A Low-Latency Zone-Based Cooperative Spectrum Sensing

Transcription

1 1 A Low-Latency Zone-Based Cooperatve Spectrum Sensng Deepak G. C., Student Member, IEEE, and Kevan Navae, Senor Member, IEEE Abstract In ths paper we propose a spectrum sensng scheme for wreless systems wth low latency requrement such as machne-to-machne communcatons. In such systems wth hgh spatal densty of the base statons and users/objects, spectrum sharng enables spectrum reuse across very small regons. Ths however needs effcent ncorporaton of sensors locaton nformaton nto spectrum sensng. We propose a mult-channel cooperatve spectrum sensng technque n whch an ndependent network of sensors, namely montorng network, detects the spectrum avalablty. The montorng network dvdes the coverage area nto overlapped but ndependent zones. Ths enables explotng hgh spatal dstrbuton wthout ncorporatng exact sensors locaton. Correspondng to each zone, a zone aggregator ZA) s ntroduced whch processes the sensors output. The aggregated decson n each zone assocated wth the ZA s locaton s then passed to a decson fuson center DFC). The secondary base staton SBS) accordngly allocates the avalable channels to maxmze the spectral effcency. We formulate the functon of the DFC as an optmzaton problem wth the objectve of maxmzng the spectral effcency. For energy detector sensors, we further obtan optmal detecton threshold for dfferent cases wth varous spatal denstes of ZAs and SBSs. Ths provdes extra degrees of freedom n desgnng the spectrum montorng network and provdes quanttatve nsght on network desgn. We further devse an effcent protocol for the proposed technque wth very low sgnalng complexty and show that the proposed method reduces the spectrum sensng latency and results n a hgher spectrum effcency. Extensve smulatons confrm our analytcal results and ndcate a sgnfcant mprovement n sensng latency and accuracy. Index Terms Cogntve rado, cooperatve spectrum sensng, spectral effcency, spectrum montorng. I. INTRODUCTION Cogntve rado network CRN) utlzes dynamc spectrum access DSA), where the secondary users SUs) share the rado spectrum wth the prmary users PUs). In DSA, SUs should perodcally sense the spectrum avalablty to avod nterferng wth the PUs communcaton actvtes. In wreless communcatons, data s often transmtted wthn tme frames. Number of data bts transmtted n each tme frame s drectly related to the the system throughput. In DSA, part of each tme frame s allocated to spectrum sensng thus no transmsson s allowed 1], ]. By ncreasng the sensng duraton the sensng accuracy s also ncreased however, the remanng tme for transmsson thus the throughput s decreased. Ths results n a fundamental trade-off between sensng accuracy and system throughput 3]. As a consequence, choosng the optmal value of sensng duraton s a challengng task 4]. The authors are wth the School of Computng and Communcatons, Lancaster Unversty, Lancaster, UK, LA1 4YW, E- mal: k.navae@lancaster.ac.uk. The work n ths paper s supported by EU Mare Cure CIG S3SE. Ths paper was presented n part at the Intl. Symp. on Wreless Comm. System ISWCS), Ilmenau, Gernamy, 013. Conventonally, the spectrum avalablty s sensed at the SUs. Fundamental characterstcs of multuser wreless envronments ncludng multpath fadng, user moblty and hdden termnal problem, as well as lmted sensng duraton result n reducng sensng accuracy. Therefore, n such envronments conventonal sensng mechansms are not able to effcently sense the spectrum avalablty wth an acceptable level of accuracy requred for protectng the PUs 5]. To address the sensng accuracy ssue, cooperatve spectrum sensng technques are ntroduced, see, e.g., 6], 7], 8]. Spectrum avalablty decson s made by combnng the collected sensng nformaton by SUs based on a rule, e.g., AND, OR or K-out-of-N 3]. In such methods, the spectrum avalablty nformaton obtaned from multple SUs can also be processed usng more sophstcated technques. Instances nclude weghtng 9], multdmensonal correlaton 10] and mnmzng the collson probablty at the PUs 5]. In weghtng, the share of the provded nformaton by each sensor n the fnal decson s determned by a weghtng vector whch s a system desgn parameter. Further, 10] leverages the spato-temporal correlatons between spectral observatons among varous nodes and across dfferent tme nstants to mnmze the sensng cost and maxmze ts accuracy. Varous settngs have been proposed for mplementng cooperatve spectrum sensng, see, e.g., 11] and references theren. Cooperatve spectrum sensng proposed n 1] dvdes the coverage area nto clusters, where the SUs perform spectrum sensng and base staton acts as decson fuson center. The users consdered as the cluster heads then make spectrum avalablty decsons. In such a cooperatve sensng model, a hgher sensng duraton results n a shorter data transmsson duraton whch results degradaton n achevable data rate. In addton, the sgnalng overhead s also hgher n the secondary system and the performance s hghly senstve to the reportng channel condton. The logcal cluster formaton proposed n 13] s desgned to tackle the ssues due to the mperfect reportng channel condtons. In 14], the cluster formaton s proposed based on the heterogeneous characterstcs of PUs and SUs such that users n the same cluster sense the dentcal set of channels to ncrease the sensng accuracy. The cluster heads however act locally therefore unable to ncorporate ther locaton nformaton nto the network wde channel allocaton. In addton, varous decentralzed cooperatve schemes are proposed, e.g., 15], where no fuson center exsts and therefore the SUs themselves dffuse the receved decsons. In addton to the centralzed and decentralzed cooperatve schemes, a relay-based multple hops cooperatve sensng s proposed n 16], where source to destnaton spectrum nformaton s forwarded by the relay nodes, where ether amplfy-and-forward or decode-and-forward s mplemented.

