Fast Discovery of Spectrum Opportunities in Cognitive Radio Networks

Transcription

1 Fast Dscovery of Spectrum Opportuntes n Cogntve Rado Networks Hyol Km and Kang G. Shn Real-Tme Computng Laboratory Department of Electrcal Engneerng and Computer Scence The Unversty of Mchgan, Ann Arbor, M Emal: {hyolkm,kgshn}@eecs.umch.edu Abstract We address the problem of rapdly dscoverng spectrum opportuntes for seamless servce provsonng for secondary users (SUs) n cogntve rado networks (CRNs). Specfcally, we propose an effcent sensng-sequence that ncurs a small opportunty-dscovery delay by consderng (1) the probablty that a spectrum band (or a channel) may be avalable at the tme of sensng, (2) the duraton of sensng on a channel, and (3) the channel capacty. We derve the optmal sensng-sequence for channels wth homogeneous capactes, and a suboptmal sequence for channels wth heterogeneous capactes for whch the problem of fndng the optmal sensng-sequence s shown to be NP-hard. To support the proposed sensng-sequence, we also propose a channel-management strategy that optmally selects and updates the lst of backup channels. A hybrd of maxmum lkelhood (ML) and Bayesan nference s also ntroduced for flexble estmaton of ON/OFF channel-usage patterns and predcton of channel avalablty when sensng produces nfrequent samples. The proposed schemes are evaluated va n-depth smulaton. For the scenaros we consdered, the proposed suboptmal sequence s shown to acheve close-to-optmal performance, reducng the opportunty-dscovery delay by up to 47% over an exstng probablty-based sequence. The hybrd estmaton strategy s also shown to outperform the ML-only strategy by reducng the overall opportunty-dscovery delay by up to 34%.. NTRODUCTON Dynamc Spectrum Access (DSA) s key to solve the problem of wreless spectrum scarcty, rooted from neffcent spectrum utlzaton by the current statc resource allocaton polcy. DSA can enhance spectrum utlzaton by allowng cogntve rados (CRs), also referred to as secondary users (SUs), to reuse legacy spectrum dynamcally and opportunstcally wthout nterruptng ncumbent/lcensed spectrum users, also referred to as prmary users (PUs). Spectrum sensng plays an mportant role n realzng DSA, by (1) detectng PUs presence, and (2) dscoverng spectrum opportuntes. A spectrum sensor montors a spectrum band/channel 1 to detect PU sgnals and thus determne the channel s avalablty for use by SUs. f thus-dscovered channels are utlzed by SUs, they are referred to as n-band channels; else, they are called out-of-band channels. Opportunty dscovery s an act of searchng for spectrum opportuntes by sensng out-of-band channels. Opportunty 1 Spectrum band and channel wll be used nterchangeably throughout ths paper. (a) Event-drven channel reuse model ON (busy) OFF (dle) (b) Tme-drven channel reuse model ON (busy) OFF (dle) opportunty dscovery channel reuse tme slot Ch 1 Ch 2 Ch 3 Ch 1 Ch 2 Ch 3 Fg. 1. llustraton of two channel reuse models, n case a CRN seeks a sngle dle channel at most. n general, however, a CRN may need more than one dle channel for ts operaton. dscovery s trggered when a CR network (CRN) experences a shortage of opportuntes to utlze, and t can be trggered perodcally (tme-drven) or on-demand (even-drven). n case of event-drven trggerng, an n-band channel s utlzed untl ts PUs return to the channel whch s detected by perodc n-band sensng. Upon the PUs return, the channel must be vacated promptly. Opportunty dscovery s trggered when a channel vacaton makes the amount of opportuntes (e.g., the total bandwdth of n-band channels) to be utlzed drop below the spectrum demand of a CRN. n case of tme-drven trggerng, tme s dvded nto slots, and an opportunty dscovery s trggered at every slot. n-band channels dscovered va opportunty dscovery are utlzed untl the slot expres and hence, all n-band channels should be vacated at the end of the slot. The former model was ntroduced n [1], [2] and employed n EEE [3]. The latter model was used n [4] [7]. Two channel reuse models are llustrated n Fg. 1. A. Motvaton n both spectrum reuse models, fast opportunty dscovery s essental to seamless servce provsonng for CR devces.

2 n CRNs, qualty-of-servce (QoS) depends greatly on the amount of explored spectrum opportuntes snce t determnes the bandwdth provded to SUs and thus lmts the maxmum throughput n the CRN. The amount of explored opportuntes, however, fluctuates n tme due to frequent n-band channel vacatons. Therefore, spectrum opportuntes must be dscovered as promptly and as much as needed at the tme of each channel vacaton, to avod severe degradaton of servce qualty. To facltate fast opportunty dscovery, out-of-band channels are dvded further nto backup and canddate channels, as suggested n EEE Opportunty dscovery searches backup channels for addtonal opportuntes, where backup channels are specally chosen to maxmze the chance of fndng opportuntes as much as needed. Out-of-band channels other than backup channels are referred to as canddate channels. Canddate channels are not searched untl they are mported to the backup channel lst. The lst of backup (or canddate) channels s denoted as BCL (or CCL). n ths paper, we focus on fast dscovery of spectrum opportuntes va effcent schedulng of out-of-band spectrum sensng. Two mportant ssues n opportunty dscovery are consdered: (1) how to buld a sensng-sequence that helps fnd spectrum opportuntes wth mnmal delay, and (2) how to construct and update BCL by mportng/exportng channels from/to CCL. B. Contrbutons We propose a mechansm for fast opportunty dscovery that conssts of three parts to whch our work makes man contrbutons. Frst, an optmal sensng-sequence s proposed to mnmze the latency n fndng the target amount of opportuntes n BCL. We consder heterogeneous channel characterstcs, ncludng sgnal detecton tme T, channel capacty C, and the probablty Pdle of a channel to be dle. 2 The optmal sequence s derved for channels wth homogeneous capactes,.e., C = C,. For a more general case (.e., channels wth heterogeneous capactes), a necessary condton for optmalty s derved. t s also shown that fndng the optmal sequence s NP-hard, and hence, we propose a suboptmal sensng-sequence algorthm of polynomal tme complexty. The effcency of the algorthm s evaluated va smulaton. Second, optmal constructon and effcent update of BCL s proposed. Our scheme suggests an optmal choce of ntal backup channels that maxmzes the chance of havng enough opportuntes n BCL whle mnmzng the sze of BCL. An effcent BCL update algorthm s also proposed that mports/exports channels from/to CCL wth less computatonal overhead so that BCL can be kept up-to-date. Thrd, we propose a strategy that estmates ON/OFF channel-usage patterns and predcts channel avalablty by selectvely applyng maxmum lkelhood (ML) and/or