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Wireless Sensor Network, 2009, 1, 397-406 doi:10.4236/wsn.2009.15048 Published Online December 2009 (http://www.scirp.org/journal/wsn). Copyright © 2009 SciRes. WSN 397 Modeling and Analysis of Random Periodic Spectrum Sensing for Cognitive Radio Networks Caili GUO, Zhiming ZENG, Chunyan FENG, Qi LIU School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China Email: guocaili@bupt.edu.cn Received June 18, 2009; revised August 20, 2009; accepted August 21, 2009 Abstract A random periodic spectrum sensing scheme is proposed for cognitive radio networks. The sensing period, the transmission time for primary users and cognitive radios are extended to general forms as random vari- ables. A generalized Markov analytical model for sensing period optimization is presented, and the applica- tions of the proposed analytical model by using examples involving primary user systems with both voice and data traffic are illustrated. The analysis and numerical results show that sensing period does affect the maximum rewards of the channel, and the analytical model is justified by its flexibility since it uses general forms of the sensing period, the transmission time for primary users and cognitive radios. Hence the model can be easily adapted for the analysis of many different applications. Keywords: Cognitive Radio Networks, Random Periodic Spectrum Sensing, Generalized Markov Process, the Optimal Sensing Period 1. Introduction Due to energy consumption and hardware implication of Cognitive Radios (CRs), it is undesirable and impractical to assume the spectrum sensing to be continuous. In a practical CR network, such as an IEEE 802.22 network [1], a periodic spectrum sensing scheme where the spec- trum is sensed periodically to determining the pres- ence/absence of Primary Users (PUs) is preferable. The sensing time and sensing period are two key sensing pa- rameters for periodic sensing scheme. The former is a pre-defined amount of time used to achieve the desirable level of detection quality and is mainly depended on PHY-layer sensing methods, such as energy detection, matched filter and feature detection. And the latter de- fined as the interval between two successive detection processes has a significant impact on the sensing effi- ciency of CRs. In the case of the sensing period is rela- tively large, both some opportunities may go undiscov- ered and interference to PUs may occur, whereas blindly reducing the sensing period is not desirable either, as it increases the sensing overhead. Thus the design of any periodic sensing scheme involves balancing the tradeoffs among spectrum utilization, interference to PUs, and sensing overhead by selecting an appropriate sensing period. We usually consider a spectrum consist of several channels, and each channel can be a frequency band with certain bandwidth, a spreading code in a CDMA network or a set of tones in an OFDM system. Here we use the term channel broadly. In CR networks, the control of quiet period, during which all CRs should suspend their transmissions so that any CR monitoring the channel may observe the pres- ence/absence of PU signals without interference, can be synchronous or asynchronous [1–2]. Accordingly there are two kinds of periodic sensing schemes: One is syn- chronous sensing period and the other is asynchronous sensing period. Most of the existing works focused on the synchronous sensing period schemes [3–4]. As a simple solution for design and implementation, the syn- chronous sensing period scheme sets a pre-determined fixed sensing period for all channels. While it does not need the scheduling of quiet period for each channel among CRs, it shows less flexible. Recent researches [5–7] showed that the asynchronous sensing period scheme is more favorable, in which sensing period can be adjusted adaptively according to the channel-usage characteristics of each channel by the MAC-layer sens- ing protocol or through a dedicated control channel [8]. Kim [5] proposed an adaptation algorithm in which the The material in this paper is based on “Random Periodic Spectrum Sensing with Sensing Period Optimization for