision tolerable level, while collision probabilities of the other channels are very much less than collision tolerable level. In plot (c), collision probability mean value for every channel of the CSSMCRA scheme and the CSS-MHRA scheme are less than its collision tolerable level, 1n ¼ 0:01ðn ¼ 1; 2; 3; 4; 5Þ, but collision probability mean value for every channel of the RCSS scheme is greater than its collision tolerable level. Moreover, collision probability mean value of the CSS-MMIP scheme is unbalanced: collision probability mean value of the 4th channel is greater than its collision tolerable level, and collision probability mean value of the 5th channel is very much greater than its collision tolerable level, while collision probabilities of the other channels are very much less than collision tolerable level. From the above analysis and simulation results, we can obtain the following results:
Fig. 4. Performance comparison (collision tolerable level 5)).
1n ¼ 0:01 (n = 1, 2, 3, 4,
but they are less than that of RCSS scheme and greater than that of CSS-MMIP scheme. In plot (b), after the channel-usage esti-
(1) The performances of CSS-MCRA scheme and CSS-MHRA scheme are always better than that of the RCSS scheme. (2) The performance of the CSS-MCRA is better than that of the CSS-MHRA scheme if switching latency is zero or very short, while the performance of the CSS-MHRA is better than that of the CSS-MCRA scheme if switching latency is long. (3) Though the performance of CSS-MMPP scheme, such as throughput, handoff rate and collision rate etc, is always better than that of the CSS-MCRA scheme and the CSS-MHRA scheme, the CSS-MMIP scheme always selects the same channel every time and this results in that collision probability of this channel is very much higher than its collision tolerable level and spectrum holes utilizations of other channels are very low.
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6. Conclusion
CHs ¼ arg min fun g if Pcn 6 1n
In this study, we consider a cognitive radio system with multiple primary channels and one secondary user. On the basis of this model, we present two opportunistic channel selection algorithms: minimum collision rate algorithm (MCRA) and minimum handoff rate algorithm (MHRA), and, respectively, propose two opportunistic channel selection schemes: channel selection scheme based on minimum collision rate algorithm (CSS-MCRA) and channel selection scheme based on minimum handoff rate algorithm (CSSMHRA). Analysis and numerical results both show that The RCSS scheme and CSS-MMIP scheme cannot satisfy the constraint of collision tolerable level of every primary channel. Compared to this, the CSS-MCRA scheme and CSS-MHRA scheme can optimize the throughput of the secondary user under the constraint of collision tolerable level of every primary channel. Moreover, under the constraint of collision tolerable level, the CSS-MCRA scheme is better than the CSS-MHRA if switching latency is zero or very small, while the CSS-MHRA scheme is better than the CSS-MCRA scheme if switching latency is long enough. In practical systems, there exist many cases that the idle period is not exponential distribution. Though we only investigate the case that the idle period follows exponential distribution, we can also adopt similar method to analyze the case that the idle period follows other distributions, such as Pareto distribution, Weibull distribution and obtain their analytical solutions. Though we only consider a single user scenario in this study, the secondary users can utilize this work result in multi-user case. In multi-user cooperative case, the secondary users can utilize this work result and adopt a cooperation protocol to effectively access the idle channel. In multi-user competitive case, the secondary users can utilize this work result and adopt a competition mechanism to maximize channel utilization, minimize collision and achieve an optimal state such as Nash equilibrium. Studying effective cooperation protocol and competition mechanism will be the future important works.