Bayesan estmaton. We capture the tradeoff between two estmaton technques: the former s smple but ts performance degrades 2 Note that we use as channel ndex n ths paper. greatly wth nfrequent samples; the latter requres more computaton but performs better wth a small number of samples [8] and s useful to model tme-varyng channel parameters by updatng pror and posteror dstrbutons. On the other hand, our scheme consders the mpact of mperfect sensng on the predcton of channel avalablty (Pdle ), by consderng probablty of mss detecton (PMD) and probablty of false alarms (PFA). C. Related Work Among a number of studes on spectrum sensng, a few notable body of work s found to be related to fast opportunty dscovery. Datla et al. [9] proposed a lnear backoff, lnearly decreasng the preference on sensng a channel whenever the channel s sensed occuped. Ths s heurstc and does not optmze the opportunty-dscovery delay. Zhao et al. [6] proposed a decentralzed CR MAC protocol that senses a subset of backup channels at each tme slot to jontly optmze sensng and transmsson. However, the scheme does not prortze the chosen channels, but rather senses all of them. Chang and Lu [4] suggested a strategy that optmally determnes whch channel to probe and when to transmt, but they focused on the case of sngle channel transmsson only. Km and Shn [2] ntroduced a sensng-sequence that sorts channels n descendng order of the probablty Pdle. However, such a sequence only maxmzes the chance of fndng an dle channel, nstead of mnmzng the overall dscovery-delay. n EEE [1], the concept of backup and canddate channels are ntroduced to facltate dscovery of opportuntes, but no algorthm s specfed on how to construct BCL and CCL effcently. Moreover, none of the above fully consdered the heterogenety of lcensed channels. On the other hand, Motamed and Baha [7] used Bayesan learnng to predct the avalablty of a channel, where the learnng process s smplfed by assumng a geometrc dstrbuton for channel-usage patterns. n ths paper, we use a general alternatng renewal process and develop a mult-stage teratve Bayesan nference. D. Organzaton Secton brefly ntroduces basc assumptons and system models used n ths paper. n Secton, we propose an effcent sensng-sequence that mnmzes the opportuntydscovery delay, by consderng the heterogeneous characterstcs of backup channels. Secton V presents constructon of the ntal BCL and an BCL-update algorthm to keep the lst up-to-date. Secton V ntroduces a strategy to estmate ON/OFF channel-usage patterns and predct channel avalablty durng each opportunty dscovery. The performance of the proposed schemes are evaluated n Secton V, and then the paper concludes n Secton V. A. Network Model. SYSTEM MODEL A sngle-hop CRN wth a group of SUs s consdered, and the CRN s assumed to search M lcensed channels

3 ON OFF Z (t) : ON OFF T OFF T ON Opportunty Dscovery n-band Channel Channel Vacaton Channel Vacaton Fg. 2. samples Channel model: alternatng renewal process wth ON and OFF states ON OFF Fg. 3. sensng-tme (T ) 1 1 llustraton of the sensng process on a channel sensng for spectrum opportuntes t needs. Although our proposed schemes can also be appled to mult-hop CRNs, sensng n such a case must consder locaton-dependency of the observed sgnals. One possble approach s to dvde the network nto clusters, where SUs n each cluster cooperate for spectrum sensng and channel allocaton. t s also assumed that there s no nterference from other CRNs n M channels, whch can be accomplshed by coordnated channel allocaton between CRNs [1], [11]. Each SU s assumed to have been equpped wth a sngle antenna, wdely-tunable to any combnaton of N channels by usng sgnal processng technques, such as NC-OFDM [12]. Havng one antenna per SU may help reduce the sze of a secondary devce and avod potental nterference between colocated antennas due to ther close proxmty [13]. B. Channel Model A channel s modeled as a renewal process alternatng between ON and OFF states. The ON (OFF) state represents a tme perod wthn whch a PU sgnal s present (absent). Once sensng fnds a channel n ts OFF state (.e., an dle channel), SUs can utlze the channel untl ts next state transton to ON state. Ths type of channel model was ntroduced n [2], [7], [14] where ts potental for modelng spectrum opportuntes was demonstrated. Fg. 2 llustrates the channel model. Suppose s the channel ndex ( = 1, 2,..., M), and let Z (t) denote the state (ON or OFF) of channel at tme t, such that { Z (t) = 1, f channel s ON (or busy) at t, Z (t) =, otherwse. For an alternatng renewal channel [15], the sojourn tmes of ON and OFF states are represented by random varables TON and TOF F wth probablty densty functons (pdfs) f TON (t) and f T OF F (t), t >, respectvely. 3 ON and OFF states are also assumed to be ndependent of each other. On the other hand, channel utlzaton, u [, 1], defned as the average fracton of tme durng whch channel s n 3 f T ON (t) and f T OF F (t) can be any dstrbuton functons. Backup Channel Fg. 4. ON state, s gven as Channel Export Channel mport Canddate Channel Out-of-band channel The state transton dagram of a channel u = C. Sensng and Access Model E[T ON ] E[T ON ] + E[T OF F ]. A spectrum sensor s assumed to be co-located wth a transcever,.e., a SU can be dynamcally reconfgured to a transcever or a sensor. When a SU acts as a spectrum sensor, t montors channel durng a certan tme perod, called sensngtme T, whch s determned by the underlyng detecton method (e.g., energy or feature detecton) and the type of PU sgnals [16]. T s assumed small relatve to E[T OF F ] and E[TON ] such that channel s state remans unchanged durng the sensng-tme. Sensng s akn to a samplng process, producng a bnary random sequence snce ON and OFF states correspond to sample 1 (busy) and (dle), respectvely. Fg. 3 llustrates ths sensng process. A CRN s assumed to requre as much spectrum opportuntes as B req, whch s the total spectrum demand from ts SUs. Snce all C s are not the same and could be smaller than B req, B req may be fulflled by fndng more than one dle channel. Whenever B req s not met by the current n-band channels, an opportunty dscovery s trggered and backup channels are searched sequentally durng whch SUs synchronously tune to one backup channel at a tme followng a gven sensngsequence. Once a backup channel s detected dle, t becomes an n-band channel and s merged nto one logcal channel (.e., a combnaton of all n-band channels) for SUs to utlze them. Opportunty dscovery completes when the sum of nband channels capactes reaches B req. The beneft of sequental search of backup channels s twofold: (1) t prevents a CRN from beng parttoned whle swtchng channels, and (2) t enhances the detectablty of ncumbents va collaboratve sensng [17] [19]. On the other hand, a CRN may choose a proper channel access mechansm (e.g., FDMA, TDMA, or CSMA) to determne how to reuse the logcal channel, the choce of whch s outsde of the scope of ths paper. D. Transton of Channel Assocaton Fg. 4 llustrates the state transtons of a channel among three channel assocatons: n-band, backup, and canddate