2 Ths tackles the ssues of erroneous report channel by ncreasng the cooperaton footprnt. As a matter of fact, whether t s centralzed, decentralzed or relay-asssted cooperatve model mentoned n 6]- 16], the formaton of clusters s very challengng due to the tme varyng nature of the wreless channel, and user s moblty. Merts of ncorporatng the locaton nformaton are recognzed n conventonal cogntve rado 17] as well as n advance cooperatve communcaton 11]. However, embeddng the locaton nformaton n the CRN desgn mght ncrease the sgnalng overhead. The dynamc cluster formaton algorthm also causes very hgh sgnalng overhead. Therefore, an ndependent spectrum montorng network has been proposed n ths paper to mprove the cooperatve sensng effcency wth reduced complexty. A two channel sensng technque under mperfect spectrum sensng based on an access, and a backup channel s also proposed n 18], where both channels are sensed n a sngle tme slot to mprove the system performance by jontly consderng spectrum sensng and spectrum access. Although cooperatve sensng often mproves the sensng accuracy, the correspondng sgnalng overhead further reduces the overall system throughput. In the prevously proposed cluster based cooperatve sensng approaches, n addton to the sgnalng overhead due to the cluster head selecton, cooperatve spectrum sensng also ntroduces extra spectrum sensng latency. Ths s due to the fact that the SUs need to allocate an extra part of ther fxed tme frame to transmt the sensng nformaton to a fuson center and then wat for the sensng decson to be made and receved back. To address ths ssue, the sensor selecton algorthms have been proposed n 19], 0]. However, cooperatve sensng fals to provde requred low-latency access whch s of an mmense mportance n uses-cases ncludng machne-tomachne MM) communcatons 1]. MM plays an mportant role n the structure of the Internet-of-Thngs IoT) whch wll be manly connected through wreless communcatons. To tackle the latency ssues due to the sensng duraton, ] proposes offloadng the cooperatve sensng to an ndependent montorng network. It comprses of sensors deployed n the coverage area and contnuously montor the spectrum avalablty. The sensng nformaton s then communcated by the sensors to a central entty on separate sgnalng channels. In ths settng, by careful desgn of system parameters, the same level of accuracy s acheved wthout reducng the system throughput. There s, of course, cost assocated wth buldng the montorng network, whch s justfed n ] consderng extraordnary prce of rado spectrum n moble communcaton bands. An ndependent network of sensors s further consdered n 3], 4] for nomadc cogntve networks n urban and sub-urban areas. The advantages of consderng a separate montorng network are twofold. Frstly, t lowers the correspondng sensng latency due to the reduced sensng duraton, thus the spectral effcency s ncreased by offloadng the spectrum sensng task to an ndependent montorng network. Secondly, the spectrum sensng accuracy s sgnfcantly mproved due to cooperatve sensng. The above mentoned technques mprove the sensng accuracy and ts latency but smply gnore the sensors locaton nformaton. Due to very hgh number of objects n the coverage area, ncorporatng the locaton nformaton nto sensng s capable of enablng spectrum reuse across very small regons n the network coverage area. In ths paper we refer to ths as mcro-spectrum-reuse. Incorporatng the exact locaton of the sensors however mght ntroduce a new dmenson to the spectrum sensng complexty and ncreases ts assocated costs. Instead n ths paper we propose a smple Zone-Based Cooperatve Spectrum Sensng. The sensng archtecture n the proposed method s based on dvdng the coverage area nto zones and defnng a zone aggregator ZA) as an ntermedate entty. We consder a general case n whch the spectrum s dvded nto number of channels e.g., sub-channels n multcarrer systems). The ZAs then process the sensng outcome of the sensors for each channel located n ther correspondng zone. The aggregated decson for each zone s then passed to a fuson center. In our proposed scheme, to address the overhead ssue we further devse a one-bt-per-channel sgnalng scheme between the ZAs and the fuson center. In our proposed method a central decson fuson center DFC) located, e.g., n the secondary base staton SBS) then utlzes the aggregated sensng nformaton n the network zones. SBS accordngly allocates the avalable channels to maxmze the spectral effcency and keep the nterference at the PUs below the system requred threshold. We formulate the correspondng functon of the DFC as an optmzaton problem and show that t s a convex optmzaton problem. We then obtan optmal detecton threshold for dfferent cases wth varous spatal denstes of ZAs and SBSs. We further obtan a close form for the optmal sensng threshold based on a weght-based approach. Varous factors are nvolved n the effcency of the proposed method n ths paper, ncludng number of zones and base statons, the spatal dstrbuton of the sensng devces and the zone sze. We nvestgate the mpact of these factors on the system performance and propose technques for effcent desgn of the correspondng parameters. Ths provdes extra degrees of freedom n desgnng the spectrum montorng network and provdes quanttatve nsght on deployment of such networks. In our analyss, we focus on energy detecton as the man spectrum sensng method at the sensors. The analyss presented here can be extended to desgn the parameters for cases where other spectrum sensng technques are utlzed n the sensors. In the proposed method, the latency assocated wth the spectrum sensng s the tme requred for sgnalng between the SUs and the DFC. For a gven requred spectrum sensng accuracy, we also show that the the proposed method n ths paper provdes a lower latency n comparson wth conventonal sensng methods 1. Therefore, the proposed method provdes enablng technques and protocols for adoptng DSA n low latency MM communcatons. The analyss presented n ths paper are unque as they provde quanttatve nsght on the achevable gan on the 1 Hereafter, conventonal sensng s referred to any spectrum sensng technque n SUs n whch the tme frames are dvded nto sensng, and transmsson duratons.