Cognitive Radio Net- works”, by Caili Guo, Zhiming Zeng, Chunyan Feng and Qi Liu which appeared in the proceedings of 11th IEEE International Conference on Communications Systems, ICCS 2008, Guangzhou, China, November 2008. C. L. GUO ET AL. 398 optimal sensing period is uniquely determined for each channel to maximize the discovery of opportunities as well as minimize the delay in locating an idle channel. However, this approach clearly did not consider the im- pact of sensing period selection on interference to PUs. In [6], we extended [5] to a Flexible Sensing Period (FSP) mechanism that introduces the “period control factor” to control each channel’s sensing period adap- tively to tradeoff undiscovered opportunities and inter- ference to PUs with sensing overhead effectively, but as far as each channel is concerned, the FSP also consider that sensing period is still fixed. In order to combat the fluctuation of sensing period induced by the varying of channel-usage characteristics, in [7] we described a Fuzzy Spectrum Sensing Period Optimization (FSSPO) algorithm where each channel’s sensing period is adap- tively adjusted in real time with fuzzy logic and parame- ters optimization. Existing approaches of asynchronous sensing period in [5,6] and [7] only considered how to adjust sensing pe- riod which is usually regarded as a constant once it is determined, and they all assumed that the sensing results are perfect. In this paper, the random periodic sensing scheme we proposed extends the sensing period, the time of transmission for primary users and cognitive radios to random variables and more practical situation where sensing error exists is considered. As the PUs have the highest priority, we also introduce a back-off mechanism where a random back-off time is generated whenever PUs release the channel and CRs have to delay for the back-off time before occupying the channel. Here we focus on how to model the proposed random periodic sensing scheme to a generalized Markov process and how to derive the optimal sensing period. To support the proposed analytical model for sensing period optimiza- tion, we also illustrate the applications of the analytical model by using examples involving PU systems with both voice and data traffic. The rest of the paper is organized as follows. Section 2 introduces the random periodic spectrum sensing scheme. A generalized Markov analytical model for sensing pe- riod optimization is constructed in Section 3. Then in Section 4, how to obtain performance measures of chan- nels is considered. Example applications of the proposed analytical model for real networks are illustrated in Sec- tion 5. Numerical examples are presented and discussed in Section 6. Finally, we conclude the paper and suggest future directions in Section 7. 2. Random Periodic Spectrum Sensing Scheme In CR networks, a channel usually could be modeled as an ON-OFF source alternating between ON (busy) and OFF (idle) periods depending on PUs’ channel-usage pattern. The sojourn time of a ON period is used for transmission of PUs themselves and that of a OFF pe- riod captures the time period in which the channel can be utilized by CRs’ transmission without causing any harmful interference to PUs. The distribution of the so- journ time in the ON state can assumed to be general, and so is that in the OFF state. Thus the ON-OFF chan- nel-usage stochastic process describing the behavior of the channel occupation can form an alternative renewal process. A renewal period models a time period in which the PUs and CRs occupy the channel once alternatively. Hence there are only busy and idle two possible states in a renewal period accordingly. Considering that the sensing period of each channel is a random variable and sensing errors are possible present at any moment as well as a back-off mechanism is intro- duced, in this paper we further subdivide the channel in a renewal period into five kinds of states: normal busy, available idle, delay idle, false alarm and miss detection. Below we will describe each state in detail. Normal busy and available idle are two kinds of nor- mal available states. The former denotes that PUs are being served