4 channels, where a state transton s trggered by one of the followng four events: opportunty dscovery, channel vacaton, channel export, and channel mport. Frst, durng the opportunty dscovery, a backup channel becomes an n-band channel f t s sensed dle. Next, n-band channel vacaton makes the channel a backup or canddate channel, dependng the channel s lkelhood of havng opportuntes agan n the near future. For example, an n-band channel wth long ON/OFF perods (e.g., TV bands) s better put nto CCL than BCL upon the channel s vacaton snce the channel would have been for a long ON perod. On the other hand, channel exports/mports are trggered to update the entres of BCL: f a backup channel s less useful than a certan canddate channel, t may be exported to CCL, and the canddate channel can be mported to BCL nstead. Further detals on these state transtons wll be presented n Secton V.. OPTMAL SENSNG SEQUENCE FOR FAST DSCOVERY OF OPPORTUNTES n ths secton, we propose an effcent sensng-sequence of backup channels that ncurs a small delay n dscoverng as much opportuntes as a CRN needs. n buldng such a sequence, the heterogeneous characterstcs of backup channels are consdered by usng a tuple of {T, C, Pdle }. T may dffer between channels because t depends on the type of PU sgnals. C can be a physcal bandwdth or Shannon capacty whch vares wth the tme-varyng channel condton (e.g., fadng) and nterference temperature [2]. Pdle depends on the channel s ON/OFF usage pattern and hence vares wth channels. Dervaton of Pdle for alternatng renewal channels was ntroduced n [2]. Suppose there are N(< M) backup channels wth ther {T, C, Pdle } known, and B req s the amount of opportuntes requred for a CRN to support spectrum demands from ts SUs. Then, upon trggerng an opportunty dscovery, the CRN needs to dscover as much opportuntes as B = B req B n band where B n band s the sum of n-band channels capactes at the tme of opportunty dscovery. Note that B n band = n the tme-drven channel reuse model. A. Optmal Sensng-Sequence: Analyss Let S = {s 1, s 2,..., s N } S be an ordered lst of N channels, where s j s the channel ndex of j-th channel n the sequence (.e., s j : postve nteger, 1 s j N) and S s the set of all possble channel sequences ( S = N!). Suppose T, C and Pdle = Pr(Θ = ) are known a pror, where Θ {, 1} s the bnary state of channel, {1, 2,..., N} ( means the channel s dle). Our objectve s to determne the optmal sensng-sequence S that mnmzes the average delay n fndng dle channels whose cumulatve capacty exceeds B. Ths can be stated formally as Fnd Subject to [ sτ S = argmn E τ S S s τ 1 =s 1 T C Θ < B, and =s 1 ] s τ =s 1 C Θ B, where Θ s an ndcator functon such that { 1, f Θ =, Θ =, otherwse. Note that τ s a random varable, and hence, the expected delay (.e., average sensng-tme) s consdered n the objectve functon. To fnd the optmal sequence, brute-force searchng n S s not desrable snce ts computatonal complexty s O(N!). Here, we derve an effcent channel-sortng algorthm to buld an optmal sensng-sequence requrng much less computaton. The proposed algorthm s based on the dervaton of a necessary condton for optmalty. We begn wth ntroducton of some notatons to use n the analyss. Let L be the optmal sensng-sequence and L be ts counterpart constructed by swtchng the order of k-th and (k + 1)-th channels n L. That s, L = (l 1,..., l k 1, l k, l k+1, l k+2,..., l N ), L = (l 1,..., l k 1, l k+1, l k, l k+2,..., l N ). On the other hand, DL B s defned as the average delay n locatng dle channels whose cumulatve capacty exceeds B, usng a sensng-sequence L. PL B s defned as the probablty that the sum of capactes of dle channels n a sensngsequence L may be less than B. Formally, DL B and PB L are defned as follows: D B L P B L := E τ [ lτ =l 1 T ( ) := Pr C Θ < B. L n addton, let us defne the followng ordered lsts: ] = (l 1, l 2,..., l k 1 ), L k = (l 1, l 2,..., l k 1, l k ),,k+1 = (l 1, l 2,..., l k 1, l k+1 ), L k+1 = (l 1, l 2,..., l k 1, l k, l k+1 ),,k+1,k = (l 1, l 2,..., l k 1, l k+1, l k ), L c k+1 = (l k+2,..., l N ). Snce a channel s sensed only when those channels precedng n the lst provde less opportuntes than B, we can express DL B and DB L as D B L = D B + P B T l k + P B L k T l k+1 +P B L k+1 D B L c k+1, DL B = DB + PL B k 1 T l k+1 +PL B k 1,k+1,k DL B. c k+1, + P B,k+1 T l k Snce D B L DB L and PB L k+1 = P B,k+1,k, we have P B T l k +PB L k T l k+1 PL B k 1 T l k+1 +P B,k+1 T l k (1)

5 Usng PL B k = PL B k 1 (1 P l k dle ) + PB C l k equaton reduces to: T l k (PL B k 1 P B C l k )P l k dle T l k+1 P l k dle, the above (P B P B C l k+1 )P l k+1 dle B. Optmal Sensng-Sequence for a Specal Case: Homogeneous Channel Capactes For homogeneous channel capactes (.e., C = C, ), the optmal sensng-sequence s determned as shown n Theorem 1. Theorem 1: f C = C,, then the optmal sensngsequence s bult by sortng channels n ascendng order of T /P dle. Proof: By substtutng C for C lk and C lk+1 n Eq. (2), the nequalty condton reduces to: T l k P l k dle T l k+1 P l k+1 dle. (2), for 1 k N 1, (3) whch s a necessary condton for optmalty. However, snce there exsts a sngle and unque sequence satsfyng such a necessary condton, 4 the condton also becomes suffcent. Therefore, the resultng sequence s optmal. C. Suboptmal Sensng-Sequence for Heterogeneous Channels Wth a more general channel condton (.e., heterogeneous channel capactes), however, there s no handy rule lke Eq. (3). The form of Eq. (2) suggests that the problem of optmal channel orderng s state-dependent: the k-th channel n the optmal sequence s determned by consderng, whch s a sub-sequence of S wth the frst k 1 entres. To fnd the optmal sequence, all N! possble sequences must be searched to fnd a complete set of sequences satsfyng Eq. (2) snce there could be more than one such sequence. Once such sequences are found, ther DL B must be compared to fnd the one provdng mnmal DL B. Therefore, the problem of fndng the optmal sequence agan becomes as complex as brute-force search (.e., O(N!)), whch s NP-hard. Here, we propose a suboptmal algorthm of polynomal tme complexty whle guaranteeng dscovery of a sensng sequence that satsfes the optmalty condton Eq. (2). n ths algorthm, S s formed by teratvely determnng the k-th entry k = 1, 2,..., N whle updatng. Let s denote by stage k the k-th teraton of fndng the k-th entry. At stage k, T /{(PB P B C )Pdle } are calculated for N k + 1 channels (except k 1 channels n ). Then, the channel wth mnmal T /{(PB P B C )Pdle } s pcked as kth entry of S. The computatonal complexty of the proposed algorthm s O(N 2 ), snce N +(N 1) = N(N +1)/2. n Secton V, t wll be shown that the proposed suboptmal algorthm acheves near-optmal performance under the varous channel condtons tested. 