Moreover, the secondary user can not select the nth channel if the cumulative collision probability of the nth channel Pcn is not less than the collision probability level of the nth channel 1n . Otherwise, the secondary user may override the constraint of collision tolerable level of the nth channel. Therefore, we can obtain that the selected channel is
ðn ¼ 1; 2; . . . ; NÞ:
n¼1;2;...;N
CHs ¼ arg min fun g;
ðI4Þ
n¼1;2;...;N
where
( un
¼
if
Pcn 6 1n
1 if
Pcn > 1n
nn
:
ðI5Þ
Appendix B. Proof of Proposition 2 Assume that xn is the duration from the first time slot of current spectrum hole to current time slot. Now, we analyze the following two cases: (1)
1n P Pcn;max
Now the secondary user can start to transmit at current time slot (i.e., the xn th time slot) in current spectrum hole, and keep transmitting until collision occurs. That is to say, available transmission access time is limitless in this spectrum hole, i.e.,
T an ¼ 1:
ðII1Þ
The available transmission time expectation can be obtained
En ðxn ; T n Þmax ¼ En ðxn ; 1Þ ¼ ¼
Z
Z
1
ðt xn Þfn ðtÞdt
xn
1
un teun t dt xn
Z
xn
Acknowledgements (2) This work is partially supported by the National Basic Research Program of China (No. 2007CB310608), the National High Technology Research and Development (863) Program of China (No. 2007AA01Z2B6), the National Natural Science Foundation of China (No. 90204001) and the Tsinghua-Fujitsu Joint Research Program.
ðI3Þ
1
un eun t dt ¼
xn
1 un xn e : un
ðII2Þ
1n < Pcn;max
According to (15), we can obtain:
R x þT PCn ¼ P Cn;max xnn n fn ðtÞdt 6 1n R xn þT n ) v n xn un eun t dt 6 1n
ðII3Þ
) eun xn eun ðxn þT n Þ 6 1n =vn Appendix A. Proof of Proposition 1
) T n 6 lnð1 1n eun xn =vn Þ=un :
We first analyze this case that P cn 6 1n ðn ¼ 1; 2; . . . ; NÞ. Assume that PIn;t is the probability that the tth time slot of the nth channel is still idle under the condition that all the first t 1 time slots are idle. We have
Pcn;t ¼ 1 P In;t :
ðI1Þ
We can compute conditional probability
PIn;t
R ts
Thus, we can obtain:
T an ¼ maxfT n g ¼ 1=un ln ðeun xn 1n =vn Þ xn :
The available transmission time expectation can be given as:
En ðxn ; T n Þ ¼
R ts
1 0 fn ðxÞdx 1 0 un eun x dx ¼ ¼ eun ts =eun ðt1Þs ¼ eun s ¼ R ðt1Þs R ðt1Þs 1 0 fn ðxÞdx 1 0 un eui x dx
¼
Z
xn þT n
Thus,
þ Tn un s
¼1e
ðI2Þ
: P cn;t
From (I2), it is easily seen that decreases monotonically as un decreases. Therefore, Pcn;t is minimal as un is minimal, i.e., we can obtain that the selected channel is
ðt xn Þfn ðtÞdt þ T n
xn Z xn þT n xn
Pcn;t
ðII4Þ
Z
un teun t dt xn
Z
Z
1
fn ðtÞdt
xn þT n xn þT n
un eun t dt
xn 1
un eun t dt
xn þT n
1 un xn 1 e T n eun ðxn þT n Þ eun ðxn þT n Þ þ T n eun ðxn þT n Þ un un 1 1 1 ¼ eun xn eun ðxn þT n Þ 6 n : ðII5Þ un un un vn
¼
1922
Q. Xiao et al. / Computer Communications 32 (2009) 1914–1922
Thus, it can easily obtained that
En ðxn ; T n Þmax ¼ 1n =ðun vn Þ if T n ¼
T an :
[4] [5]
In summary, the available transmission time is
( Tn ¼
1=un lnðe
un xn
c n < P n;max c n P P n;max
1n =vn Þ xn
1 1
1
;
the expected available transmission time is
( En ðxn ; T n Þ ¼
1n =un vn un xn
e
=un
1 1
c n < P n;max c n P P n;max
[7] [8]
;
and the selected channel is
CHs ¼ arg max fEn ðxn ; T n Þg:
[6]
[9]
[10]
n¼1;2;...;N
[11] [12]
References [1] United State Frequency Allocation Chart. Available from:
[13] [14]
[15]
Spectrum Company. Available from: