Modeling and Analysis of Random Periodic Spectrum Sensing for Cognitive Radio Networks

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1 Wireless Sensor Nework, 9,, doi:.436/wsn Published Online December 9 (hp:// 397 Modeling and Analysis of Random Periodic Specrum Sensing for Cogniive Radio Neworks Absrac Caili GUO, Zhiming ZENG, Chunyan FENG, Qi LIU School of Informaion and Communicaion Engineering, Beijing Universiy of Poss and Telecommunicaions, Beijing, China guocaili@bup.edu.cn Received June 8, 9; revised Augus, 9; acceped Augus, 9 A random periodic specrum sensing scheme is proposed for cogniive radio neworks. The sensing period, he ransmission ime for primary users and cogniive radios are exended o general forms as random variables. A generalized Markov analyical model for sensing period opimizaion is presened, and he applicaions of he proposed analyical model by using examples involving primary user sysems wih boh voice and daa raffic are illusraed. The analysis and numerical resuls show ha sensing period does affec he maximum rewards of he channel, and he analyical model is jusified by is flexibiliy since i uses general forms of he sensing period, he ransmission ime for primary users and cogniive radios. Hence he model can be easily adaped for he analysis of many differen applicaions. Keywords: Cogniive Radio Neworks, Random Periodic Specrum Sensing, Generalized Markov Process, he Opimal Sensing Period. Inroducion Due o energy consumpion and hardware implicaion of Cogniive Radios (CRs), i is undesirable and impracical o assume he specrum sensing o be coninuous. In a pracical CR nework, such as an IEEE 8. nework [], a periodic specrum sensing scheme where he specrum is sensed periodically o deermining he presence/absence of Primary Users (PUs) is preferable. The sensing ime and sensing period are wo key sensing parameers for periodic sensing scheme. The former is a pre-defined amoun of ime used o achieve he desirable level of deecion qualiy and is mainly depended on PHY-layer sensing mehods, such as energy deecion, mached filer and feaure deecion. And he laer defined as he inerval beween wo successive deecion processes has a significan impac on he sensing efficiency of CRs. In he case of he sensing period is relaively large, boh some opporuniies may go undiscovered and inerference o PUs may occur, whereas blindly reducing he sensing period is no desirable eiher, as i increases he sensing overhead. Thus he design of any The maerial in his paper is based on Random Periodic Specrum Sensing wih Sensing Period Opimizaion for Cogniive Radio Neworks, by Caili Guo, Zhiming Zeng, Chunyan Feng and Qi Liu which appeared in he proceedings of h IEEE Inernaional Conference on Communicaions Sysems, ICCS 8, Guangzhou, China, November 8. periodic sensing scheme involves balancing he radeoffs among specrum uilizaion, inerference o PUs, and sensing overhead by selecing an appropriae sensing period. We usually consider a specrum consis of several channels, and each channel can be a frequency band wih cerain bandwidh, a spreading code in a CDMA nework or a se of ones in an OFDM sysem. Here we use he erm channel broadly. In CR neworks, he conrol of quie period, during which all CRs should suspend heir ransmissions so ha any CR monioring he channel may observe he presence/absence of PU signals wihou inerference, can be synchronous or asynchronous [ ]. Accordingly here are wo kinds of periodic sensing schemes: One is synchronous sensing period and he oher is asynchronous sensing period. Mos of he exising works focused on he synchronous sensing period schemes [3 4]. As a simple soluion for design and implemenaion, he synchronous sensing period scheme ses a pre-deermined fixed sensing period for all channels. While i does no need he scheduling of quie period for each channel among CRs, i shows less flexible. Recen researches [5 7] showed ha he asynchronous sensing period scheme is more favorable, in which sensing period can be adjused adapively according o he channel-usage characerisics of each channel by he MAC-layer sensing proocol or hrough a dedicaed conrol channel [8]. Kim [5] proposed an adapaion algorihm in which he Copyrigh 9 SciRes.

2 398 C. L. GUO ET AL. opimal sensing period is uniquely deermined for each channel o maximize he discovery of opporuniies as well as minimize he delay in locaing an idle channel. However, his approach clearly did no consider he impac of sensing period selecion on inerference o PUs. In [6], we exended [5] o a Flexible Sensing Period (FSP) mechanism ha inroduces he period conrol facor o conrol each channel s sensing period adapively o radeoff undiscovered opporuniies and inerference o PUs wih sensing overhead effecively, bu as far as each channel is concerned, he FSP also consider ha sensing period is sill fixed. In order o comba he flucuaion of sensing period induced by he varying of channel-usage characerisics, in [7] we described a Fuzzy Specrum Sensing Period Opimizaion (FSSPO) algorihm where each channel s sensing period is adapively adjused in real ime wih fuzzy logic and parameers opimizaion. Exising approaches of asynchronous sensing period in [5,6] and [7] only considered how o adjus sensing period which is usually regarded as a consan once i is deermined, and hey all assumed ha he sensing resuls are perfec. In his paper, he random periodic sensing scheme we proposed exends he sensing period, he ime of ransmission for primary users and cogniive radios o random variables and more pracical siuaion where sensing error exiss is considered. As he PUs have he highes prioriy, we also inroduce a back-off mechanism where a random back-off ime is generaed whenever PUs release he channel and CRs have o delay for he back-off ime before occupying he channel. Here we focus on how o model he proposed random periodic sensing scheme o a generalized Markov process and how o derive he opimal sensing period. To suppor he proposed analyical model for sensing period opimizaion, we also illusrae he applicaions of he analyical model by using examples involving PU sysems wih boh voice and daa raffic. The res of he paper is organized as follows. Secion inroduces he random periodic specrum sensing scheme. A generalized Markov analyical model for sensing period opimizaion is consruced in Secion 3. Then in Secion 4, how o obain performance measures of channels is considered. Example applicaions of he proposed analyical model for real neworks are illusraed in Secion 5. Numerical examples are presened and discussed in Secion 6. Finally, we conclude he paper and sugges fuure direcions in Secion 7.. Random Periodic Specrum Sensing Scheme In CR neworks, a channel usually could be modeled as an ON-OFF source alernaing beween ON (busy) and OFF (idle) periods depending on PUs channel-usage paern. The sojourn ime of a ON period is used for ransmission of PUs hemselves and ha of a OFF period capures he ime period in which he channel can be uilized by CRs ransmission wihou causing any harmful inerference o PUs. The disribuion of he sojourn ime in he ON sae can assumed o be general, and so is ha in he OFF sae. Thus he ON-OFF channel-usage sochasic process describing he behavior of he channel occupaion can form an alernaive renewal process. A renewal period models a ime period in which he PUs and CRs occupy he channel once alernaively. Hence here are only busy and idle wo possible saes in a renewal period accordingly. Considering ha he sensing period of each channel is a random variable and sensing errors are possible presen a any momen as well as a back-off mechanism is inroduced, in his paper we furher subdivide he channel in a renewal period ino five kinds of saes: normal busy, available idle, delay idle, false alarm and miss deecion. Below we will describe each sae in deail. Normal busy and available idle are wo kinds of normal available saes. The former denoes ha PUs are being served normally and he laer sands for he channel are being uilized for he ransmission of CRs. When he channel is in normal available, i is sensed once every random ime inerval T, i.e. sensing period, o make sure wheher i is in normal busy or available idle. As soon as he service of PUs complees, a random back-off ime inerval T is generaed o preven CRs from occupying he channel a once, wihin which he channel is in delay idle sae. The back-off mechanism can help decrease boh he connecion cos generaed by swiching channel sae frequenly and he shor-erm inerference probabiliy induced by non-negligible delay for relinquishing bands by CRs. Corresponding o he binary hypoheses es of specrum sensing: B (null hypohesis indicaing ha he sensed channel is available for CRs) vs. B (alernaive), here are wo kinds of sensing errors: false alarm (he overlook of an available channel) due o misaking B for B and miss deecion (he misake of idenifying an unavailable channel as an opporuniy) due o misaking B for B. When false alarm or miss deecion is presen, he channel will ransfer o false alarm or miss deecion sae. The presence of sensing errors also has significan effecs on he performance of sensing schemes. Common o mos of he periodic specrum sensing schemes, he sensing period selecion of random periodic specrum sensing scheme has srong impac on he sensing efficiency. In order o analyze he opimal sensing period effecively, an analyical model for sensing period opimizaion is consruced in nex secion. 3. Analyical Model Owing o he mulipliciy of condiionaliy and correlaion ha exiss among he various random variable in- Copyrigh 9 SciRes.