3 3 spectral effcency usng cooperatve sensng based on an ndependent montorng network. Usng smulatons we nvestgate the accuracy of spectrum sensng n the proposed method as a functon of dstrbuted sensng nformaton. The acheved throughput gan of the proposed method for varous network parameters, e.g., sensng duraton, detecton threshold, prmary actvtes, s also nvestgated. In addton, the proposed zone-based cooperatve spectrum sensng method s compared aganst the reference model where there s no cooperaton among the clusters or SBS. Comparsons are also made wth the cases where the spectrum sensng nformaton s combned usng only OR/AND method. In the followng we summarze the contrbutons presented n ths paper: 1) We propose a novel spectrum sensng method based on an ndependent spectrum montorng network and devse the assocated system, algorthms and sgnalng protocols whch ncorporate zone locaton nformaton n the spectrum sensng. The proposed method n ths paper enables mcro-spectrum-reuse and results n hgher spectral effcency, lower sgnalng overhead, and thus the lower latency. ) An analytcal framework s developed wth the objectve of maxmzng system throughput under varous montorng network scenaros subject to spectrum sensng accuracy and maxmum tolerable mposed nterference at the PUs. 3) Extensve smulatons confrm our analytcal results and ndcate the throughput performance and sensng latency mprovement usng the proposed sensng method. The smulaton results also outlne the parameter desgn explan the role of varous factors ncludng spatal densty of ZAs, and SBSs, prmary system actvty, and sensng threshold on the sensng performance. The rest of the paper s organzed as follows: System model s presented n Secton II. The zone-based cooperatve spectrum sensng technque, and ts performance analyss are presented n Sectons III, and Secton IV, respectvely. Secton V descrbes the extensve smulaton results, whch s followed by conclusons n Secton VI. II. SYSTEM MODEL A schematc of the system s shown n Fg. 1 n whch a prmary base staton PBS) provdes servce to the PUs whch are randomly dstrbuted wthn the coverage area. The secondary system s also a cellular network whch utlzes orthogonal frequency dvson multplexng OFDM), where the frequency spectrum s dvded nto N non-overlappng channels. Due to the small-scale frequency-dependent mult-path propagaton characterstcs, each SU may experence dfferent channel gans across dfferent sub-channels, ndexed by = 1,..., N, each wth bandwdth of B Hz. The same spectrum s also utlzed by the prmary system n the downlnk. Dependng on the PU actvty and ts requred qualty of servce QoS) at a specfc tme and locaton, SUs may have access to M channels, where 0 M N. Wthout loss of generalty, Zone 1 : Zone Aggregator : Sensng Devces SU SBS/DFC PBS Fg. 1. The zone-based cooperatve spectrum sensng. Zone we also assume that all the base statons are equpped wth a sngle omndrectonal antenna. The analyss can be easly extended nto sectorzed cells by consderng each sector as a cell wth a sngle antenna. A. Spectrum Montorng Network The spectrum sensors are dstrbuted unformly wthn the coverage area. In practce, ther locaton can be engneered by the servce provders. For smplcty, we further assume a homogenous network of sensors, where sensng parameters of all the sensor nodes are the same. Unlke the conventonal sensng methods, where SUs sense the channel sequentally before accessng them, n the proposed method, the sensng task s offloaded to a spectrum montorng network. In ths settng, each sensng devce detects the prmary spectrum actvty on a subset of channels, {1,..., N}, wthn a crcular regon wth radus, r sen and reports ther avalablty to the SBS. As a result of the proposed ndependent sensng network, the sensng order of multple channels becomes rrelevant due to the suffcently longer sensng duraton avalable. Durng transmttng the channel avalablty reports to the zone aggregators, the sensng functon s stopped. The connectvty of the sensng network therefore depends on r sen and dstrbuton of sensng devces. To assocate the sensng nformaton wth the locaton, we then dvde the coverage area nto overlapped zones. The zones are chosen assumng a unform dstrbuton of sensng devces. In each zone, there s a zone aggregator ZA) whch receves the sensng nformaton from sensors located n ts crcular sensng zone wth radus r ZA. The sensng devces and ZAs collectvely form a montorng network whch s desgned for cooperatve spectrum sensng n the secondary network. Each ZA s assocated to the locaton of ts covered zone and broadcast a plot sgnal ncludng a zone dentfcaton ZID). Montorng network utlzes a narrow band pre-allocated spectrum ndependent from the prmary and secondary systems. The receved nformaton n the ZAs s then processed and forwarded to a decson fuson center DFC) located, e.g., PU

4 4 n the SBS ndexed by s = 1,..., S. Based on the sensng nformaton provded by the correspondng ZAs, DFC then decdes the avalablty of each channels n that partcular zone. Here, ZAs are ndexed by z = 1,..., Z, where Z s the number of zone aggregators n the system. B. Sensng Devces Sensors utlze energy detecton technque for detectng the avalablty of the channels. Energy sensng has been consdered here due to ts smplcty and tractablty as t does not need a pror channel nformaton, see, e.g., 5], and 6]. The sampled sgnals receved at the sensor durng the sensng duraton are y k) = w k), and y k) = g k)x k)+ w k), under hypothess H 0 and H 1, respectvely, where H 0 H 1 ) represents the absence presence) of the prmary sgnals. In addton, y k) s the k-th receved sample over channel and g k) s the channel gan whch s assumed to be constant durng the sgnalng duraton. Nose sgnal, w k), s assumed to be ndependent and dentcally dstrbuted crcularly symmetrc complex Gaussan wth zero mean and varance of E w k) ] = σw. Tme s slotted nto frames n whch the frame duraton and the sensng duraton for each sensng devce are denoted by T, and T s,, respectvely. The samplng frequency s f s, thus the number of samples durng the sensng duraton s K = T s, f s. The receved sgnal energy s E y) = 1 K K k=1 y k). In cases, where the PUs are communcatng wth the PBS, the transmtted sgnal s also beng receved by the sensng devces whch are located wthn the transmsson range of the PU. Therefore, the sensors perodcally sense channel and obtan the correspondng test statstcs,.e., energy levels, and the hypothess test s then performed based on the measured parameters and the system defned parameters. The performance of the spectrum sensng technques s characterzed