Cooperative Spectrum Sensing in Cognitive Radio Networks with Kernel Least Mean Square

Transcription

1 Cooperatve Spectrum Sensng n Cogntve Rado Networks wth Kernel Least Mean Square Xguang Xu, Hua Qu, Jhong Zhao, Badong Chen Abstract Spectrum sensng s a key technology n cogntve rado networks to detect the unused spectrum. Cooperatve spectrum sensng scheme s wdely employed due to ts quck and accurate performance. In ths paper, a new cooperatve spectrum sensng by usng Kernel Least Mean Square (KLMS) algorthm s proposed for the case where each secondary user (SU) makes a bnary decson based on ts local spectrum sensng usng energy detecton, and the local decsons are sent to a fuson center (FC), where the fnal decson s made on the spectrum occupancy status. In our approach, the KLMS s utlzed to enhance the relablty of the fnal decson. Snce KLMS performs well n estmatng a complex nonlnear mappng n an onlne manner, the proposed method can track the changng envronments and enhance the relablty of decson FC. he desrable performance of the new fuson scheme s confrmed by Monte-Carlo smulaton results. Keywords cooperatve spectrum sensng; cogntve rado; KLMS; energy detecton. I. INRODUCION HE ever-ncreasng demands of ubqutous wreless applcatons and devces gve rse to sgnfcant use of rado spectrum. he spectrum congeston ow becomng a serous problem due to rapd growth n the applcaton of wreless servces. hs problem arses due to the neffcent fxed frequency allocaton of the spectrum. Federal communcatons commsson (FCC) observed that only % of the allocated spectrum s fully utlzed for varous applcatons. hs motvates the regulatory board to focus on cogntve rado whch s based on dynamc spectrum access prncple []. Cogntve rado whch has been suggested as a novel way to enhance effcency of avalable spectrum [-5], allows opportunstc access to unoccuped lcensed bands by unlcensed (secondary) users. Wth the rapd change the wreless envronment t has the capablty to select the unused spectrum, and by adaptng the parameters t coordnates access to the channel wth the other users' channels and vacates that channel wth the arrval of the lcensed user. So, spectrum sensng plays a very crtcal task n cogntve rado hs work was supported by the Natonal Natural Scence Foundaton of Chna (no. 6379,no. 6375), and the Natonal Hgh echnology Research and Development Program 863 (no. 4AAA76). All authors are wth the School of Electronc and Informaton Engneerng, X an Jaotong Unversty, X an, Chna (correspondng author to provde phone:89493; e-mal: xuxguang@stu.xtu.edu.cn, qh@mal.xtu.e du.cn, zhaohong@mal.xtu.edu. cn, chenbd@mal.xtu.edu.cn). networks to protect the prmary user (PU) from nterferences of the secondary user (SU) [6]. Spectrum sensng schemes can be classfed tradtonally n three categores: matched flter detecton, cyclostatonary feature detecton, and energy detecton. Although matched flter detecton needs less sensng tme and known as an optmal way for sgnal detecton, t requres a pror knowledge of the characterstcs of the prmary user (PU) sgnal [7]. On the other hand, cyclostatonary feature detecton s computatonally complex and needs to know the cyclc frequences of the prmary sgnals, whch may not be realstc for many applcatons. Compared wth the prevous two schemes, the energy detecton n general has low computatonal and mplementaton complexty and more mportantly, t doeot requre any pror knowledge of the PU sgnals. Hence t s wdely used n cogntve rado networks [8]. However, when the detectng channels experence severe path loss or shadowng effect, the sensng performance of the SU may be degraded serously and the hdden termnal problem may occur [9]. In order to mprove the sensng performance, cooperatve spectrum sensng was proposed [6,]. In a cooperatve spectrum sensng scheme, every SU carres out local energy detecton ndependently and transmts the decson results to the fuson center (FC), then the fnal