3 C. L. GUO ET AL. 399 volved in he random periodic sensing scheme, he analysis and performance evaluaion, especially he deerminaion of opimal sensing period is usually difficul. Therefore, a se of simplifying assumpions is o be made for analyical model o be racable. We assume he following The sojourn ime of normal busy and available idle are coninuous random variables and drawn from general cumulaive disribuion funcions (c.d.f.) represened by F () and F () respecively. Suppose he probabiliy densiy funcions (p.d.f.) for F i () (i=,) are f i (), means are, and F ( ) f ( x) dx exp[ ( x) dx], i i dfi(). i i i The sensing period T is also a coninuous random variable and follows an arbirary disribuion wih c.d.f., p.d.f. and mean are G( ), g( y ) and, respecively, and G () g ( y) dy exp[ ( ) ] ET ( ) y dy dg (). Delay idle sae can ransfer o normal busy or available idle. I is assumed ha if a PU reappears during T he can claim he channel and he delay idle will ransfer o normal busy wih a consan rae γ. Oherwise, if he back-off imer expires and no one claims he channel, delay idle ransfers o available idle insead. In his case, T follows an arbirary disribuion, and is c.d.f., p.d.f. and mean are G( ), g( y ) and, respecively, and ET ( ) dg( ) G () g ( y) dy exp[ ( y) dy] We assume ha α and β denoe false alarm and miss deecion probabiliies respecively, and he sojourn imes of false alarm and miss deecion are arbirarily disribued wih c.d.f.s Hi (), i,. Le hi () and i be heir p.d.f.s and means, and i i i i i H () h( zdz ) exp[ ( zdz ) dh() When miss deecion occurs he channel ransfers o delay idle, whereas when false alarm occurs, in order o render mahemaical racabiliy, we also assume ha he channel skips normal occupy and ransfers o delay idle oo, for he normal occupy ime included is small enough compared o oal ime of he long-run channel and can be negleced. We assume ha he sensing ime is small relaive o disribuion parameers,,, ET ( ), ET ( ) and i ( i,), and can be negligible. I is also assumed ha channel is in delay idle iniially, and all random variables are muually independen. Consider he sochasic process S (),, where S() denoes he sae of he channel a ime, as following sands for he channel is in delay idle, and he channel is occupied neiher by PUs nor by CRs. (, ik ) means ha he channel is in normal available saes, where i =/ represens ha he channel is in available idle/normal busy and k sands for he imes of he channel has been sensed, k =,,,. (, j) denoes ha he sensing error is presen, where j =/ means ha he sysem is in false alarm/miss deecion. I is easy o see ha, {S(), } is a non-markovian sochasic process. In order o make he process Markovian, we need o incorporae he missing informaion by adding supplemenary variables o he sae descripion. Hence a ime, le X i () (i =/) be he remaining normal busy/available idle ime, Y i () (i =/) he remaining sensing/delay ime, and Z i () (i =/) he remaining false alarm /miss deecion ime. Formally, he evoluion of he sochasic process describing he dynamic behavior of he channel can be fully characerized by a generalized Markov process S (), Xi(), Y i(), Zi(), and he following sae probabiliies are defined Pik (, x, y) dx P{ S() (, i k), x Xi () xdx, y Y ( ) y dy}, i,; k,,, P(, y) dy P{ S(), y Y() ydy} P j(, z) dz P{ S() (, j), z Zi() zdz}, j, Noaions: s : Fi( ) Fi( ), : fi ( s) fi( ) e d, Fi ( s) [ fi ( s)]/ s f, f, g : f f ( s) f f ( s), g g ( s) ˆ ˆ ˆ ˆ f, f, gˆ : f f ( ) f f ( ), gˆ g ( ), :, M, M, M3, M4: M, M s, M3 s, M4 s Ex, Ex, E y : Ex exp[ ( s) x], Ex exp[ ( s ) x], E y exp[ ( s ) y] The possible saes of channels and he ransiions among hem are shown in Figure. Figure. The sae ransiion model of he generalized Markov process. Copyrigh 9 SciRes.

4 4 C. L. GUO ET AL. According o Figure, a few new performance measures could be defined. The probabiliy of he channel in available idle sae, normal busy sae and delay idle sae are Available Idle Probabiliy, Normal Busy Probabiliy and Delay Idle Probabiliy, respecively. Sensing Frequency is defined he frequency of he occurrence of channel sensing when he channel is in sae (, ik), i,. False alarm occurs if and only if he channel ransfers from sae (, k)( k,, ) o sae (,); while miss deecion occurs if and only if he channel ransfers from sae (, k)( k,, ) o sae (,). So False Alarm Frequency and Miss Deecion Frequency are defined accordingly. Also define R(), R( ), L () 9, L( ), L ( ) and L 3( ) are he Insananeous Probabiliy of Available Idle, Normal Busy, Delay Idle, Insananeous Frequency of Sensing, False Alarm and Miss Deecion a an arbirary ime, respecively. Then define R, R, L, L, L and L 3 are he seady sae forms of R (), R ( ), L ( ), L( ), L ( ) and L 3( ), respecively, e.g., R lim R( ). In CR neworks, each channel will go hrough one or all kinds of saes in which available idle and normal busy generae rewards by he using for he ransmission of CRs and PUs, respecively, delay idle and false alarm wase opporuniies, miss deecion induces inerference o PUs, and sensing has overhead. I is assumed ha he expeced rewards per uni ime generaed by he channel are e or e when he channel is in available idle or normal busy, respecively. And he expeced losses per uni ime induced by he delay of channel is c, he expeced cos of each sensing is c, he expeced false alarm and miss deecion expenses every ime are c and c 3, respecively. We also assumed ha expeced oal rewards generaed by he channel during (,] are R, hen 3 i i j j i j () R () e R () dc L () d c L () d where e, e, c, c, c and c 3 are weighing facors ( e e c cc c3 ). Taking Laplace ransform on boh sides of (), we have 3 i i j j i j () R () s [ er () s c L () s c L ()]/ s s And he expeced rewards per uni ime in he seady sae is R lim R) / lim s R s) s 3 (3) er c L c L i i j j i j where performance measures R i (i =, ), L and L j (j =,, 3) could be expressed as funcions of he mean sensing period E(T) (denoed by x ) and all of hem will be illusraed how o obain in Secion 4. Then aking suiable value for x o make R maximum can bring ou he opimal sensing period x. Tha is 3 i i j j x i j (4) x argmax er c L c L ) 4. Derivaion of Performance Measures In order o derive performance measures for searching he opimal sensing period, he seady sae probabiliies wih exac soluions in closed form should be calculaed. How o calculae hem using probabiliy analysis and supplemenary variables mehod is discussed below. According o Figure, we have he following differenial difference equaions ( x) v( y) pk (, x, y) k,, x (5) ( x) v( y) p(, x, y) pk (, x, y) x (6) k ( x) v( y) pk (, x, y) k, x (7) v( y) p(, y) y (8) ( z) p(, z) z (9) ( z) p(, z) z () The above equaions are o be solved under he boundary condiions p (,) k k ( z) p(, z) dz( ) p (, x,) p (, x, y) dxdy ( z) p (, z) dz p (,) v ( y) p (, y) dy () k ( x) pk (, x, y) dxdy k, (3) p (,) p (, y) dy (4) k k p (, x,) v ( y) p (, x, y) dxdy k,(5) k k p (,) v ( y) p (, x, y) dx (6) k k p (,) v ( y) p (, x, y) dxdy (7) And he iniial condiions Copyrigh 9 SciRes.