4 f we deal wth the sequences, wthout dfferentatng them, whch are created by swtchng the order of channels wth same T /P dle. The ntal step (.e., k = 1) of the algorthm must be handled carefully, because = and (PL B k 1 P B C l k ) = at k = 1. Let L and L be defned the same as before except that they dffer by the frst two entres n the sequence. That s, Then, L = (l 1, l 2, l 3,..., l N ), L = (l 2, l 1, l 3,..., l N ). DL B = T l 1 + PB {l T l 2 1} + PB {l 1,l 2} DB {l 3,...,l N }, DL B = T l 2 + PB {l T l 1 2} + PB {l 2,l 1} DB {l 3,...,l N }, whch gves Consderng (1 P B {l 2 } ) T l1 (1 P B {l 1 } ) T l2. (4) P B {l k } = { 1 P l k dle, f C l k B, 1, otherwse, we can have the followng three cases. Case 1: C l1 B, and C < B for l 1. n ths case, Eq. (4) becomes T l1 P l1 dle T whch s always true snce P l 1 dle T >. Therefore, we schedule channel l 1 frst. Case 2: there exst at least two channels wth C B. Let the ndces of such channels be l k and l k+1. Then, Eq. (4) becomes T l k P l k dle T l k+1 P l k+1 dle Therefore, the frst channel to be scheduled s the one havng mnmum T among those wth C Pdle B. Case 3: C < B,. n such a case, Eq. (4) becomes. To avod a random choce, we follow the specal case rule n Theorem 1: the frst channel s the one wth mnmum T. Pdle The proposed sensng-sequence algorthm s descrbed n Fg. 5. D. Dscusson A CRN may sometmes fal to fnd the necessary amount B of opportuntes after searchng N channels. n such a case, the CRN must retry opportunty dscovery untl enough opportuntes are dscovered. We set the retry perod to tretry whch s a desgn parameter. Once the frst opportunty dscovery fals, the overall dscovery delay untl B s accomplshed depends more on tretry, rather than the optmalty of sensng sequence. Therefore, t s desrable to have an enough number of good channels n BCL so that opportunty dscovery may be successful at the frst tral. The constructon of such BCL wll be dscussed n the next secton..

6 := { C B}; f ( == ) then ( S1 := argmn 1 N T /Pdle) ; ( else S1 := argmn T /Pdle) ; k := 2; whle (k N) { := { S 1,..., S k 1} ; Sk := argmn / T {(P / L B k 1 P B C )Pdle k := k + 1; } S := {S 1,..., S N }; return; Fg. 5. Pseudo-code of the optmal sensng-sequence algorthm V. BACKUP CHANNEL LST (BCL) MANAGEMENT A. Constructon of ntal BCL When a BCL s constructed ntally, there could be many canddates for ts entres. n EEE 82.22, for example, there are 68 TV channels (channels 2 to 69) n the VHF/UHF bands (54 86 MHz) [21]. f CR devces are allowed to operate n heterogenous spectrum bands, the number of canddate channels may even grow larger. Upon selectng the ntal backup channels, two conflctng objectves must be met: the BCL should (1) contan as few channels as possble snce the cost of channel sequencng grows fast at the rate O(N 2 ) as shown n Secton, and (2) have many good channels to ncrease the chance of fndng enough opportuntes at the frst opportunty-dscovery attempt. To acheve both objectves, we propose the followng strategy: frst, all M lcensed channels are ordered accordng to the sensng-sequence algorthm n Secton, and then the ntal BCL s constructed by choosng the frst N channels of the sequence where N s mnmzed whle achevng the second objectve. The problem of constructng the ntal BCL s formally stated as follows. Suppose L M = {l1, l2,..., lm } s the (sub)optmally-ordered lst of M channels. Also, let = {l1, l2,..., ln }, N M be a sub-lst of L M wth ts frst N entres. Our objectve s to fnd an optmal N such that N channels may contan opportuntes more than B req wth probablty thpotental, whch s a pre-defned threshold (e.g., thpotental=.9). That s, { } N = mn N C B req thpotental, } C B req { := Pr C Θ B req } ; = 1 P B req, where C B req, capacty potental of B req n, represents the probablty that may contan more opportuntes than B req. We assume C B req L M thpotental. ntally, Pdle cannot be predcted correctly as there s no sample collected from any channel. Once a channel becomes a backup, t may be sensed durng opportunty-dscovery attempts (by sequental sensng of channels n BCL), and the collected samples are then used to estmate the channel s ON/OFF pattern. The resultng estmates wll be used to predct Pdle.5 Nevertheless, t may be possble to obtan some pror knowledge on Pdle. For example, a certan TV channel s average broadcastng tme s known to be 18 hours per day, so we can assume the ntal Pdle to be 1/4. f there s no such nformaton avalable, a best guess wll be Pdle = 1/2. B. BCL Update Strategy The ntal entres of BCL may need to be updated snce they were chosen by guessng Pdle. As samples are accumulated on backup channels, the optmal entres can be more accurately derved. f channels have tme-nvarant ON/OFF dstrbutons f T ON (t) and f T OF F (t), the best BCL update strategy conssts of: Learnng: by extensvely sensng M channels, collect enough samples for each channel and produce accurate estmates. Sngle-tme optmzaton: order M channels and construct the BCL optmally. Keep ths BCL forever. Unfortunately, channels are usually tme-varyng, renderng the above strategy neffectve. nstead, the BCL could be reconstructed perodcally by sortng all M channels repeatedly. However, ts large overhead of sortng M channels makes the approach mpractcal. So, we propose an effcent and lghtweght BCL update strategy that sorts BCL or CCL separately and only when necessary, wth no samplng requred on canddate channels. n ths strategy, BCL s updated perodcally every tupdate seconds. At every BCL update, C B req s calculated wth most recent channel estmates, where s the current BCL wth N backup channels. Accordng to C Breq, one of the followng actons s taken: channel export (BCL CCL), channel mport (BCL CCL), channel swap (BCL CCL), and mandatory channel export (BCL CCL). 1) Channel export: f C B req > thpotental upper, we export a certan number of least preferred channels from BCL snce t contans more channels than necessary. We use thpotental upper = thpotental + ɛ 1 (ɛ 1 > ) to avod any mpetuous channel export. To export channels, the (sub)optmal sequence of all N (not M!) backup channels s constructed and the optmal BCL sze N s calculated agan. Then, the last (N N ) channels n the sequence are exported to CCL. 2) Channel mport: f C Breq < thpotental lower, a number of canddate channels are mported from CCL to satsfy C B req L thpotental, where L N s an extended BCL after mportng the CCL channels. We use N thpotental lower = thpotental ɛ 2 (ɛ 2 > ) to 5 Secton V wll cover more detals on ON/OFF-pattern estmaton and P dle predcton.