decson on the presence or absence of the PU s made based on combned nformaton from dfferent cogntve rado users. here are three classcal fuson strateges for decson fuson at the FC: OR rule, AND rule and Maorty rule whch can be generalzed as the k-out-of-n rule. In [-3], the performance of the energy detecton vestgated usng these fuson schemes. Besdes, a cooperatve spectrum sensng method based on the well-known least mean square (LMS) algorthm was proposed n [4]. Compared wth the prevous three fuson schemes, the LMS algorthm can enhance the detecton capablty effectvely snce t s an adaptve learnng based algorthm. In ths work, a new cooperatve spectrum sensng method s proposed, whch s based on the kernel least mean square (KLMS) algorthm [5,6]. he KLMS s a nonlnear extenson of LMS, whch belongs to the famly of kernel adaptve flterng (KAF) algorthms [7,8]. he KAF algorthms are developed by mplementng the well-establshed lnear adaptve flterng algorthm a reproducng kernel Hlbert space (RKHS) [5-]. Snce KLMS s an onlne unversal learnng machne for arbtrary nonlnear mappng, the proposed method can track the

2 changng envronments and enhance the relablty of decsons sgnfcantly. he rest of the paper s organzed as follows. Secton II gves prelmnares of the channel model, energy detector and KLMS algorthm. he proposed fuson scheme based on KLMS s then presented n Secton III. In Secton IV, the performance of the new method s demonstrated, followed by the concludng remark Secton V. II. PRELIMINARIES Obvously, spectrum sensng s a crtcal functonalty of cogntve rado networks; t allows SU to detect spectral holes (the unused spectrums whch are belong to the prmary system) and to opportunstcally use under-utlzed frequency bands wthout causng harmful nterference to prmary systems. In general, the spectrum sensng problem can be formulated as follows. o detect a weak prmary sgnal, t could pose a bnary hypothess testng problem as follows: H : y( t) n( t) H : y( t) hx( t) n( t) where H represents the absence of prmary sgnal, the receved sgnal yt () contans only addtve whte Gaussan nose (AWGN), and H represents the presence of prmary sgnal, yt () ncludes of a prmary sgnal xt () and nose nt (), h ndcates the wreless channel gan from the PU to the recever SU. Note that, the wreless channel experences severe path loss or shadowng effect generally. A. Local spectrum sensng We start by consderng the problem of sgnal cogntve user detecton. Some known detecton result [,] for ths case as they are central to the dscussons to follow are revewed. We shall use the same energy detecton model when we analyze the cooperatve spectrum sensng usng KLMS algorthm n the next secton. As energy detector has the lowest computatonal and mplementaton complextes, each PU apples ths method to do the local spectrum sensng. he mechansm of energy detector s to square the recevng sgnal and ntegrate t over tme duraton to create the test statstc Y whch has the followng form []: Y ~ : H u u ( ) : H Y has a central ch-square dstrbuton u wth u degrees of freedom whch u s the tme-bandwdth product ( u W ), when there o sgnal from the transmtter (.e. H ). Whle, when the recever receves both sgnal and nose (.e. H ), Y has a non-central ch-square dstrbuton ( ) u wth a non-centralty parameter and the same degrees of freedom, where s the receved nstantaneous () () SNR of the target sgnal. he probabltes of false alarm and detecton can be evaluated by Pr( Y H) and Pr( Y H), respectvely, as follows: Pf Q( u, ) (3) P (, ) d Qu (4) where s a predefned threshold value. In general, we choose a proper P, and then fgure out. Q(, ) s the f regularzed Gamma functon and Qu ( a, b ) s the generalzed Marcum Q-functon defned by: x a Q ( a, b u u ) x e I u ( ax ) dx u a b (5) I() s the modfed Bessels functon of the frst knd [3]. B. KLMS algorthm We utlze the KLMS [3] algorthm to the cooperatve spectrum sensng after the local spectrum sensng. KLMS