by false alarm and mss detecton probabltes. False alarm s referred to the cases, where H 1 s decded whle the channel s n fact avalable. Smlarly, mss detecton s defned as the cases, where H 0 s decded whle the channel s n fact unavalable. For a channel, the probablty of false alarm, and mss detecton are represented by P f,, and P m,, respectvely, and detecton probablty s defned as P d, = 1 P m,. The lower the detecton probablty, the hgher s the chance of collson between PU and SU transmsson; thus lower s the the system spectral effcency. Smlarly, havng a hgher false alarm results n under-utlzaton of the practcally avalable prmary spectrum by the SUs ]. The mss detecton and false alarm probabltes are obtaned as Ch-squared dstrbuton wth K degrees of freedom, however t s shown, accordng to the central lmt theorem, that for a large number of ndependent and dentcally dstrbuted..d) samples K > 40) obtaned from prmary transmtter, the cumulatve densty functon CDF) of the estmated energy can also be approxmated by a normal dstrbuton, see, e.g., 7]. In such cases, the false alarm and detecton probabltes are 3]: and where P f, ε, T s, ) = PrE y) > ε H 0 ) ) ) ε Q 1 Ts,f s, 1) P d, ε, T s, ) = PrE y) > ε H 1 ) ) ) ε T s, f s Q γ 1, ) γ + 1 σ w σ w γ = E x ] g σ w s the average receved SNR of the PUs sgnal on channel. Here, ε and T s, are the energy detecton threshold and sensng duraton for the sensng devces. Moreover, ε and T s, are the desgn parameters and they represent the trade-off between P f, ε, T s, ), and P m, ε, T s, ) = 1 P d, ε, T s, ) whch s often referred to as recever operatng characterstcs ROC) curve 8]. III. ZONE-BASED COOPERATIVE SPECTRUM SENSING In the proposed method, spectrum sensors report the locally sensed channel decson to ther correspondng ZAs. ZAs then transmt ther aggregated decson to the SBS. In cases where the SUs request for the new channel, an avalable channel from {1,..., N} s granted to the SU. Therefore, the effcency of the proposed method depends on the accurate detecton of the PU actvty on each channel rather than sensng duraton, snce n the proposed method, sensors are, n fact, ndependent from the secondary network. The logcal AND rule s mplemented at the ZAs whch s appled on the sensng nformaton collected from ndvdual sensors n ts correspondng zone. Based on AND rule, for a channel to be avalable n a zone all sensors located n a zone must unanmously agree on the channel avalablty. In other words, f any sensor n a gven zone observes channel as busy, channel s consdered busy thus the SUs located n that zone are not granted access to channel by the SBS. Ths rather pessmstc strategy s desgned to best protect the actve PUs wthn the zone. As a result, the achevable spectral effcency n ths case acts as a lower bound to the maxmum achevable spectral effcency. Other technques, e.g., k-out-of- N, can be appled dependng on the nterference suppresson capablty of the prmary system. In addton, usng ths fuson method mantans the mathematcal tractablty to obtan the sensng thresholds later n the paper. Here, SBS may also act as ZA n cases where the cell sze s small such that sensors have drect communcaton wth the SBS. Correspondng to each channel, one bt nformaton s generated by each sensor, where 0 ndcates the channel s avalable and, 1 otherwse. For nstance, f there are 10 sensors n a zone montorng a total of 18 channel, for each sensng perod, a total 180 bts of sgnalng s transmtted n that zone. ZA then feeds back the channel avalablty to the DFC as a bnary vector, where each entry shows the avalablty of

5 5 Sensng Devces ZAs DFCs SUs Channel Info + LOC Frame 1 Frame Frame N One Cooperatve Ts,,s,l),s,l) Channel s Status l Locaton D, Z 1) AND D, Z ) AND D, Z 3) AND D Decson Z k Zones F uson REQB, Z k ) RES, I th ) INT ) NEW Channel, I th ) T ER, Z k ) T q START END START END Conventonal Sensng Zone-based Cooperatve Sensng Technque T q T s T T q T T s Fg. 3. The tme frame n the proposed method conssts of the query duraton T q), and transmsson duraton T T q). In the conventonal sensng, a frames conssts of the sensng duraton, T s, and transmsson duraton T T s). Fg.. Sgnalng dagram of the zone-based cooperatve spectrum sensng. the correspondng channel n that zone. DFC then allocates channels to maxmze mcro-spectrum-reuse. Sgnalng dagram for the proposed zone-based cooperatve sensng technques s shown n Fg.. The sensng devces are synchronzed and they sense the channels perodcally. Therefore, every sensng devce s programmed to sense the channels and reports ts sensng decson back to ts correspondng ZA. The proposed protocol n ths paper s based on provdng best-effort servce to the SUs. The SU whch requres access to the channel transmts a request message REQ) to the SBS ncludng ts requred bandwdth B) as well as ts correspondng ZIDs Z k ). The receved ZIDs by each SU act as a locaton ponter. The DFC then allocates channels, {1,..., N}, to the SU n that zone f any) as well as correspondng thresholds, I th. Here I th s a system defned parameter and t s set by prmary system accordng to ther capacty to suppress the nter-zone nterference, va a response message RES). Furthermore, the DFC s able to ncorporate other nformaton n ts decson makng, such as channel and traffc varatons. Thus DFC has a potental to act as a knowledge-based/expert entty whch keeps record of relevant prmary channel nformaton such as traffc actvtes and load varatons, transmsson power, and channel power gan. The SUs then start communcatng on the allocated channels whle constantly checkng the ZIDs. Here, we adopt the coexstence beacon protocol as n 9] n whch channel nformaton s embedded n the transmsson. In our proposed method and later n the smulaton, a unque dentty s set for the PUs and SUs whch s also embedded n ther transmtted sgnal. As soon as a PU starts transmsson, then usng ths unque dentty feld, the sensng devses are capable of recognzng that the detected sgnal s n fact from a PU transmtter. The montorng network contnuously senses the channels. Therefore, f a PU starts transmttng on a gven channel, the SUs transmsson on that channel s mmedately stopped and other avalable channels, f any, wll be allocated to that SU. Smlarly, f a SU moves nto another zone,.e., ts correspondng ZID s changed, the allocated channel n ts orgnal zone s released and a new channel, f avalable, s allocated to the SU n ts new zone. Alternatvely, to dentfy whether a detected sgnal s from a PU transmtter, nterframe quet perod IFQP) protocol 9] can also be used. In such cases, the DFC sends an nterrupt message INT) to the SU to mmedately release the allocated channels). If SU stll requres access and prevously allocated channels are no longer avalable, a NEW message s sent by the DFC allocatng new channels) f avalable), where NEW message has same parameters as RES message. In cases, where the SU does not requre access anymore, a termnatng message TER) s sent to the DFC to release the correspondng channel {1,..., N} wthn zone Z k. In the proposed protocol for the zone-based cooperatve spectrum sensng, the requred sgnalng between the sensors and the ZAs, and smlarly ZA and the DFC s desgned to be very lmted to reduce the spectrum resources allocated to the montorng network. Note that a gven channel mght be avalable n more than one zones thus based on the proposed method n ths paper, mcro-spectrum-reuse s expected n multple zones nsde the SBS coverage. A. Off-Loadng and Sensng Latency Off-loadng of the spectrum sensng actvtes to the ndependent sensng devces has a drect mplcaton on the latency, and thus on the system throughput. Due to a separate sensng network whch mantans almost real-tme prmary channel avalablty status, the correspondng channel allocaton latency n the secondary user s sgnfcantly reduced comparng to the cases wthout the spectrum montorng network. Ths has been nvestgated later n Secton IV and valdated through the smulatons n Secton V. The tme frames structure of the proposed method and that of the conventonal sensng are shown n Fg. 3. Here, T s s the sensng duraton for the conventonal spectrum sensng and T q s the duraton of the requred communcaton between the secondary system and the secondary base staton. Hereafter, we refer to T q as the query tme, where T q << T s. The low latency of the proposed sgnalng method s due to substtutng the sensng duraton T s wth T q. The extra transmsson tme, T s T q, results n ncreasng the total system spectral effcency and ts correspondng cost s deployng the spectrum montorng network. Therefore, careful analyss s requred to

6 6 evaluate whether the gan on the spectral effcency domnates the costs of deployng the montorng network. Wthout sensng devces, a porton of the frame duraton,.e., T s, must be sacrfced for spectrum sensng by the SUs. As a result, a shorter tme s avalable to the SUs for data transmsson. Therefore, off-loadng the sensng task to the sensng devces sgnfcantly ncreases transmsson duratons wthout reducng the sensng accuracy. The optmal sensng duraton, T s s not defned n WRAN standard 9], however t s shown n 3] that the optmal s 4% to 5%. In the proposed method, Tq T s s chosen to be less than 1%. Because of the ndependent spectrum sensng network, the sensng devces are able to sense the channel throughout the frame duraton. Therefore, usng the zone-based cooperatve sensng protocol enables smultaneous sensng, n the montorng network, and data transmsson at the secondary system. In ths case, the only tme nterval requred for obtanng the avalablty of the channel s T q whch s the duraton of sgnalng between REQ messages sent by the SU and RES message sent by the DFC. The sgnalng duraton n the proposed method s a very small fracton of sensng duraton of the conventonal approach of spectrum sensng. T s T IV. SENSING DESIGN A. Spectrum Sensng Accuracy Inaccurate sensng ether negatvely affects the prmary system performance through creatng nterference n cases of mss detecton), or results n a lower spectral effcency n the secondary network by mssng an actual access opportunty n cases of false alarm). To nvestgate the sensng accuracy, here we smply assume that the sensors are unformly dstrbuted n the network coverage area. Lemma 1. In a montorng network wth Z ZAs/cell ndexed by z = 1,..., Z and S cooperatve SBS ndexed by s = 1,..., S, the probablty of accurate sensng for equprobable hypotheses channels 30], {1,..., N}, at the SBS s: P SBS) cs, { Z { ] Z S = 1 1 P d ε, T s, )} + P f ε, T s, )},. Proof. See Appendx A. Remark 1. The probabltes for hypotheses H 0, and H 1 are denoted by P H0, and P H1, respectvely. Equprobable channel assumpton ndcates that half of the channels are busy at any observaton wndow. However, the analytcal and smulaton results n the next sectons n ths paper are equally credble for other scenaros, for nstance, unutlzed,.e., P H0 << 0.5, underutlzed,.e., P H0 > 0.5, and crowded,.e., P H0 > 0.9 channels. Ths asssts obtanng analytcal solutons n terms of detecton threshold, and normalzed throughput. Lemma 1 ndcates that P cs, depends on probabltes of mss detecton and false alarm, as well as the number of ZAs and sensors n each zone. Ths provdes two new degrees of freedom whch could be exploted to mprove the sensng 3) accuracy. In practcal systems, the summaton of the two terms nsde the bracket n 3) consttutes a small value for a gven sensng devce. Ths s due to the fact that mss detecton and false alarm probabltes cannot ndependently adopt arbtrary values as they follow the correspondng sensors ROC. Note that n 3), P cs, 0, 1] whch can be obtaned by varyng the operatng ponts n ROC curve wthn the lmts,.e., P m ε, T s, ) 0.5, and P f ε, T s, ) 0.5. These cases are also descrbed n detal n 5c), 5d) n problem P 1. By applyng these constrants, t s assured that the probablty of correctly sensng the channel stays wthn the feasble range and therefore value of P cs, stays wthn 0 and 1. Ths also ensures the protecton from system falure due to the bad detectors. Therefore, the worst detecton cases, e.g., P f ε, T s, ) 0.5 and P m ε, T s, ) 0.5, are excluded n the proposed method. As a result, f a channel s badly detected, the resources wll not be allocated by the SBS to any user to protect the prmary users from probable nterference. B. Optmal Sensng for Maxmum Spectral Effcency Here, we formulate the system functon as an optmzaton problem wth the objectve of maxmzng the spectral effcency. In addton, R 00, and R 01 are the SUs throughput condtoned over hypotheses H 0, and H 1, respectvely. Therefore, based on condtonal probablty of correctly sensng the channel and 3], 4], the achevable throughput s obtaned as T ) Ts, T Pcs, H0 P H0 R 00 + P cs, H1 P H1 R 01. Assumng equprobable hypotheses 30], the secondary system throughput for channel s reduced to Rε, T s, ) = T T s, T Pcs, P H0 R 00 + P cs, P H1 R 01 ),. 4) Here, P cs, represents the measure of spectral effcency of the secondary system. A hgher sensng accuracy contrbutes towards a hgher spectral effcency thus mproves system throughput. For a specal case of Z = S = 1, usng 3) and 4) the total secondary system throughput, Rε, T s, ), s T T s, T 1 pf )P H0 R p f )P H1 R 01 K L ), where, K L = 1 p d )P H0 R p d )P H1 R 01 ) s the throughput loss due to the mss detecton P m > 0). Note that f P m 0, then K L 0. For gven values of Z and S, the optmal sensng parameters are obtaned va the followng optmzaton problem. Problem P 1: where max Rε, T s,), 5a) ε,t s, I p ε, T s, ) = s.t. I pε, T s,) I th, 5b) P mε, T s,) P m, P f ε, T s,) P f,, 5c) 5d) P m, ε, T s, )P t,s g 6)