normally and the latter stands for the chan- nel are being utilized for the transmission of CRs. When the channel is in normal available, it is sensed once every random time interval T, i.e. sensing period, to make sure whether it is in normal busy or available idle. As soon as the service of PUs completes, a random back-off time interval T0 is generated to prevent CRs from occupying the channel at once, within which the channel is in delay idle state. The back-off mechanism can help decrease both the connection cost generated by switching channel state frequently and the short-term interference probability induced by non-negligible delay for relinquishing bands by CRs. Corresponding to the binary hypotheses test of spec- trum sensing: B0 (null hypothesis indicating that the sensed channel is available for CRs) vs. B1 (alternative), there are two kinds of sensing errors: false alarm (the overlook of an available channel) due to mistaking B0 for B1 and miss detection (the mistake of identifying an un- available channel as an opportunity) due to mistaking B1 for B0. When false alarm or miss detection is present, the channel will transfer to false alarm or miss detection state. The presence of sensing errors also has significant effects on the performance of sensing schemes. Common to most of the periodic spectrum sensing schemes, the sensing period selection of random periodic spectrum sensing scheme has strong impact on the sens- ing efficiency. In order to analyze the optimal sensing period effectively, an analytical model for sensing period optimization is constructed in next section. 3. Analytical Model Owing to the multiplicity of conditionality and correla- tion that exists among the various random variable in- Copyright © 2009 SciRes. WSN C. L. GUO ET AL.399 volved in the random periodic sensing scheme, the analysis and performance evaluation, especially the de- termination of optimal sensing period is usually difficult. Therefore, a set of simplifying assumptions is to be made for analytical model to be tractable. We assume the fol- lowing The sojourn time of normal busy and available idle are continuous random variables and drawn from general cumulative distribution functions (c.d.f.) represented by F1(t) and F2(t) respectively. Suppose the probability den- sity functions (p.d.f.) for Fi(t) (i=1,2) are fi(t), means are 1 i , and, 0() . 0 ()()1 exp[()] t ii i Ftf xdxxdx ii tdF t 0 t 1 The sensing period T is also a continuous random variable and follows an arbitrary distribution with c.d.f., p.d.f. and mean are 1()Gt,1() g y and 1 1 , respectively, and ( )] 1 1 11 00 () ( tt G tgy 1 y dy) 1dy[exp()ET 1 0()tdG t . Delay idle state can transfer to normal busy or available idle. It is assumed that if a PU reappears during T0 he can claim the channel and the delay idle will trans- fer to normal busy with a constant rate γ. Otherwise, if the back-off timer expires and no one claims the channel, delay idle transfers to available idle instead. In this case, T0 follows an arbitrary distribution, and its c.d.f., p.d.f. and mean are 2()Gt, 2() g y and 1 2 , respectively, and 22 2 00 ()( )1[( )] tt Gtgy dyexpy dy 1 2 02 0 () ()ETtdG t We assume that α and β denote false alarm and miss detection probabilities respectively, and the sojourn times of false alarm and miss detection are arbitrarily distributed with c.d.f.s (), 1,2 i. Let () i ht andi Ht i be their p.d.f.s and means, and 000 ()( )1[( )() tt iii ii H th zdzexpzdztdHt When miss detection occurs the channel transfers to delay idle, whereas when false alarm occurs, in order to render mathematical tractability, we also assume that the channel skips normal occupy and transfers to delay idle too, for the normal occupy time included is small enough compared to total time of the long-run channel and can be neglected. We assume that the sensing time is small relative to distribution parameters12 0 ,,,(),()ET ET and (1,2) ii , and can be negligible. It is also assumed that channel is in delay idle initially, and all random variables are mutu- ally independent. Consider the stochastic process (), 0St t, where S(t) denotes the state of the channel at time t, as following 0 stands