s an adaptve kernel-based algorthm developed n RKHS. he great attracton of kernel-based flter RKHS s the usage of the lnear structure of ths space to mplement well-establshed lnear adaptve algorthms and to obtan nonlnear flter n the nput space that leads to unversal approxmaton capablty wthout the problem of local mnma. he kernel-nduced mappng s employed to transform the nput s nto a hgh-dmensonal feature space as φ( s ). As smlar to LMS, KLMS denote ω φ( s ) as the system output. So, fndng ω through stochastc gradent descent may prove as an effectve way of nonlnear flterng as LMS does for lnear problems. Usng the LMS algorthm on the new example sequence { φ( s ), d () } yelds: ω() e( ) d( ) ω( ) φ( s ) ω( ) ω( ) e( ) φ( s ) where ω () denotes the estmate (at teraton ) of the weght vector n hgh-dmensonal feature space, d () denotes the desred output, he repeated applcaton of the weght-update equaton (6) through teratons yelds: ω( ) ω( ) e( ) φ( s ) e( ) φ( s ) he output of the system to a new nput s * can be solely expressed n terms of nner products between transformed nputs: (6) (7)

3 ω( ) φ( s *) e( ) φ( s ) φ( s *) e( ) φ( s ) φ( s * ) By the kernel trck, the flter output n the nput space by kernel evaluatons s: * * (8) ω( ) φ( s ) e( ) ( s, s ) (9) So the followng sequental learnng rule for the algorthm s: y( s ) ω( ) φ( s ) e ( ) ( s, s ) where ( s, s ) s the Gaussan kernel: () s s ( s, s) exp( ) () where s the kernel sze whch s an mportant parameter to be chosen properly. s s s a a s a Fg.. Network topology of KLMS at teraton. y () d () Algorthm : Kernel least-mean-square algorthm ntalzaton: choose step-sze parameter and kernel sze e() d(), c() s computaton whle s, d ( ) avalable do % compute the output y( ) e( ) ( s, s ) % compute the error e( ) d( ) y( ) % store the new center c( ) c( ), s end whle e () It s KLMS whch s the LMS n RKHS, and flterng s done by kernel evaluaton. KLMS allocates a new kernel unt for the new tranng data wth nput s as the center and e () as the coeffcent. he coeffcents and the centers are stored n memory durng tranng. he algorthm s summarzed n algorthm and llustrated n Fgure. a s the coeffcent vector at teraton, and c () s the correspondng set of centers. KLMS obtans adaptve nonlnear regresson wth the sample by sample adapton lnear algorthm n RKHS wthout convergng to local mnma, whch enable better trackng of system perturbatons. sent to the correspondng author only. III. COOPERAIVE SPECRUM SENSING WIH KLMS As can be seen the proposed cooperatve spectrum sensng scheme usng KLMS n Fg., frst, each SU makes a bnary decson ( denotes H or represents H ) based on ts local spectrum sensng usng energy detecton. hen, the decson s sent to the FC, where the fnal decson s made on the spectrum occupancy status ( H or H ). he fuson center mechansm s based on the KLMS algorthm n whch each s s (), s (), s ( N) are nput each tme slots n n n n appled to make a fnal relable decson, yn ( ). sn () denotes the local decson of CR user at tme slot n.he proposed fuson algorthm s llustrated n Algorthm. Snce the relabltes of the local decsons are not equvalent to each other due to fadng and shadowng effects, SUs decsons are mapped to a set of {, }, as descrbed n Algorthm. Note that, the PU status (the desred output, d ) s supposed to be known after each acknowledgement tme slot [4]. Algorthm : Proposed fuson algorthm. nput: Number of SUs (N) and ther decsons (SU matrx) ntalze: Map the decsons (r = SU ): and,choose step-sze parameter and kernel sze. Set the ntal e() d() whle s, d ( ) avalable do y( ) e( ) ( s, s ) e( ) d( ) y( ) f y ( ) then return H else return H end f end whle IV. SIMULAIONS In ths secton, usng numercal analyses va Matlab, we evaluate the proposed kernel learnng algorthm as mentoned above and compare the performance of the proposed algorthm wth three other algorthms: the classcal scheme OR rule and AND rule, the LMS algorthm whch s dscussed