7 7 s the aggregated nterference receved at the PUs. For channel, 5b) ensures that the receved nterference remans below the gven threshold level, I th. Ths wll protect the PUs aganst the potental sensng errors 31]. In addton, the mnmum detecton probablty of spectrum holes s enforced by 5c) and 5d). In P 1, P t,s s the SU s maxmum transmt power, g s the channel gan between the secondary transmtter and the prmary recever, and P m, and P f are the maxmum mss detecton, and false alarm probabltes, respectvely. These parameters are provded by the related communcaton standards, see, e.g., 9]. In P 1, P H0 R 00 + P H1 R 01 s constant durng a tme frame duraton, T. Moreover, n the proposed method, T s, = T q T, therefore T Ts, T s almost constant See Fg. 3) whch s referred to as T T x throughout ths paper. Consequently, the only optmzaton parameter n P 1 s P cs,, whch s a functon of ε, and T s,. Based on the above, P 1 s then reduced to the followng optmzaton problem: Problem P : { 1 1 P d ε, T s,) max ε,t s, s.t. P mε, T s,)p t,s g I th, P mε, T s,) P m, P f ε, T s,) P f,. } Z + { P f ε, T s,)} Z ] S, 7a) 7b) 7c) 7d) To obtan the solutons of P, usng the Lemmas n Appendces B-D, 7d) s approxmated by σ w ε 1 + γ )σ w. To further smplfy P we use the followng Lemma n 3]. Lemma. 3] For σw ε 1+γ )σw, P m ε, T s, ) and P f ε, T s, ) are decreasng convex functons of T s,. It s also shown n 3] that, gven the stated condtons of Lemma n Appendx B, P mε,t s,) T s, < 0, and P f ε,t s,) T s, > 0. It s further straghtforward to prove the followng Lemma based on Lemmas 4, 5, and 6 n Appendces B-D. Lemma 3. For a gven T s,, f P m ε, T s, ) 0.5, and P f ε, T s, ) 0.5, then P m ε, T s, ), and P f ε, T s, ) are both convex functons of ε. Based on Lemmas, 3, and those n Appendces B-D, we then conclude that both P m ε, T s, ) and P f ε, T s, ) are convex functons of ε, where sensng duraton s fxed at T s, under the condtons to protect the PUs. Here, the condtons to maxmze the throughput are: P d ε, T s, ) 0.5, and P m ε, T s, ) 0.5, whch are the requrements of IEEE 80. standards 9]. Based on the above, P s approxmated as the followng. Problem P 3: max ε s.t. 1 { } Z { ] Z S 1 P d ε ) + P f ε )}, 8a) P m ε, T s, )P t,s g I th, σ w ε 1 + γ )σ w,. 8b) 8c) In P 3, 8c) s convex under the stated condtons n Lemma 4. The nterference constrant at the PU, 8b), s due to the mperfect channel sensng, where g s the gan of channel. Here, P t,s > 0 s the transmsson power of the SU and P m, ε, T s, ) s a convex functon of ε under the condton gven n Lemma 4. Snce non-negatve sum of convex functons s a convex functon n the same doman, the nterference constrant s also a convex functon of ε. To show the convexty of P 3, we further need to nvestgate 8a). Note that throughout ths paper P mf) ε, T s, ) and P mf) ε ) are nterchangeably used for brevty. Corollary 1. In the zone-based cooperatve spectrum sensng, for any combnaton of S and Z, the throughput, 8a), s a concave functon of ε. Proof. See Appendx E. Based on the above, P 3 s a convex optmzaton problem. C. Optmal Detecton Threshold Here, we utlze Lagrangan method to fnd the solutons of P 3. We then apply Lagrange dualty property as n 33]. The Lagrangan functon correspondng to P 3 s Lε, λ 1, λ, λ 3 ) = 1 =1 { } Z { } ] Z S 1 P d ε ) + P f ε ) N N + λ 1 I th P m P t,s g ) + λ ε max ε ) + =1 N λ 3 ε ε mn ), 9) =1 where, ε max = 1 + γ )σ w, ε mn = σ w, and λ 1, λ, λ 3 are non-negatve Lagrangan dual varables correspondng to the constrants. Here, λ 1 s scalar because channel accessed exclusvely by only one PU. The nterference constrant protects the PUs on channel = 1,..., N n case of mss detecton. Smlarly, λ and λ 3 are the Lagrangan multplers assocated wth detecton threshold constrants. Throughput ths paper, vectors are presented usng bold fonts. The correspondng dualty gap s expected to be very close to zero as P 3 s concave and the Slater s condton 33] s satsfed. The KKT condtons for any set of ε, λ 1, λ, λ 3 are 33]: Lε, λ 1, λ, λ 3 ) = 0, Iε ) I th, λ 1 > 0, λ 0, λ 3 0, N λ 1I th P m, P tx g ) = 0, =1 N λ ε max ε ) = 0, =1 10a) 10b) 10c) 10d) 10e) N λ 3 ε ε mn ) = 0,. 10f) =1

8 8 Here, we follow a smlar approach as n 31] to obtan the solutons. If the condton σw < ε < 1 + γ )σw holds, the constrant 10b) becomes lnear,.e., Iε ) = I th. Therefore, for any λ 1 0, λ 1I th Iε )) = 0. In the consdered mult-channel scenaro, we now assume that the channels are dentcally dstrbuted and sensed smlarly, thus the results obtaned are vald for all channels, {1,..., N}. Therefore, we hereafter drop the channel ndex,, for brevty. From the Lagrangan statonary pont, 10a), we get Lε, λ 1, λ, λ 3 ) = 0. 11) If both Z and S vary, then t s not easy to obtan a closed form soluton for P 3. Instead, we solve ths problem separately for dfferent numbers of Z and S smlar to the approach used n provng Corollary 1. Here, ε S s obtaned whch s defned as sensng detecton threshold for all channels, where S s constant. Smlarly, ε Z s then obtaned whch s defned as sensng detecton threshold for all channels, where Z s constant. We then show that the optmal detecton threshold s a lnear combnaton of ε S and ε Z. The optmal detecton threshold for varous desgn scenaro has been summarzed n Table I. In the followng, we nvestgate each scenaro n detal. 