for the channel is in delay idle, and the channel is occupied neither by PUs nor by CRs. (, )ik means that the channel is in normal available states, where i =0/1 represents that the channel is in available idle/normal busy and k stands for the times of the channel has been sensed, k =0,1,2, ··· . (2, j) denotes that the sensing error is present, where j =1/2 means that the system is in false alarm/miss detec- tion. It is easy to see that, {S(t), t≥0} is a non-Markovian stochastic process. In order to make the process Mark- ovian, we need to incorporate the missing information by adding “supplementary variables” to the state description. Hence at time t, let Xi (t) (i =1/2) be the remaining nor- mal busy/available idle time, Yi (t) (i =1/2) the remaining sensing/delay time, and Zi (t) (i =1/2) the remaining false alarm /miss detection time. Formally, the evolution of the stochastic process describing the dynamic behavior of the channel can be fully characterized by a generalized Markov process (),(), (),()|0 ii i StXtY tZtt, and the following state probabilities are defined 1 02 2 (,,){ ()(,),(), ()},0,1;0,1, 2, (,){ ()0,()} (,){ ()(2,),()},1,2 ik i ji PtxydxPStikxXtx dx yYt ydyik PtydyPStyY tydy PtzdzPStjzZtzdzj Notations: 0 1211 22 1211 22 1234 11 22 :()1(),: ()(), ()[1()]/ ,,:()(),( ) ˆˆ ˆˆ ˆˆ ,,:()(),() ,:1,1 ,,, :, st iii iii F tFtfsftedtFs fss ffgffsffsggs ffgffffg g MMMM MM 23 14 ,,sMsMs 12112 2 ,,:exp[( )], exp[() ], x xy x EE EEsxE sx x exp[ () ] y Es y The possible states of channels and the transitions among them are shown in Figure 1. Figure 1. The state transition model of the generalized Markov process. Copyright © 2009 SciRes. WSN C. L. GUO ET AL. 400 According to Figure 1, a few new performance meas- ures could be defined. The probability of the channel in available idle state, normal busy state and delay idle state are Available Idle Probability, Normal Busy Probability and Delay Idle Probability, respectively. Sensing Fre- quency is defined the frequency of the occurrence of channel sensing when the channel is in state(, ),0,1iki . False alarm occurs if and only if the channel transfers from state(0 to state (2,1); while miss de- tection occurs if and only if the channel transfers from state to state (2,2). So False Alarm Frequency and Miss Detection Frequency are defined accordingly. Also define, , , )(0,1,2)kk )(0,1, 2)kk 1 (1, ()Rt2()Rt 09() L t,1() L t2() , L t and 3() L tare the Instantaneous Probability of Available Idle, Normal Busy, Delay Idle, Instantaneous Frequency of Sensing, False Alarm and Miss Detection at an arbi- trary time t, respectively. Then define R1, R2, L0, L1, L2 and L3 are the steady state forms of 1() R t2(), R t, 0() L t,1() L t2(), L t and 3() L t, respectively, e.g., 11 ( )lim t R Rt . In CR networks, each channel will go through one or all kinds of states in which available idle and normal busy generate rewards by the using for the transmission of CRs and PUs, respectively, delay idle and false alarm waste opportunities, miss detection induces interference to PUs, and sensing has overhead. It is assumed that the expected rewards per unit time generated by the channel are e1 or e2 when the channel is in available idle or nor- mal busy, respectively. And the expected losses per unit time induced by the delay of channel is c0, the expected cost of each sensing is c1, the expected false alarm and miss detection expenses every time are c2 and c3, respec- tively. We also assumed that expected total rewards gen- erated by the channel during (0,t] are R, then 3 2 00 00 0 11 ()() ()() tt t iij j ij RteRtdtcLtdtcLtdt (1) where and c3 are weighting factors ( ). Taking Laplace transform on both sides of (1), we have 12012 ,,,,eeccc 123 ccc 1 e 20 1ec 3 2 00 11 () [()()()]/ iij j ij RseR scLscLss (2) And the expected rewards per unit time in the steady state is 2 0 3 2 00 11 lim) /lim) ts iij j ij RRttsR eRc Lc L s (3) where performance measures Ri (i = 1, 2), L0 and Lj (j = 1, 2, 3) could be expressed as functions of the mean sensing period E(T) (denoted by x ) and all of them will be il- lustrated how to obtain in Section 4. Then taking suitable value for x to make R maximum can bring out