5 C. L. GUO ET AL. 4 p (, y) ( y) (8) Taking Laplace ransforms of Equaions (5) (8) wih respec o and solving he equaions, we can derive P (, s x, y) P (, s x, y) k M M ( f )( f ) k ( f ) k g E F ( x) (9) 4 x G ( y) / D( s) k,,... {[ M ( g )( f )( f ) M g ( f )] E F ( x) G ( y) M g ( f ) E F ( x) G ( y)} / D( s) k 4 x 4 x P (, s x, y) k [ f( g) M( f)( f) g( f f) M4( f)]( f) Ex F( x) G ( y) / D( s) k,... where P (, s y) ( M4MM4M f M4M fm4m ff) E yg( y)/ D() s () P( s, z) [ Mf( M M4) fg M ffm4fg M ffg]exp( sz) H( z) / D( s) (3) P ( s, z) ( M M f g M M f f g ) exp( sz) H ( z) / D( s) (4) 4 4 D() s ( M M M / M ) ( M / M M M f ) ( M / M MM ) f ( MM M / M ) f f ( M f M f f ) h ( s) {[ M / M ( M M )/ M ] [( M M )/ M ( M )/ M ] f [( M M )/ M3 M4 / M] f [ M4 / M ( M4 M)/ M3] ff} g 4 [ M f ( s ) f M f f ] h () s g ( M M f M M f f ) h () s g () () (5) In accordance wih he definiions of and R ( ), we obain k k R( ) R () P (, x) dx (6) k k R () P (, x) dx (7) Taking Laplace ransform on boh sides of Equaions (6), (7) and using Equaions (9) (5), we ge R () s (8) ( M M g M M f g ) F ( s )/ D( s)s 4 4 R ( s) [ M ( M M ) g M f 4 ( M M ) g f ] F ( s ) 4 ( M g M f g ) F ( s ) 4 4 (9) DD() M( )/ [ M( )/ ] fˆ [ M ( )/ ] fˆ ˆ [ M ( )/ ] f fˆ { M( )/ {[ ( ) ]/ }ˆ f {[ ˆ ( ) M ]/ } f (3) {[ M ( ) M]/ } fˆ ˆ f} gˆ ( Mfˆ ˆ ˆ ˆ )(/ ) ( ˆ M f f f f M ˆ ˆ f ˆ f) g(/ ) ( Mfˆ ˆ ˆ M f ˆ f) g(/ ) Wih he same derivaion of R and R, we can ge L ( M M ˆ ˆ f M f (33) ˆ ˆ S M f f ) G ( )/ D According o Figure, as he channel is in sae (, ik), i,, i is being sensed. Using sae ransfer frequency formula shown in [9], we ge where, D(s) is given by Equaion (5). By applying he limiing heorem of Laplace ransform and L Hospial s rule, we ge L () ( x)[ P k(, x) Pk(, x)] dx (34) R lim R ( ) lim sr ( s) s ˆ ( ˆ ˆ) M g M f g F ( )/ D (3) R lim R( ) lim sr ( s) s [ M ˆ ˆ gˆ M f ( M ) gˆ f ] (3) ˆ F ( ) [( gˆ gˆ f) F ( )]/ D where k Taking Laplace ransform on Equaion (34) and using Equaions (9) (5), we obain L () s {( MM4g MM4 fg) f { M( MM4)] g M f (35) ( M M4) g f} f ( M 4g M4g f) f}/ D( s) Then Copyrigh 9 SciRes.

6 4 C. L. GUO ET AL. L lim L ( ) lim sl ( s) s [ M fˆ fˆ gˆ fˆ gˆ M fˆ fˆ M ˆ ˆ ( ) f fgˆ ]/ D Similarly, we can derive L ( M ˆ ˆ ˆ f f gˆ M f ˆf fˆ gˆ M fˆ fˆ gˆ )/ D L ( M fˆ gˆ M fˆ fˆ gˆ )/ D 3 (36) (37) (38) Subsiuing Ri ( i,), L and Lj ( j,,3) by (3), (3), (33), (36), (37) and (38) ino (4), respecively, he opimal sensing period x is deermined by Fi (), i.e., he disribuions of sojourn ime of normal busy and available idle. For he sojourn ime of normal busy is used for ransmission of PUs hemselves and ha of available idle can be uilized by CRs ransmission when PUs have no daa o ransmi, Fi () are usually deermined by he raffic generaed by PUs services in pracical neworks. 5. The Applicaions of Sensing Period Opimizaion This secion illusraes he applicaions of he analyical model developed here by using examples involving PU sysems wih boh voice and daa raffic. 5.. Opimizaion for PUs wih Voice Traffic A ypical phone conversaion is marked by periods of acive alking/alk spurs (or ON periods) inerleaved by silence/ lisening periods (or OFF periods). The duraion of each period is exponenially disribued, i.e., he sojourn ime of normal busy and available idle follow exponenial disribuions wih probabiliy densiy funcions i fi() ie, and means i are consans. I is a special case for analyical model menioned above in which i s can be subsiue by i z. The ransien rae of available idle o normal busy and ha of normal busy o delay idle are hus reduced o consans i. 5.. Opimizaion for PUs wih Daa Traffic In he pas, exponenial disribuions are also frequenly employed o model inerarrival imes of daa calls for is simpliciy, bu exponenial disribuions may no be appropriae in modeling daa raffic. Taking , an imporan applicaion ha consiues a high