1) Scenaro 1 Z = 1, S = 1): In ths case, 11) s rewrtten as L 1 ε, λ 1) = ] T T x 1 P m ε) + P f ε)) ) + λ 1 I th P m ε)p t,s g ) = 0, whch results n the followng equaton: T T x P d ε) + λ 1 P t,s P d ε) 1) P f ε) = T T x. 13) To fnd the soluton, we utlze P dε) obtaned n Lemma 5, and Lemma 6, respectvely. For a gven T s, straghtforward mathematcal dervatons result n a closed form expresson for the optmal SNR threshold for all channels ε SZ) = σ w γ c + ) ] T T x γ f s T s T T x + λ 1 P t,s g, 14) and P f ε) where γ c = γ + 1) 1. ) Scenaro Z =, S = 1): In ths case, smlar to 1) amd 13) and straght mathematcal dervaton, we get the optmum SNR threshold for any channel as ε S = σ w γ γ c + f s T s ) ] P f T T x. 15) P m T T x + λ 1 P t,s g Here, ε S s the optmum SNR threshold vald for the frame duraton T. 3) Scenaro 3 Z = 3, S = 1): Smlar to the above, here we get ) ] ε S = σ w γ c + 3P f T T x γ f s T s 3P. 16) mt T x + λ 1 P t,s g Fnally based on the results above, and followng the same lne of argument as n Corollary 1, for a fxed S and any number of ZAs,.e., z = 1,..., Z, we can generalze the optmal SNR threshold as shown n 17). 4) Scenaro 4 Z = 1, S = ): In ths case, at a partcular tme and locaton, a SBS may receve sensng nformaton from more than one ZAs. In ths scenaro, smlar to the case where Z s varable, we use Lagrangan statonary pont, 10a). For S =, t s smple to show that ε Z = σ w γ γ + 1) 1 + f s T s P m + P f )T T x P m + P f )T T x + λ 1 P t,s g ) ]. 19) 5) Scenaro 5 Z = 1, S = 3): Smlar to the prevous cases, the optmal threshold can be obtaned for dfferent values of S, for nstance S = 3. Fnally, followng the same steps as n obtanng 17), we can generalze the optmal soluton for any number of SBSs as shown n 18). Note that n 14)-19), the mss detecton and false alarm maxmum tolerable values are selected such that P m < 0.5, and P f < 0.5. The detals are dscussed n Secton IV. D. Unfed Detecton Threshold As t s seen above, the optmal values of detecton thresholds, ε S and ε Z, both depend on Z and S. In addton, due to the random nature of wreless channel the exact number of sensng devces that ther sensng nformaton receved at ZA cannot be consdered fxed. For nstance, some sensng devces may fal to communcate wth the ZAs and apparently wth SBS. In some cases, the communcaton channel between sensng devces may also undergo deep fadng n whch the sensng network scenaro s changed. Therefore, a unfed detecton mode s necessary so that the proposed technque works for any possble scenaro and varous combnatons of Z and S. Here we propose a lnear combnaton of ε S and ε Z as follows: ε = αε S + 1 α)ε Z, 0) where α s related to Z and S: f Z < S then α s 0 < α < 0.5 to emphasze on the contrbuton of ε Z comparng to ε S n 0). Ths s smply because ε Z s the detecton threshold for cases, where Z < S. In contrast, where Z > S, system sets 0.5 < α < 1, so ε S contrbutes more than ε Z n ε. However, n cases where Z and S are equal, system sets α = 0.5 and apparently ε S and ε Z contrbute equally n 0). In the smulatons presented n ths paper, α s selected wthn the ranges mentoned above based on the denstes of Z and S, for nstance, when Z S, α s selected on the lower range of 0.5 < α < 1. For the cases where S = 0, and Z = 0, the system sets α = 1, and α = 0, respectvely. In cases where due to the random tme varyng nature of wreless communcaton, such as channel fadng, nterference, hdden termnal problem, etc., ether or both of Z and S are equal to zero, then the optmal detecton threshold s undefned because ε S and ε Z are. As a matter of fact, ths stuaton does not normally occur n the proposed model of zone-based

9 9 Scenaro 1 Z = 1, S = 1) Scenaro Z =, S = 1) Scenaro 3 Z = 3, S = 1) Scenaro 4 Z = 1, S = ) Scenaro 5 Z = 1, S = 3) ε S = σ w γ ε Z = σ w γ TABLE I THE OPTIMAL SNR THRESHOLD FOR DIFFERENT SCENARIOS ε X = σ w γ ε X = σ w γ ε X = σ w γ ε X = σ w γ ε X = σ w γ γ + 1) 1 + f s T s γ + 1) 1 + f s T s γ c + f st s ) T T x T T x +λ 1 P t,s g ) ] γ c + P f T T x f st s P mt T x +λ 1 P t,s g ) ] γ c + 3P f T T x f st s 3P m T T x+λ 1 P t,s g γ + 1) 1 + f st s γ + 1) 1 + f st s ) ] P m+p f )T T x P m+p f )T T x +λ 1 P t,s g ) ] 3P m+p f ) T T x 3P m+p f ) T T x +λ 1 P t,s g ] ) ] ZP Z 1 f T T x ZP Z 1. 17) m T T x + λ 1 P t,s g SP m + P f ) S 1 ) ] T T x. 18) SP m + P f ) S 1 T T x + λ 1 P t,s g cooperatve spectrum sensng but should be consdered as a specal case to avod sngulartes. Here we propose a specfc treatment to tackle ths ssue as descrbed n the followng. Accordng to 17) and 18), S = 0, and Z = 0 ndcate ε Z, and ε S, respectvely. At the same tme, the sensng system controls α to avod such a condton. Therefore, for S 0, sensng system sets α 1. Therefore, lm S 0 ε ZS).1 α) 0, 1) whch ndcates that optmal detecton threshold solely depends on the ε S n 0). Smlarly, f Z 0, the sensng system selects α 0, thus, lm Z 0 ε SZ).α) 0, ).e., the optmal detecton threshold solely depends on the ε S n 0). Usng ths method, we are able to obtan a unfed verson of optmal spectrum sensng threshold. In the next secton we provde a step by step algorthm for obtanng an estmaton for ε based on the above analyss. In obtanng the optmal detecton threshold whch maxmzes the system throughput, we adopt the bsecton method. E. An Algorthm for Estmatng ε The proposed method to estmate ε s presented n Algorthm 1, where γ, P d ε), and P f ε) are sub-channel dependent parameters whch are dfferent for each sub-channel. Here, the channel ndependent parameters are adjusted to obtan the optmal channel detecton threshold such that the system throughput s maxmzed whle the constrants are also satsfed by the spectrum sharng system. Algorthm 1 : ε Estmaton for Zone-Based Cooperatve Spectrum Sensng Input: T s,,p f T s, ), P d T s, ), f s, γ, ε 1,mn, ε 1,max, δ, I th Output: ε, λ, 1: fnd the value of α from control packets of SBS and ZAs : calculate λ 1,mn, and λ 1,max from ε 1,mn, and ε 1,max, respectvely usng 0) 3: for = 1,..., N do 4: whle I th I c < δ do 5: fnd the effectve λ 1 usng bsecton method: λ 1 = λ1,mn+λ1,max 6: calculate optmal SNR threshold, ε, from 17), 18), 0) 7: obtan P m ε ) and nterference at the PUs,.e., I c = P t,s g P m ε ) 8: f I c > I th then λ 1 λ 1,mn 9: else λ 1 λ 1,max 10: end f 11: end whle 1: end for 13: obtan ε and λ 1 and throughput gan Rε ), for all channels In the proposed method, T s T s a gven system parameter thus the optmzaton varable for each channel s the detecton threshold, ε. We also note that 0) s a monotoncally decreasng functon of λ 1,.e., for every λ a 1 < λ b 1, we get ελ a 1) > ελ b 1). Therefore, bsecton method s adopted to fnd the detecton threshold by solvng the P 3 subject to the constrants n 8b) and 8c).