the op- timal sensing period x . That is 3 2 00 11 arg max) iij j xij x eRc Lc L (4) 4. Derivation of Performance Measures In order to derive performance measures for searching the optimal sensing period, the steady state probabilities with exact solutions in closed form should be calculated. How to calculate them using probability analysis and supplementary variables method is discussed below. According to Figure 1, we have the following differ- ential difference equations 210 ()()(,, )00,1,2 k xvyptxy k tx (5) 1110 0 0 ()()(,,)(,,) k k x vy ptxyp txy tx (6) 111 ()()(,, )01,2 k xvyptxyk tx (7) 20 ()(,) 0vy pty ty (8) 121 ()(,) 0zptz tz (9) 222 ()(,) 0zptz tz 1 (10) The above equations are to be solved under the bound- ary conditions 0 112 00 0 222 0 (,0) (,,)( )(,) () (,)() k k pt pt x ydxdyzptzdz zp tzdzt 002 0 0 (,0)()(,)pt vyptydy (12) 0 201 0 (, ,0) ()(,, )1,2 k k ptx xptxydxdy k (13) 10 0 0 (,0)(, )pt ptydy (14) 1111 0 (, ,0)( )(,,)1,2 kk ptxvyptxydxdyk (15) 2110 0 0 (,0)( )(, ,) k k pt vyptxydx (16) 221 1 0 0 (,0)( )(,,) k k ptvyptxydxdy (17) And the initial conditions Copyright © 2009 SciRes. WSN C. L. GUO ET AL. Copyright © 2009 SciRes. WSN 401 0 14 2 1 (, ,) (1)(1)()( ) ()/()0,1,2... k x Psxy kk M Mf ffgEF Gy Dsk x 0(0,)( )py y (18) (19) Taking Laplace transforms of Equations (5)–(18) with respect to t and solving the equations, we can derive 10 11 11 1141141 (, ,) {[(1)(1)(1)(1)]()()(1)()()}/() xx Psxy M gffMgfEFxGyMgfEFxGyDs (20) 1 111 11212214111 (, ,) [(1)(1)(1)()(1)]()()()/()1, 2... k k x Psxy fgMffgffMffEFxGyDsk (21) 04141241141212 (,)()( )/() y PsyMMMMfMMfMMffEGyDs (22) 2111 12411212421211 (,)[()]exp()() /()PszMfMMfgMffMfgM ffgszHz Ds (23) 2214 21 42 12 (,)() exp()()/()PszMMfgMMffgszHz Ds (24) where 1411311314111314 214114 21 * 1111214122412 1133121134121 4121 1 ()(/) (/) (/)(/) ()(){[/()/][()/( [( DsMMMMMMMMfMMMMfMMMMff )/] M fMffhsMMMM MMM MMMf MM 3412224122412132 1 ** 4222 11121114214212 )//][/()/ ]} [()] ()()() MMMfMM MMMffg Mfs fMffhsgMMfMMffhsg (25) 1 22 1 2 11111 1 11 1111 2 122212122 22 212121112 22 1212 12 ˆ (0)()/[()/ ] ˆˆ [()/] [()/] ˆ {()/{[()]/} ˆ {[()]/} {[( ) DD MMf MfM ff Mf Mf MM In accordance with the definitions of and , we obtain 1()Rt 2()Rt 10 0 0 ()(, ) k k RtPtxdx (26) 21 0 0 ()(, ) k k Rt Ptxdx (27) Taking Laplace transform on both sides of Equations (26), (27) and using Equations (19)–(25), we get * 1 * 1414 122 () ()()/() s Rs M MgMMfgFsDs (28) 1 ˆ 21 121 2 21 221 112 11 121 11 11 2 ˆˆ ˆ ]/ }} ˆˆˆ ˆ ()(1/)( ˆˆ ˆ )(1/) ˆˆˆ ˆ ()(1/) 1 ˆ f fg M fMfff f Mff g MfMf fg (32) With the same derivation of R1 and R2, we can get 2 2 * 211241 * 1241 1 * 24241 22 () [() ()]() () RsMMM gMf MMgfFs MgMf gFs() (29) 2 21 011 1 * 12 ˆˆ ( ˆˆ )()/ LMMfMf SM ffD G 1 (33) According to Figure 1, as the channel is in state (, ),0,1ik i , it is being sensed. Using state transfer frequency formula shown in [9], we get where, D(s) is given by Equation (25). By applying the limiting theorem of Laplace transform and L’Hospital’s rule, we get 101 0 0 ()()[(, )(, )] kk k LtxP txPtxdx (34) 11 1 0 * 11122 lim()lim() ˆ ˆˆ () ts RRtsRs ()/ M gM fgFD (30) Taking Laplace transform on Equation (34) and using Equations (19)–(25), we obtain 22 2 0 1112122 ** 112212 2 lim()lim() ˆˆ ˆˆ [( ˆ ˆˆ ()[() ()]/ ts RRtsRs )] M gMfMgf FggfFD 12 2 21 12 114 14 1124 1 124 24 24 () {() {( )] ()} () LsMMg MMfgf }/() M MMgMf MMgff M gMgffDs (35) (31) where Then C. L. GUO ET AL. 402 2 2 11 1 0 11 21111 11 lim( )lim() ˆˆ ˆˆ ˆˆ [ ˆˆˆ () ]/ ts LLt sLs 2 ˆ M ffgfgMf MffgD f (36) Similarly, we can derive 2 22 21111 1 211 ˆˆ ˆ ˆ ( ˆˆˆ ˆˆ )/ LMf fgMf 1 ˆ f f gMffgD (37) 22 31 11 ˆˆˆ ˆ ()LMfgMffg ˆ /D ) (38) Substituting , L0 and by (30), (31), (33), (36), (37) and (38) into (4), respectively, the optimal sensing period (1,2) i Ri(1,2,3 j Lj x is determined by, i.e., the distributions of sojourn time of normal busy and available idle. For the sojourn time of normal busy is used for transmission of PUs themselves and that of available idle can be utilized by CRs’ transmission when PUs have no data to transmit, are usually deter- mined by the traffic generated by PUs services in practi- cal networks. () i Ft () i Ft 5. The Applications of Sensing Period Optimization This section illustrates the applications of the analytical model developed here by using examples involving PU systems with both voice and data traffic. 