7 avod mpetuous channel mport. To mport channels, canddate channels are sorted n the (sub)optmal order, and are mported to BCL one by one n the order of preference untl C B req L thpotental s met. N 3) Channel swap: One may want to restrct the sze of BCL wthn some range such as N lower N N upper. N lower helps reserve a mnmal number of backup channels so that opportunty-dscovery would be successful, and N upper upperbounds the computatonal overhead n sortng backup channels. When N lower and N upper are used, channel export (or mport) cannot be processed f N = N lower (or N upper ). n such a case, we swap the least preferred backup channel wth the most preferred canddate channel f the swap helps decrease/ncrease C B req as desred. 4) Mandatory channel export: n our scheme, channels are categorzed nto two classes: (1) those wth long ON/OFF perods (class-l), and (2) those wth short ON/OFF perods (class-s). The former ncludes TV bands where ON/OFF perods are n the order of hours at least, and the latter ncludes channels where ON/OFF perods typcally last tens of mllseconds [7]. A mandatory channel export s trggered when a class- L channel (ether n-band or backup channel) s sampled to be ON (.e., busy). Such a class-l channel s better to be expelled from BCL snce the channel s unlkely to become avalable soon. Once expelled, the channel s forced to stay n CCL untl ts tno MPORT TMER expres. tno MPORT TMER s a desgn parameter and can be unquely determned for each channel. A smlar concept was found n EEE [1], where a backup channel detected busy s marked as occuped by PUs and never sensed untl Non-Occupancy Perod (recommended to be 1 mnutes) expres. Note that canddate channels wth ther tno MPORT TMER unexpred are not consdered for channel mport. V. CHANNEL STATE PREDCTON STRATEGY Predcton of channel avalablty (.e., Pdle ) at the tme of opportunty dscovery s ndspensable to achevng the mnmal dscovery-delay snce Pdle s one of the key factors n the constructon of a (sub)optmal sensng-sequence. For alternatng renewal channels, Km and Shn [2] derved Pdle wth a gven set of samples whle consderng the correlaton between the samples. Pdle s formulated by the estmates on ON/OFF channelusage patterns, and hence, the estmaton method should be carefully chosen to produce accurate estmates. n addton, samples collected by the spectrum sensor does not always represent the actual channel state, because there s no perfect sgnal detector wth P M D = P F A =. Our proposed approach to the above two ssues wll be dscussed n the followng subsectons. A. Estmaton of Channel-Usage Patterns n [2] we ntroduced ML estmaton for renewal channels and also showed that, when ML estmaton s employed, the samplng rate must be lower-bounded to acheve accurate estmates on channel-usage patterns. Specfcally, the samplng perod must be set to be proportonal to mn{e[ton ], E[T OF F ]}. Therefore, class-s channels must be sensed more frequently than class-l channels, to acheve the same level of accuracy. However, performng addtonal sensng on class-s channels may ncur a hgh sensngoverhead. To acheve accurate estmaton on class-s channels wthout requrng addtonal sensng, Bayesan estmaton can be used. Unlke large-sample asymptotc estmators (e.g., ML) whose estmaton accuracy degrades as the channel s less nfrequently sampled, Bayesan estmaton s known to perform reasonably well even f the number/frequency of samples s lmted [8]. Bayesan nference s also useful to model tmevaryng parameters by updatng pror and posteror dstrbutons of the unknown parameters. Usng these features of Bayesan estmaton, we propose the followng strategy for accurate estmaton of channel-usage patterns. Class-L channels: perform ML estmaton. Class-S channels: perform Bayesan estmaton. Although Bayesan learnng on channel avalablty has been ntroduced n [7], t models a channel yeldng uncorrelated samples and consders statonary probablty u for Pdle. Wth alternatng renewal channels, however, samples are correlated, and hence, the model n [7] s not sutable. Therefore, we propose an teratve Bayesan nference for alternatng renewal channels. A sngle-step Bayesan nference and ts extenson to a mult-stage teratve estmaton wll be used. We wll then dscuss how to reduce the computatonal complexty of Bayesan estmaton. 1) Sngle-Step Bayesan nference: A sngle-step Bayesan nference [8] s summarzed as follows. Suppose a sequence of k samples Z k = (Z t 1, Zt 2,..., Zt k ) s gven for channel, where t j denotes a tmestamp of the j-th sample. For an alternatng renewal channel, the jont probablty mass functon (pmf) of Z k s denoted as f(z k θ ), whch depends on the vector θ Θ of the dstrbuton parameters of f T ON (t) and f T OF F (t) [2]. When π(θ ) s a pror (subjectve) dstrbuton of θ, the posteror dstrbuton of θ wth a new observaton Z k s π(θ Z k) = π(θ )f(z k θ ) π(θ )f(z k m(z k ) = θ ) π(θ Θ )f(z k θ )dθ, where m(z k ) s the margnal jont pmf of Z k. Then, the estmates of θ are obtaned as ˆθ = E π(θ Z k ) [θ ], where E[ ] s taken over the posteror dstrbuton π(θ Z k ). 2) teratve Bayesan nference: We extend the sngle-step procedure n V-A1 to provde an teratve Bayesan process where estmates are produced each tme a new sample s collected. Fg. 6 llustrates the concept of our teratve Bayesan nference. The process starts wth an ntal pror dstrbuton