10 10 V. SIMULATION RESULTS AND ANALYSIS In ths secton, we evaluate the performance of the proposed zone-based cooperatve spectrum sensng. We further compare ts performance aganst the benchmark systems ncludng the case where there s no cooperaton among the clusters/sbs, and the case where the decsons are dffused usng OR/AND rule. We then compare the correspondng resource allocaton framework n terms of latency, detecton probablty, communcaton actvty of prmary systems etc. We consder a cogntve rado system, where N = 16 and T = 100 ms. The mean sgnalng duraton for each SU, ET s ], s mantaned at 3 ms. The samplng rate s f s = 0 ksample/second and therefore the samplng overhead s f s T s = 60. We also set σw = 1. We further assume that P H0 = 0.5. The traffc on the sub-channels s randomly generated and SUs always have data packets ready to be transmtted unless otherwse stated. The channel between prmary and secondary system s modeled as Raylegh fadng wth scale parameter of 1. The prmary channel protecton and spectrum utlzaton level are defned accordng to the IEEE 80. standard 9] as P d 0.9, and P f 0.1, respectvely. A. Comparatve Study of Sensng Accuracy The proposed zone-based cooperatve spectrum sensng, as defned n 3), s valdated by consderng the approprate value of detecton probablty whch fulflls the requrement of constrant 5c) as well as WRAN 80. standard. Correspondngly, the false alarm probablty s obtaned from the correspondng ROC curve. Therefore, the nstantaneous P d and P f are chosen for a gven combnaton of S and Z to test the spectrum sensng accuracy of the proposed method. For comparson, we consder Z = 1 as the conventonal cooperatve spectrum sensng based on Lemma 1 at the SBSs and therefore there s no channel reusablty. The case of hgher Z represents the specal scenaro that the multple antennas are transmttng at the BSs and the cell s dvded nto sectors. In ths case, each sector can be consdered as a sngle antenna cell and therefore number of ZAs and SBSs are ncreased. We consder the case Z = 1 as a benchmarkng scenaro. In Fg. 4, the normalzed system throughput, whch s drectly related to the system spectral effcency, s plotted versus the number of zone aggregators for dfferent number of SBSs. Here, t s seen for the case Z = 1 that the normalzed throughput s 0.6 whereas n a zone-based cooperatve spectrum sensng method as ndcated by Z, t s sgnfcantly mproved from 0.9 to 0.96 when ZAs are set to and 3, respectvely. Ths s due to the fact that the proposed method has better channel sensng accuracy than any conventonal cooperatve channel sensng. The hgher sensng accuracy ensures that no access to that partcular channel s granted by the SBS to protect the PUs. The result also provdes nsght on the rate of spectral effcency ncreased by ncreasng S as a result of the proposed mcro-spectrum-reuse technque. Fg. 4 confrms the ncrease of normalzed throughout from 0.9 to 0.98 when cooperatve SBSs are ncreased from to 3. Fg. 5 compares the channel sensng accuracy of the proposed method aganst the non-cooperatve as well as channel Normalzed system throughput Cooperatve SBS= Cooperatve SBS=3 Cooperatve SBS=4 Cooperatve SBS= Number of ZAs wthn the transmsson range of SBS. Fg. 4. Normalzed throughput vs. dfferent values of Z and S. Probabltes of correct sensng and detecton Fg Correct sensngp cs)-proposed Detecton-OR combnng Detecton-sngle sensor Average SNR db) Probablty of correctly detectng the channel vs. average receved SNR when false alarm rate s fxed. assgnment wth cooperatve sensng 34] n whch the OR fuson methods s mplemented for varous receved SNR. The performance gan n terms of the sensng accuracy s acheved wth the expense of nstallng new sensng nfrastructure. In addton to sensng accuracy, t also ncreases the transmsson duraton for the SUs whch contrbutes to acheve hgher throughput wth less system complexty. In ths partcular case, the smulaton s performed for AWGN channel usng QPSK modulaton wth samplng overhead T s f s = 100 and P f s no more than 0.1. The sensng network s set by Z = 3 and S = for the proposed method and 3 cooperatve sensors for OR fuson method. It can be observed that the correctly sensng probablty of the proposed method s mproved 0.99) n comparson to non-cooperaton 0.6) and when hard decsons are fused wth OR method 0.85) at 4 db receved SNR.

11 11 Spectrum detecton threshold dbm) Pm Constrant=0.05 Pm Constrant=0.10 Pm Constrant=0.15 Pm Constrant=0.0 Pm Constrant= Sensng duraton msec) Mss detecton probablty False alarm probablty Ts = 3 msec Ts = 6 msec Ts = 9 msec Prmary channel ndex Fg. 6. Optmal spectrum detecton threshold vs. sensng duraton latency) for varous mss detecton constrants. Fg. 7. Probablty of mss detecton and false alarm of the frst eght channels for dfferent values of T s. B. Tradeoff Between Sensng Latency and Detecton Threshold In Fg. 6, the optmal spectrum detecton threshold, ε, s plotted versus sensng duraton at the spectrum sensors for dfferent values of maxmum acceptable mss detecton probablty, where one ZA aggregates channel nformaton from four channel sensors. As t s seen, for long sensng duraton n the secondary system, obtanng the optmal detecton threshold deems rrelevant and not related to the maxmum acceptable mss detecton probablty. However n the proposed method, the sensng duraton s represented by the short sgnalng duraton,.e., less than ms n Fg. 6, the optmal detecton threshold must be obtaned to mprove the system throughput. Therefore, the length of transmsson duraton does not need to be compromsed whlst latency s reduced. The obvous tradeoff s relaxng the sensng duraton T s > ms) n whch the transmsson duraton s shorter, and hgher latency s then beng assocated wth the spectrum sensng. In contrast, the sensng duraton, thus the latency, can be reduced T s < ms), where a hgher complexty s expected as the approprate sensng threshold must be evaluated through the proposed algorthm. Note that n the proposed method the latency assocated wth the sensng s very small and the cost s lmted to the correspondng computatonal complexty requred for evaluatng the optmal detecton threshold. C. Performance Evaluaton wth Optmal Detecton Here, we examne the performance of the proposed cooperatve spectrum sensng method to maxmze the system throughput n whch the aggregate nterference to the PU s consdered to be less than the threshold. In the smulaton settngs, the condtons n Lemma and Lemmas n Appendces B-D are held. Ths means that for the smulated system, P 3 s convex thus the optmal solutons are 17) and 18). In the proposed method, the sensng duraton, T s, s sgnfcantly smaller compared to the frame duraton, T, therefore t s ndependent of the optmzaton procedure. However, n Average system throughput per channel Operatng ZAs =1 Operatng ZAs =3 Operatng ZAs = Number of SBSs transmttng channel nformaton S) Fg. 8. The average throughput per channel vs. number of SBS. the conventonal spectrum sharng methods, where SUs sense and utlze the deal channels, optmal choce of T s s crucal. Under the scenaro mentoned above, P m ε ), and P f ε ) for an optmal value of detecton threshold have been obtaned as shown n Fg. 7. Whle obtanng P m ε ) for an optmal detecton threshold, P f ε ) s kept fxed and vce versa. As expected, the longer the sgnalng duraton, the lower wll be the mss detecton and false alarm probabltes. In addton, lowerng T s, from 9 ms to 6 ms sgnfcantly reduces P m ε ) and P f ε ) for all channels. On the other hand, reducton of T s from 6 ms to 3 ms does not reduce sensng accuracy n the same proporton. Ths suggests a way to adjust the sgnalng duraton based on the requred spectrum detecton accuracy. In Fg. 8, the average throughput per channel s plotted versus the number of SBSs whch transmt the cooperatve control packet for the channel detecton. We observe that as the number of SBSs are optmal for a gven cluster heads, the throughput s maxmzed. However, lower number of SBS wll receve less nformaton about channel avalablty and, as a result, the throughput per channel decreases. In addton, when