5.1. Optimization for PUs with Voice Traffic A typical phone conversation is marked by periods of active talking/talk spurts (or ON periods) interleaved by silence/ listening periods (or OFF periods). The duration of each period is exponentially distributed, i.e., the so- journ time of normal busy and available idle follow ex- ponential distributions with probability density functions () it ii f te , and means 1 i are constants. It is a special case for analytical model mentioned above in which 1 i s can be substitute by. The tran- sient rate of available idle to normal busy and that of normal busy to delay idle are thus reduced to con- stants 1 iz i . 5.2. Optimization for PUs with Data Traffic In the past, exponential distributions are also frequently employed to model interarrival times of data calls for its simplicity, but exponential distributions may not be ap- propriate in modeling data traffic. Taking Email, an im- portant application that constitutes a high percentage of internet traffic, as an example, its traffic can also be characterized by ON/OFF states. During the ON-state an email could be transmitted or received, and during the OFF-state a client is writing or reading an email. Ac- cording to traffic models included in the UMTS Forum 3G traffic and ITU RM.2072, the Pareto distribution, which is one of popular heavy-tailed distributions, can be used to close capture the nature of Email traffic for both ON and OFF state, i.e., the sojourn time of normal busy and available idle follow Pareto distributions with prob- ability density functions 1 () , i i ii ii ft t t , and means /( 1) ii i , where0 i is called the shape parameter and 0 i is called the scale parameter. In order to derive performance measures to search the optimal sensing period, 1 i i ii t and means /(1) ii i should substitute() i f tand 1 i in Equations (5)–(18). 6. Numerical Results and Discussions Through numerical experiments, we examine the impact of sensing period selection on maximum expected re- wards of the channel for different traffic types under various channel parameters in this section. 6.1. Performance Analysis According to the characteristics of channels, we first set the channel parameters as the following 0.02, 10.033, 10.2,c3 c 20.1, 0.2,0.1 0.5 ,12 0.1,ee 02 0.05,cc , and let us assume that T0 follows the uniform distribution with parameters 1yand 10y , written 0 T~ (Uy 1 ,10)y , and 10y. Two traffic types of PUs are considered, i.e., Type I: voice traffic and Type II: data traffic. In the case of voice traffic, the sojourn time of normal busy and available idle follow exponential distributions with10.04, 20.01 ; for data traffic, the sojourn time of normal busy and available idle follow Pareto distributions with 1 0.8, 1 5 and 22 2.5,60 , i.e., means are 10.04 and 20.01 , respectively. Here 11 and 22 are selected for easy comparison. To validate the feasibility of the proposed analytical model for sensing period optimization, numerical exam- ples are carried out for the following three sensing schemes, i.e., 1) Scheme 1: Tx , that is, it is exactly a fixed period sensing scheme that sensing is performed at once where Tx . 2) Scheme 2: T follows the uniform distribution with parameters x and 1x , written ~( ,1TU xx) . 3) Scheme 3: T follows the exponential distribution with parameter x , written ~(TEPx). Copyright © 2009 SciRes. WSN C. L. GUO ET AL.403 With MATLAB, from (4) we can obtain the optimal sensing periods x and the maximum expected rewards R of the channel per unit time in the steady state for each sensing scheme. Figure 2 and Figure 3 illustrate the ex- pected rewards of the channel for various values of x under Type I and Type II traffic types respectively. For Type I voice traffic, Figure 2 shows that the maximum expected rewards of the channel is varied ac- cording to the distribution of sensing period T. The op- timal sensing periods for each scheme are {6. 