percenage of inerne raffic, as an example, is raffic can also be characerized by ON/OFF saes. During he ON-sae an could be ransmied or received, and during he OFF-sae a clien is wriing or reading an . According o raffic models included in he UMTS Forum 3G raffic and ITU RM.7, he Pareo disribuion, which is one of popular heavy-ailed disribuions, can be used o close capure he naure of raffic for boh ON and OFF sae, i.e., he sojourn ime of normal busy and available idle follow Pareo disribuions wih probabiliy densiy funcions fi(), i ii i i, and means ii /( i ), wherei is called he shape parameer and i is called he scale parameer. In order o derive performance measures o search he i ii opimal sensing period, and means /( ) i ii i should subsiue fi() and i in Equaions (5) (8). 6. Numerical Resuls and Discussions Through numerical experimens, we examine he impac of sensing period selecion on maximum expeced rewards of he channel for differen raffic ypes under various channel parameers in his secion. 6.. Performance Analysis According o he characerisics of channels, we firs se he channel parameers as he following.,.33,.,.,., ee., c c.5, c., c3.5, and le us assume ha T follows he uniform disribuion wih parameers y and y, wrien T~ U( y, y ), and y. Two raffic ypes of PUs are considered, i.e., Type I: voice raffic and Type II: daa raffic. In he case of voice raffic, he sojourn ime of normal busy and available idle follow exponenial disribuions wih.4,.; for daa raffic, he sojourn ime of normal busy and available idle follow Pareo disribuions wih.8, 5 and.5, 6, i.e., means are.4 and., respecively. Here and are seleced for easy comparison. To validae he feasibiliy of he proposed analyical model for sensing period opimizaion, numerical examples are carried ou for he following hree sensing schemes, i.e., ) Scheme : T x, ha is, i is exacly a fixed period sensing scheme ha sensing is performed a once where T x. ) Scheme : T follows he uniform disribuion wih parameers x and x, wrien T ~ U ( x, x ). 3) Scheme 3: T follows he exponenial disribuion wih parameer x, wrien T ~ EP( x). Copyrigh 9 SciRes.

7 C. L. GUO ET AL. 43 Wih MATLAB, from (4) we can obain he opimal sensing periods x and he maximum expeced rewards R of he channel per uni ime in he seady sae for each sensing scheme. Figure and Figure 3 illusrae he expeced rewards of he channel for various values of x under Type I and Type II raffic ypes respecively. For Type I voice raffic, Figure shows ha he maximum expeced rewards of he channel is varied according o he disribuion of sensing period T. The opimal sensing periods for each scheme are x {6.5, 3.,7.8} and he maximum expeced rewards are R { 9.8,6.,4.9}. So he opimal sensing scheme is sensing randomly wih sensing period T following he exponenial disribuion when x 7.8 under he above-menioned channel parameers, for he scheme obained R 4.9 is maximum compared o oher wo schemes. For Type II daa raffic, Figure 3 shows ha he opimal sensing periods for each scheme are x {.7,7.9,.3} and he maximum expeced rewards are R {77.7,3.7,9.}. From Figure 3, i can easily find ha he opimal sensing scheme is sensing randomly wih sensing period T following he uniform disribuion. One poin ha deserves menion is ha, compared o he voice raffic, here are significan differences in maximum expeced rewards among he hree schemes in he case of daa raffic. 