4 Mean Square Error Probablty of Detecton n Prmary User h h h N n n N Sensng channels ED ED Y Decson devce Y Y ED N Decson devce Decson devce Secondary user () () s ( ) n N s s a a s an n en ( ) Fuson center usng KLMS algorthm yn ( ) dn ( ) Hor H Fnal decson Fg.. he structure of the proposed cooperatve spectrum sensng scheme. n [4]. Let sn () be the local decson of CR user at tme slot n and yn ( ) be the cooperatve decson made by the FC at tme slot n, n () yn ( ),, and a and a ndcate a PU s presence ( H ) and absence ( H ), respectvely. he AND rule refers to the FC determnes yn ( ) f s ( )=,. Smlarly, the OR rule refers to n s, yn ( ) f sn ( )=, for any.for the evaluatons, a cogntve rado network of N SU nodes operatng on a sngle channel s consdered, where each node tres to estmate the spectrum occupancy on the channel usng the local spectrum sensng. hen, the decson s sent to the FC, where the fnal decson s made on the spectrum occupancy status ( H or H ). algorthm and KLMS algorthm are.5 and.56, respectvely, and the kernel sze s. In addton, the detecton methods of all SUs are assumed to be energy detecton consderng the probabltes of false alarm Pf.. As expected, the proposed fuson algorthm outperforms the LMS algorthm. he proposed algorthm converges faster and converges to a smaller value of MSE than the LMS algorthm, due to tonlnear nature. hs s good for cooperaton to mprove the spectrum sensng relablty. It s mportant to note that smaller step-sze, result a more accurate result at a cost of convergence tme LMS KLMS Iteraton (sample) Fg. 3. Learnng curves of KLMS and LMS. Fg. 3 llustrates the learnng curves for KLMS algorthm and LMS algorthm whch s dscussed n [] n the FC. In ths scenaro, 5 users are consdered n both methods, and each user s SNR has a normal dstrbuton wth a mean of -5dB and a standard devaton of. he learnng step-szes for LMS SNR AND OR LMS KLMS Fg. 4. Probablty of detecton for KLMS and three other decson fuson methods: AND, OR, and LMS. Detecton performance of the proposed fuson scheme compared to decson fuson scheme s llustrated n Fg. 4. We evaluate the proposed kernel learnng algorthm and compare the performance of the proposed algorthm wth three other algorthms: the classcal scheme OR rule and AND rule, the LMS algorthm. he CR network s assumed to have

5 Probablty of Detecton fve SUs, and each user s SNR has a normal dstrbuton wth a mean of -5dB and a standard devaton of. he performance curves reveal that the proposed KLMS fuson scheme outperforms all of the other schemes. hs observaton ndcates the effectveness of the proposed scheme to enhance the detecton capablty SNR user number=3 user number=5 user number=7 user number=9 user number= Fg. 5. Probablty of Detecton for dfferent users SNR and user numbers. Fg. 5 llustrates the performance of KLMS algorthm when the number of cooperatve users, N, creased from 3 to. In ths scenaro, the KLMS algorthm s appled at FC. he performance curves reveal that ncreasng the cooperatve userumber from m = 3 to m = 5 result a performance ncrease about 5%. hs s because more cooperatve users correspond to lesformaton loss. he curves also reveal the ncrement of performance decreases wth the ncreasng of the cooperatve users. hs observaton ndcates that more users are not better, when the user number s large enough, because the computaton complexty wll ncrease rapdly as the cooperatve usercrease. V. CONCLUSION In ths paper, a new KLMS based cooperatve spectrum sensng method for cogntve rado networks s proposed. In the proposed method, each SU utlzes energy detecton to make a bnary decson based on ts local spectrum sensng. hen, the decsons are sent to the FC to make the fnal decson on the spectrum occupancy status. he KLMS algorthm s used as a fuson scheme n the FC. Wth the new method, the relablty of decson FC can be enhanced sgnfcantly. 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