5 ,x and the maximum expected rewards are . So the optimal sensing scheme is sensing randomly with sensing period T following the exponential distribution when 13.2,7.8} {1R09.8,106.1,114.9} 7.8x under the above-mentioned channel parameters, for the scheme obtained is maximum compared to other two schemes. 114.9R For Type II data traffic, Figure 3 shows that the opti- mal sensing periods for each scheme are {10.7,17.9,11.3}xand the maximum expected rewards are . From Figure 3, it can easily find that the optimal sensing scheme is sensing randomly with sensing period T following the uniform distribution. One point that deserves mention is that, compared to the voice traffic, there are significant differences in maxi- mum expected rewards among the three schemes in the case of data traffic. {77.7,113.7,90.2}R 6.2. Analysis of Channel Parameters In practical, the optimal sensing scheme is different with different sets of channel parameters. Next, we study ef- fects of the setting of various channel parameters on the optimal sensing scheme. 1) Effects of Distribution Parameters: in both voice Figure 2. expected rewards vs. expected sensing period for voice traffic. Figure 3. expected rewards vs. expected sensing period for data traffic. Table 1. The Optimal Rewards R Vs. Optimal Mean Sens- ing Period x for Various Distribution Parameters under 12 0.1,ee , 02 0.05cc 13 , 0.2,0.5cc 0.2, 0.1 , 0 T~ (1,10)Uy y and 10y . Type Ⅰ Type Ⅱ 112 2 12 {/, / ,,} T x R x R Tx 7.8 108.1 6.5 121.3 ~( ,1)TU xx 10.2 106.3 9.2 86.5 (0.01,0.04 ,0.02,0.03 3,0.1) ~()TEPx 11.8 105.5 7.4 94.6 Tx 9.4 110.5 10.779.8 ~( ,1)TU xx 11.9 109.8 8.8 99.6 (0.04,0.01 ,0.05,0.03 3,0.1) ~()TEPx 10.2 112.3 5.9 128.9 Tx 10.5 97.5 15.1108.2 ~( ,1)TU xx 9.3 99.3 17.5132.4 (0.04,0.01 ,0.02,0.1,0 .033) ~()TEPx 8.9 101.63.9 86.7 traffic and data traffic, the distribution parameters 12 12 ,,,, and 12 12 ,,,, 2 0.1 directly reflect the sojourn time of normal busy, available idle, delay idle, false alarm and miss detection state, respectively. The distribution parameters 11 /0.04 ,22 /0.01 0 (1 0.02,.033, ) show that the sojourn time of available idle is longest, which means low or moderate PU traffics are chosen. Other three distribution parame- ters are chosen for 3 sensing schemes, and the optimal rewards R vs. the optimal mean sensing period x are shown in Table 1, respectivel a) (112212 /, /,,, y. ) is (0.01, 0.04, 0he sojourn time of normal busy is relatively long and less opportunities can be used by transmission of CRs; b) (112 212 /, /,,, .02, 0.033, 0.1). T ) is (0.04, 0.01, he sojourn time of de- lay idle is reduced so that more opportunities can be used by CRs than 1); and c) (112212 /, /,,, 0.05, 0.033, 0.1). T ) is (0.04, 0.01 The sojourn time of miss detec-, 0.02, 0.1, 0.033). Copyright © 2009 SciRes. WSN C. L. GUO ET AL. Copyright © 2009 SciRes. WSN 404 Factors: Weighting factors e1, e2 tion is longer than that of false alarm. From Table 1, we clearly see that the optimal sensing scheme is different with regard to different distribution parameters. 2) Effects of Weighting for voice traffic: 1) fixd e (=0.dio15) an varus 2 1 ; and 2) fixed1 (= 0.2) and vious 2 ar , and two differet situations fodata traffic: 1) fixe2 n r d (=0.15 ) and various 1 ; and 2) fixed1 (=0.2) and rious2 va . As shown in Figure 4( and Figure 4(b), va ying , c0, c1, c2 and c3 can be treated as indexes regarding the importance of 1201 ,,, R RLL and L2. Generally speaking, the PU applicati GPS, can only endure minor interference for acceptable Quality of Service (QOS). For such applications, the cost of interference induced by miss detection is more important and c3 is obviously bigger than all other factors as shown in above-chosen setting 12 0.1,ee02 0. 