8 Fg. 6. teratve Bayesan nference where θ ON and θ OF F are assumed to be exponentallydstrbuted wth mean τ ON and τ OF F, respectvely. 6 Settng the pror dstrbuton as above can satsfy the condtons (5) and (6). Consderng the fact that an alternatng renewal process s sem-markov [15], f(z k+1 θ) at stage k becomes f(z k+1 θ) = f(z t1 θ)f(z t2 Z t1, θ) f(z tk+1 Z tk, θ). π(θ ), and the frst stage begns upon collecton of the frst two samples. Upon arrval of the (k + 1)-th sample (.e., at stage k), the k-th par of new estmates are computed by usng π(θ ) and f(z k+1 θ ) of (k + 1) samples. From now on, the channel ndex wll be omtted when t does not cause any ambguty, snce the estmaton procedure s ndependent for each channel. As assumed n Secton -B, a channel s consdered as an alternatng renewal process wth ON and OFF states. For an llustratve purpose, exponentally-dstrbuted ON and OFF perods are consdered wth pdfs: { f TOF F (t) = θ OF F e θ OF F t (t > ), f TON (t) = θ ON e θ ON t (t > ). Therefore, unknown channel parameters are gven as θ = (θ ON, θ OF F ), Θ = {, } {, }. t should be noted, however, that the proposed procedure can be appled to any general pdfs of T ON and T OF F. The ntal pror dstrbuton π(θ) s usually chosen wth subjectve reasonng. The crtera n selectng the pror s based on the pror knowledge of θ. For exponentally-dstrbuted ON and OFF perods, π(θ) = π(θ ON, θ OF F ) should be chosen to satsfy the followng condton: θ ON >, θ OF F >, (5) by the defnton of exponental dstrbuton. On the other hand, f some statstcs are avalable on average ON and OFF perods on a large tme-scale (e.g., a day or a week), such knowledge can be reflected n the choce of the pror. For example, suppose τ ON and τ OF F are the average ON and OFF perods n a day. Then, the pror knowledge can be used to form π(θ) such that τ ON = 1/E[θ ON ], τ OF F = 1/E[θ OF F ], (6) snce θ ON = 1/E[T ON ] and θ OF F = 1/E[T OF F ]. Here we assume τ ON and τ OF F are gven, and the pror dstrbuton s set as π(θ ON, θ OF F ) = τ ON e τ ON θ ON τ OF F e τ OF F θ OF F, or equvalently { π(u, θ OF F ) = τ ON τ OF F e (τ ON τ OF F τ ON /u)θ OF F, u = θ OF F /(θ ON + θ OF F ), The dervaton of the transton probablty f(z tj+1 Z tj, θ), j = 1, 2,..., k, for arbtrarly-formed f TON (t) and f TOF F (t) can be found n [15]. For example, wth exponentallydstrbuted ON and OFF perods, we can show f(z t1 θ) = (1 u) 1 Z t 1 u Z t1, f(z tj+1 Z tj, θ) = (1 u) 1 Z t j+1 u Z tj+1 + ( 1) Z tj +Z tj+1 u 1 Z t j (1 u) Z tj e θ OF F j /u, (7) where j = t j+1 t j. Now, m k (Z k+1 ) at stage k s derved as m k (Z k+1 ) = 1 = j=1 π(θ)f(z k+1 θ)dθ ON dθ OF F π(u, θ OF F ) (1 u) 1 Zt 1 u Z t1 k ( f(z tj+1 Z tj, θ) θof F u 2 ) dθ OF F du, whch provdes a closed-form soluton by transformng the product of sums wth k terms, k j=1 f(z t j+1 Z tj, θ), nto a sum of products wth 2 k terms. We then obtan two estmates ˆθ ON and ˆθ OF F at stage k as ˆθ ON,k = = and = 1 ˆθ OF F,k = = ( θof F u 2 = θ ON π(θ Z k+1 )dθ ON dθ OF F ( ) 1 π(u, θ OF F u 1 θof F )f(z k+1 θ) m k (Z k+1 ) ) dθ OF F du, 1 ( θof F u 2 θ OF F π(θ Z k+1 )dθ ON dθ OF F π(u, θ OF F )f(z k+1 θ) θ OF F m k (Z k+1 ) ) dθ OF F du, both of whch provde closed-form estmators wth the same transformaton as n m k (Z k+1 ). The derved Bayesan estmators work as fast as ML estmators snce both are expressed n closed forms. 6 Note that modelng θ OF F and θ ON to be exponentally-dstrbuted has nothng to do wth exponentally-dstrbuted ON and OFF perods.

9 3) mplementaton ssues: Despte ts smplcty and good performance, Bayesan nference suffers from computatonal complexty nherent n ntegraton of pdfs to produce m k (Z k+1 ) and ˆθ. n case there are no closed-form solutons for them, the complexty of h(z k+1, θ) grows exponentally as the number of stages ncreases, although the number of samples ncreases lnearly. To overcome ths problem, a few adjustments can be made to the proposed scheme. Frst, MAX BS STAGE, a desgn parameter, can be set so that the process resets to stage 1 whenever the current stage number reaches MAX BS STAGE. When t resets, the pror dstrbuton π(θ) s updated wth the most recent estmates. That s, τ ON and τ OF F n π(θ) must be replaced by 1/ˆθ ON and 1/ˆθ OF F where ˆθ ON and ˆθ OF F are the most recent estmates. Next, a pre-computed look-up table can also be used to evaluate the ntegrals. When an ntegraton does not provde an analytcal soluton, numercal ntegraton (e.g., Smpson s rule) or Monte Carlo ntegraton [8] can be used. Through a seres of computatons, the estmates of unknown parameters can be pre-computed wth sample values and ther tmestamps as nput arguments. Ths way, the delay nvolved wth computatonal complexty of Bayesan estmaton can be bounded reasonably small. B. Compensaton of Sgnal Detecton Error Usng ML or Bayesan estmaton, the unknown dstrbuton parameters of ON/OFF perods can be computed. The next step s then to accurately predct Pdle usng the estmates. As dscussed n Secton -B, the effect of mperfect sensng (.e., P MD, P F A > ) should be accounted for to make Pdle reflect the actual channel state. Here we present a Bayesan state estmaton procedure that can compensate for the sensng error. t s shown n [2] that wth alternatng renewal channels, Pdle becomes the transton probablty between samples, whch s often nonlnear. n such a case, Bayesan state estmaton s a proper choce because t s a nonlnear estmaton technque, whle other lnear estmators (e.g., extended Kalman flter (EKF)) just approxmate nonlnear estmaton [22]. The procedure of Bayesan state estmaton s summarzed as follows [22]. Suppose X tk {, 1} denotes the actual state of a channel at tme t k, and Z tk {, 1} denotes the observed channel state (.e., a sample) at tme t k. Also, suppose the state-transton functon g k and measurement functon l k are nonlnear and tme-varyng such that X tk+1 = g k (X tk ), and Z tk = l k (X tk, w k ), where w k s the measurement nose. Assumng the pdf of the ntal state X t s known, the estmator s ntalzed as f(x t Z ) = f(x t ), where Z k = {Z t1, Z t2,..., Z tk } for k 1 and Z =. For each k 1, we evaluate f(x tk Z k 1 ) = f(x tk X tk 1 )f(x tk 1 Z k 1 ), X tk 1 f(x tk Z k ) = f(z tk X tk )f(x tk Z k 1 ) X tk f(z tk X tk )f(x tk Z k 1 ), where f(x tk Z k 1 ) s the pror pmf of X tk before observng Z tk and f(x tk Z k ) s the posteror pmf of X tk after observng Z tk. Pror and posteror pmfs are updated whenever a new sample Z tk s obtaned. Snce channel parameters u and θ OF F are tme-varyng, updatng pror and posteror pmfs must be preceded by the Bayesan nference on them (Secton V-A). Then, when an opportunty-dscovery s trggered at tme t, P dle (t) can be estmated as P dle (t) = f(x tk Z k 1 ) tk =t,x tk =. n the above procedure, f(x tk X tk 1 ) and f(z tk X tk ) are yet to be determned. For exponentally-dstrbuted ON and OFF perods, f(x tk X tk 1 ) s gven as n Eq. (7). On the other hand, by defnton of P D and P F, t s clear that 1 P F, f (X tk, Z tk ) = (, ), P F, f (X tk, Z tk ) = (, 1), f(z tk X tk ) = 1 P D, f (X tk, Z tk ) = (1, ), P D, f (X tk, Z tk ) = (1, 1). V. PERFORMANCE EVALUATON To demonstrate the effcacy of the proposed schemes, we conducted four types of smulaton. The frst test n Secton V-A compares the average opportunty-dscovery delay of the proposed sensng sequence wth the optmal delay (computed usng a brute-force search). Ths test wll show that the proposed suboptmal algorthm performs reasonably well and sometmes performs as good as the optmal sensngsequence. The second test n Secton V-B shows the superorty of the proposed sensng sequence to the probabltybased sensng-sequence n [2]. The thrd test n Secton V-C demonstrates the performance mprovement of the BCL update strategy by comparng the proposed scheme wth the case of no BCL update. The last test n Secton V-D evaluates the beneft of selectng between ML and Bayesan by comparng ts performance wth ML-only estmaton. The smulaton parameters for those tests are presented n the correspondng subsectons. For all tests, we use the average delay as a yardstck n dscoverng opportuntes. The average dscovery-delay s captured by consderng two dfferent cases: (1) when opportunty dscovery completes durng the frst round of searchng backup channels, and (2) when t completes durng the successve retres, provded the frst round faled. The delay n the frst case says how effcent a sensng sequence s, whereas the second case shows how effcently the BCL s constructed/updated so that opportunty dscovery may be successful at early rounds.

10 Test 1a: varyng C (fxng s 2 C = 1.8) Test 1b: varyng T (fxng s 2 T = 12.96) Test 1c: varyng ū (fxng s 2 u =.216) u ( 1) u ( 1) u (ū.3) +.1( 1) T 48 6( 1) T ( T + 18) 6( 1) T 48 6( 1) C ( C 1.5) +.5( 1) C 1 +.5( 1) C 1 +.5( 1) C from 2. to 4.5 n step of.25 T from 25 to 35 n step of 1 ū from.35 to.55 n step of.2 TABLE CHANNEL PARAMETERS FOR TEST 1: T N msec, 1 N = 7 u ( 1) T 5 ( = 1, 2, 3), 4 ( = 4, 5, 6), 3 ( = 7, 8), (msec) 2 ( = 9, 1, 11), 1 ( = 12, 13, 14, 15) C.5 +.5( 1) E[TON ] 8: ( 1), 9: ( 9) TABLE CHANNEL PARAMETERS FOR TEST 2: 1 N = 15 Channels are smulated as alternatng renewal processes wth exponentally-dstrbuted ON and OFF perods. The channel parameters θ ON and θ OF F are assumed tme-varyng and ncreasng/decreasng by 1% every 1 seconds. To track the tme-varyng channel condton, a movng wndow of tmovng WNDOW = 2 seconds s used for each channel wth whch prevously collected samples older than tmovng WNDOW are dscarded. We adopt the event-drven channel reuse model for smulatons. That s, once a backup channel s sensed dle durng an opportunty dscovery, t becomes an n-band channel and reused untl t swtches to ON state. t s assumed that sensng can accurately measure the actual channel state (.e., P MD and P F A ). Although P MD > and P F A > n realty, ths assumpton wll help us focus on the effcacy of the proposed sensng-sequence and BCL update strateges. t should be noted, however, that ths assumpton s made only for an llustratve purpose, and our schemes can adopt the scheme n Secton V-B to reflect mperfect sensng. For every test, a sngle smulaton ran for 3, seconds, and the same test was repeated 1 tmes to take the average performance. n addton, tretry s set to.1. A. Test 1: Effectveness of the Proposed (Sub)optmal Sensng- Sequence n ths test, the average dscovery-delay of the proposed (sub)optmal sensng-sequence s compared wth the mnmum, medan, maxmum delays found by tryng all N! possble sequences va a brute-force search. Assumng perfect knowledge on channel parameters, the average delay s analytcally derved by usng the statonary probablty u such as Pdle = 1 u. 7 The dervaton excludes the case when there are less than B req opportuntes n N channels. We fx N = 7 and BCL s not updated so as to focus on the analytcally achevable performance of the sequences. Suppose u = (u 1, u 2,..., u N ), T = (T 1, T 2,..., T N), and C = (C 1, C 2,..., C N ). Then, for B req = 5, varous 7 Usng 1 u for Pdle s to obtan an analytcal average delay. n other tests, Pdle s derved usng transton probabltes. u ( 1) T 5 (1 4), 4 (5 8), 3 (9 12), (msec) 2 (13 16), 1 (17 2) C ( 1) E[TON ] 12 (class-s):.2 +.1( 1), 13 (class-l): ( 13) TABLE CHANNEL PARAMETERS FOR TESTS 3 AND 4: 1 N = 2 combnatons of channel condtons are consdered wth a tuple of { u, T, C } by (1) varyng C whle fxng s 2 C, where C and s 2 C are sample mean and sample varance of C, respectvely, 8 (2) varyng T whle fxng s 2 T, and (3) varyng ū whle fxng s 2 u. The smulaton parameters are lsted n Table. Fg. 7 plots the smulaton results. nterestngly, the proposed sequence s achevng the optmal performance n Test 1a, regardless of the average channel capacty. However, n Test 1b and 1c, there are certan thresholds of the average sensng-tme and channel-utlzaton, above whch performance degrades. n other words, the proposed sequence performs exceptonally well unless we have long sensngtmes or hghly-utlzed channels. Consderng the fact that CR targets under-utlzed channels for ts applcaton, sensng-tme seems more mportant n ths phenomenon. We are currently nvestgatng how to enhance the proposed suboptmal algorthm by addressng the above ssue, whch s part of our future work. B. Test 2: Performance Enhancement of the Proposed Sensng- Sequence aganst Other Schemes n ths test, the proposed sensng-sequence s compared wth a probablty-based sequence n [2]. Channel condtons are chosen such that they can reveal the napplcablty of the probablty-based scheme. For example, channels wth low utlzaton may be preferred by the scheme n [2], although t s better to put low prorty on such channels f they have small capacty and long sensng-tmes. Assumng the perfect knowledge 9 on channel condtons, both schemes are smulated wth B req = 8, 1, and 12. The number of channels s fxed at 15 and no BCL update s performed. The parameters used for ths smulaton are lsted n Table. n Fg. 8, Random represents the sequence wth randomlysorted channels and Worst means the one bult by reversng the proposed sequence. On the other hand, Delay Type- s the average delay when opportunty dscovery s successful 8 Specfcally, C = 1 N N =1 C and s 2 C = 1 N N 1 =1 (C C) 2. 9 The mpact of estmaton wll be nvestgated n the next two tests.