6.. Analysis of Channel Parameers In pracical, he opimal sensing scheme is differen wih differen ses of channel parameers. Nex, we sudy effecs of he seing of various channel parameers on he opimal sensing scheme. ) Effecs of Disribuion Parameers: in boh voice Figure. expeced rewards vs. expeced sensing period for voice raffic. Figure 3. expeced rewards vs. expeced sensing period for daa raffic. Table. The Opimal Rewards R Vs. Opimal Mean Sensing Period x for Various Disribuion Parameers under e e., c c.5, c., c3.5,.,., T~ Uy (, y) and y. { Type Ⅰ Type Ⅱ /, /,, } T x R x R (.,.4 T x ,.,.3 T ~ U ( x, x) ,.) T ~ EP( x) (.4,. T x ,.5,.3 T~ U( x, x) ,.) T ~ EP( x) T x (.4,.,.,., T~ U( x, x) ) T ~ EP( x) raffic and daa raffic, he disribuion parameers,,,, and,,,, direcly reflec he sojourn ime of normal busy, available idle, delay idle, false alarm and miss deecion sae, respecively. The disribuion parameers /.4, /. (.,.33,.) show ha he sojourn ime of available idle is longes, which means low or moderae PU raffics are chosen. Oher hree disribuion parameers are chosen for 3 sensing schemes, and he opimal rewards R vs. he opimal mean sensing period x are shown in Table, respecivel y. a) ( /, /,,, ) is (.,.4,.,.33,.). The sojourn ime of normal busy is relaively long and less opporuniies can be used by ransmission of CRs; b) ( /, /,,, ) is (.4,.,.5,.33,.). The sojourn ime of delay idle is reduced so ha more opporuniies can be used by CRs han ); and c) ( /, /,,, ) is (.4,.,.,.,.33). The sojourn ime of miss deec- Copyrigh 9 SciRes.

8 44 C. L. GUO ET AL. ion is longer han ha of false alarm. From Table, we clearly see ha he opimal sensing scheme is differen wih regard o differen disribuion parameers. ) Effecs of Weighing Facors: Weighing facors e, e, c, c, c and c 3 can be reaed as indexes regarding he imporance of R, R, L, L and L. Generally speaking, he PU applicai ons, such as GPS, can only endure minor inerference for accepable Qualiy of Service (QOS). For such applicaions, he cos of inerference induced by miss deecion is more imporan and c 3 is obviously bigger han all oher facors as shown in above-chosen seing e e., c c.5, c., ( c3.5 ). Table shows opimal rewards R and he opimal mean sensing period x for wo differen nework applicaions : a) In he case where he PU is no sensiive o inerference, he weighing facors c and c are boh larger han oher facors in order o maximize he uilizaion of exising opporuniies. Here (e, e, c, c, c, c 3 ) is se o (.,.,.35,.5,.35,.5). b) For energy-consrained CR neworks such as sensors and mobile ad hoc applicaions, frequen sensing is undesirable for high energy overhead, so he weighing facor c should be se relaively large and (.,.,.5,.5,.5,.) is chosen. This able demonsraes ha he opimal sensing scheme is also differen wih regard o differen weighing facors and from he Table one can easily find which scheme performs bes Performance Comparison for Differen Traffic Types According o he proposed analyical model for sensing period opimizaion, a sensing scheme wih a bigger expeced reward performs beer. Figure, Figure 3, Table and Table show ha he opimal sensing scheme is differen for differen raffic ypes. In Figure 4, we show he expeced rewards for differen schemes under.,.33,.,., e e., c c.5, c., c3.5, and wo differen siuaions Table. The opimal rewards R vs. opimal mean sensing period x for various weighing facors under.4,.,.,.33,.,.,. T~ Uy (, y), and y. (e, e, Type I Type II c, c, c, T c 3 ) x R x R (.,., T x ,. T ~ U( x,x) ,.35,. 5) T ~ EP( x ) T x T~ U( x,x) (.,.,.5,.5,.5,.) T ~ EP( x ) for voice raffic: ) fixe d (=. 5) an d various ; and ) fixed (=.) and various, and wo differen siuaions for daa raffic: ) fixed (=.5 ) and various ; and ) fixed (=.) and various. As shown in Figure 4( a) and Figure 4(b), varying ( ) among. and, we observed ha he performance of voice raffic is no sensiive o which sensing scheme is preferred. However, for daa raffic, wih he variaion of and, he opimal sensing scheme is changing among hree sensing schemes and he maximum expeced rewards have big differen, as shown in Figure 4(c) and Figure 4(d). The possible reason is ha he opimal sensing period for voice raffic is depending only on a consan mean value of he ransmission ime for primary users and cogniive radios whereas performance of daa raffic are