05,cc10.2,c ( 30.5c ons, such as ). Table 2 showptiman sensing period s optimal rewards R and the ol mea x for two different network applica- tions : a) In the case where the PU is not sensitive to in- terference, the weighting factors c0 and c2 are both larger than other factors in order to maximize the utilization of existing opportunities. Here (e1, e2, c0, c1, c2, c3) is set to (0.1, 0.1, 0.35, 0.05, 0.35, 0.05). b) For energy-constrained CR networks such as sensors and mobile ad hoc applica- tions, frequent sensing is undesirable for high energy overhead, so the weighting factor c1 should be set rela- tively large and (0.1, 0.1, 0.05,0.5,0.05,0.1) is chosen. This table demonstrates that the optimal sensing scheme is also different with regard to different weighting factors and from the Table 2 one can easily find which scheme performs best. a)r 1 (2 ) among 0.1 and 1, we observed that the performance ooice traffic is not sensitive to which sensing scheme is preferred. However, for data traffic, with the variation of 1 f v and2 , the optimal sensing scheme is changing amog three sensing schemes and the maximum ex- pected rewards have big different, as shown in Figure 4(c) and Figure 4(d). The possible reason is that the optimal sensing period for voice traffic is depending only on a constant mean value of the transmission time for primary users and cognitive radios whereas performance of data traffic are affected by not only mean value but also the distributions of the time of transmission for primary us- ers and cognitive radios. From the above discussions, we suggest that: 1) for vo n his paper dealt with the random sensing period ice traffic, the maximum expected rewards of three sensing scheme is close to each other. In real system, a fixed period sensing scheme is preferred for simplicity; and 2) however, the situation changes dramatically for data traffic, the maximum expected rewards of three sensing scheme are far different. The analytical model proposed can be used to search the optimal sensing scheme, and the analysis can be easily extended to that of any other distribution of sensing period T. 7. Conclusions and Future Work 6.3. Performance Comparison for Different ccording to the proposed analytical model for sensing Traffic Types AT period optimization, a sensing scheme with a bigger ex- pected reward performs better. Figure 2, Figure 3, Table 1 and Table 2 show that the optimal sensing scheme is different for different traffic types. In Figure 4, we show the expected rewards for different schemes under 0.02, 10.033, 20.1, 12 0.1, 0.1,ee 02 cc 1 3 0.05, 0.2,c c0.5, and two different situations scheme in CR networks. An efficient generalized Markov analytical model for sensing period optimiza- tion was proposed and studied. How our proposed ana- lytical model can be applied to PU systems with both voice and data traffic was also discussed. Both numeri- cal results and analysis for various channel parameters and traffic types of PUs were obtained and compared. We found that sensing period does affect the maximum expected rewards of the channel, and the proposed analytical model is valid for the analysis of the case where the sensing period, the transmission time for primary users and cognitive radios are all following arbitrary distributions. In this work, we assume that the sensing period for ea Table 2. The optimal rewardsvs. optimal mean sensing R period x for various weighting factors under0.04, 0. 01, 12 0.02, 0.033,0.1, 0. 2, 0.1 0 T~ (1,10)Uy y , and 10y. (e e2, 1, Type I Type II c0, c1, c2, c3) T x R x R Tx ch channel is different, i.e. the sensing period is asyn- chronous for all channels. The proposed scheme is suit- able for the scenario where each CR only sense the channel for its operating. If each CR is responsible for sensing more than one channel, the intelligence schedule algorithm of sensing period should be used to negotiate among CRs because the quiet period of each channel is also asynchronous. In future, we would like to develop practical schedule mechanisms or protocols, which deal 10.4 107.6 9.773.9 ~( ,x 1)TUx (0.1,0.1, 11.3 111.4 14.598.2 0.35,0.0 5,0.35,0. 05) ~()TEPx 8.9 105.3 10.3114.6 Tx 7.5 98.8 11.889.2 ~( ,x 1)TUx 15.2 95.6 6.2125.5 (0.1,0.1, 0.05,0.5, 0.05,0.1) ~()TEPx 12.6 101.2 4.975.4 C. L. GUO ET AL. 405 (a) (b) (c) (d) Figure 4. Performance comp arison of different traffic types under 0.02, 10.033, 20.1, 0.2, 0.1 , 12 0.1,ee 021 3 0.05, 0.2,0.5ccc c with (a) 2 =0.15, (b) 1 = 0.2, (c) 2 = 0.15, and (d) 1 = 0.2. his work was supported by Natural Science Foundation ] Y. C. Liang, W. S. Leon, Y. H. Zeng, et al., “System Lau , R. S. Cheng, R. D. 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