11 avg dscovery delay (ms) Test 1a average capacty Fg Test 1b average sensng-tme Test 1c Proposed Optmal Medan Worst average utlzaton Test 1-a/b/c: average delay of the proposed suboptmal sequence vs. optmal delay avg dscovery delay (ms) Fg Delay Type Delay Type Delay Type B req Proposed Prob-based Random Worst Test 2: proposed sensng-sequence vs. probablty-based sequence wthout any retry, whereas Delay Type- s the average delay when the frst tral fals and thus opportunty dscovery completes after successve retres (by tretry). Delay Type- + s the overall average delay consderng both cases. The proposed scheme s shown to enhance Type- delay by up to 47.12% and 3.7% over Prob-based and Random, respectvely. The overall delay (.e., Type-+) s also enhanced by up to 4.7% and 25.28%, respectvely. t can also be seen that the proposed sequence does not reduce Type- delay n ths case, whch s expected because the channel set s fxed and no BCL update s performed for ths test. t wll become clear n Test 3 that BCL update can reduce Type- delay sgnfcantly by refreshng backup channels wth more promsng ones, that maxmzes the chance of completng opportunty dscovery wthout retres. C. Test 3: Proposed BCL Update Strategy vs. No BCL Update n ths test, the effcency of the proposed BCL update strategy s evaluated and compared wth another scheme wth no BCL update. Both schemes ntalze BCL by optmally determnng the sze of BCL and ts ntal entres, wth Pdle = 1/2, assumng no pror knowledge on the ON/OFF usage patterns. As the smulaton progresses, the proposed scheme updates BCL va channel mport/export/swap and adjusts the BCL sze accordngly, whereas the latter scheme al- avg dscovery delay (ms) Delay Type Delay Type + Fg. 9. Delay Type B B req req Rato = / Test 3: proposed BCL update vs. no BCL update Proposed No BCL Update ways stays wth ts ntal BCL entres. Snce estmaton plays an mportant role n updatng BCL, both schemes perform the proposed combnaton of ML and Bayesan estmaton. We set N = 2 to have enough canddate channels after the ntal BCL constructon, and vary B req to be 8, 1, 12. The BCL update parameters are set as follows: tupdate = 3, tno MPORT TMER = 3, thpotental =.9, thpotental lower =.88, thpotental upper =.93, N lower = 5, and N upper = 15. Other smulaton parameters are lsted n Table. Fg. 9 plots the smulaton results. Both schemes start wth the same set of BCL entres where N = 7 ntally. At the frst look, one mght thnk that the proposed scheme performs more poorly than the latter scheme, based on the results on Type- delay. However, we should not overlook the fact that the latter scheme fxes the sze of BCL at 7. Therefore, ts Type- delay never exceeds the sum of sensng-tmes of the seven channels. On the other hand, our scheme flexbly adjusts ts BCL sze from 5 to 15, to maxmze the chance of successful opportunty dscovery at the frst round of searchng backup channels. Naturally, the Type- delay of our scheme could be longer than that of the no-update scheme. Then, what would be the beneft of adjustng the sze/entres of BCL by sacrfcng the Type- delay? To present the benefts clearly, we have counted the number of events when

12 avg dscovery delay (ms) Fg. 1. Delay Type Delay Type Delay Type B req Proposed ML only Test 4: proposed ML/Bayesan combned vs. ML-only strategy opportunty dscovery completes wthout retres (Type-) and after retres (Type-). We calculated the rato between two events (Type- / Type-) and plotted t at the bottom rght corner of the fgure. t s clear that our scheme ncurs Type- event a lot more than Type-, whch helps reduce the overall opportunty dscovery-delay (Type +) sgnfcantly because Type- retres are very costly. As a result, our scheme outperforms the no-update scheme n both Type- delay and the overall delay (+), showng up to 76.78% and 91.12% of performance enhancement. D. Test 4: Proposed ML/Bayesan Combned Estmaton Strategy vs. ML Estmaton Only n Test 4, performance of the proposed combnaton of ML and Bayesan estmaton s compared wth a ML-only scheme. Both schemes adopt the proposed sensng-sequence and BCL update algorthm. MAX BS STAGE s set to 4, where t may be ncreased to have better performance (.e., more accurate estmates) at the expense of computatonal complexty. Other smulaton parameters are the same as Test 3. As shown n Fg. 1, the proposed strategy acheves a smaller average delay than ML-only estmaton by enhancng Type- delay by up to 22.72%. As a result, the overall delay (+) s enhanced by up to 33.75% over the ML-only strategy. Ths s because Bayesan nference on class-s channels provdes more accurate estmates than ML estmaton, whch helps update BCL more effcently. V. CONCLUSONS n ths paper, we proposed a (sub)optmal sensng-sequence for fast dscovery of spectrum opportuntes so that a CRN can provde a seamless servce to ts SUs wth mnmal QoS degradaton. We also proposed constructon of a backup channel lst (BCL) wth an effcent BCL update algorthm to support fast opportunty dscovery. 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