affeced by no only mean value bu also he disribuions of he ime of ransmission for primary users and cogniive radios. From he above discussions, we sugges ha: ) for voice raffic, he maximum expeced rewards of hree sensing scheme is close o each oher. In real sysem, a fixed period sensing scheme is preferred for simpliciy; and ) however, he siuaion changes dramaically for daa raffic, he maximum expeced rewards of hree sensing scheme are far differen. The analyical model proposed can be used o search he opimal sensing scheme, and he analysis can be easily exended o ha of any oher disribuion of sensing period T. 7. Conclusions and Fuure Work This paper deal wih he random sensing period scheme in CR neworks. An efficien generalized Markov analyical model for sensing period opimizaion was proposed and sudied. How our proposed analyical model can be applied o PU sysems wih boh voice and daa raffic was also discussed. Boh numerical resuls and analysis for various channel parameers and raffic ypes of PUs were obained and compared. We found ha sensing period does affec he maximum expeced rewards of he channel, and he proposed analyical model is valid for he analysis of he case where he sensing period, he ransmission ime for primary users and cogniive radios are all following arbirary disribuions. In his work, we assume ha he sensing period for each channel is differen, i.e. he sensing period is asynchronous for all channels. The proposed scheme is suiable for he scenario where each CR only sense he channel for is operaing. If each CR is responsible for sensing more han one channel, he inelligence schedule algorihm of sensing period should be used o negoiae among CRs because he quie period of each channel is also asynchronous. In fuure, we would like o develop pracical schedule mechanisms or proocols, which deal Copyrigh 9 SciRes.

9 C. L. GUO ET AL. 45 (a) (b) (c) Figure 4. Performance comparison of differen raffic ypes under.,.33,.,.,., e e., c c.5, c., c3.5 wih (a) =.5, (b) =., (c) =.5, and (d) =.. (d) wih he coordinaion of channel sensing among CRs, o make he proposed sensing scheme more effecive in real CR neworks. 8. Acknowledgemens T his work was suppored by Naural Science Foundaion of China under Gran No References [] Y. C. Liang, W. S. Leon, Y. H. Zeng, e al., Sysem descripion and operaion principles for IEEE 8. WRANs, IEEE 8. 5/94r4, hp:// org//. [] V. K. N. Lau, R. S. Cheng, R. D. Murch, e al., Adapive quie period conrol, IEEE 8. 6/8r, hp:// [3] W. D. Hu, D. Willkomm, M. Abusubaih, e al., Cogniive Radios for dynamic specrum access-dynamic fre- ransmission in Cogniive Ra- quency hopping communiies for efficien IEEE 8. operaion, IEEE Communicaions Magazine, Vol. 45, No. 5, pp , 7. [4] T. Shu, S. G. Cui, and M. Krunz, Medium access conrol for Muli-Channel parallel dio neworks, In proceedings of IEEE GLOBECOM, San Francisco, pp. 5, 6. [5] H. Kim and K. G. Shin, Efficien discovery of specrum opporuniies wih MAC-Layer sensing in Cogniive Ra- in cogniive dio neworks, IEEE Transacions on Mobile Compuing, Vol. 7, No. 5, pp , 8. [6] Y. Zhang, C. Y. Feng, and C. L. Guo, A flexible sensing period mechanism of specrum sensing radio Copyrigh 9 SciRes.

10 46 C. L. GUO ET AL. Neworks, The Journal of China Universiies of Poss and Telecommunicaions, Vol. 3 No., pp. 8 3, 8. [7] C. L. Guo, Z. M. Zeng, C. Y. Feng, and Z. Q. Liu, An asynchronous specrum sensing period opimizaion model and adapive fuzzy adjusmen algorihm, Journal of Elecronics & Informaion Technology, Vol. 3, No. 4, pp. 9 94, 9. [8] C. Han, J. Wang, and S. Li, A specrum exchange mechanism in cogniive radio conexs, In proceedings of IEEE PIMRC, Finland, pp. 5, 6. [9] D. H. Shi, A new mehod for calculaing he mean failure numbers of a repairable sysem during (, ), Aca Mahemaicac Applicaae Sinica, Vol. 8, No., pp., 985. Copyrigh 9 SciRes.