A Novel Spectrum Sensing for Cognitive Radio Networks with Noise Uncertainty

Transcription

1 Ths artcle has bee accepted for publcato a future ssue of ths joural, but has ot bee fully edted. Cotet may chage pror to fal publcato. Ctato formato: DOI.9/TVT , IEEE Trasactos o Vehcular Techology A Novel Spectrum Sesg for Cogtve Rado Networks wth Nose Ucertaty Megwe Su, Chegl hao, Su Ya, B L Abstract Ths correspodece vestgates a jot spectrum sesg scheme cogtve rado etworks wth ukow ad dyamc ose varace. A ovel Bayesa soluto s proposed to recover the dyamc ose varace ad detect the occupacy of prmary frequecy bad smultaeously. The states of prmary users are detected based o partcle flterg techology, ad the, the ose parameters are tracked by usg fte dmesoal statstcs for each partcle based o margalzed adaptve partcle flterg. Smulato results are provded to valdate that the proposed method ca mprove the sesg performace sgfcatly ad target the dyamc ose varace accurately. Idex Terms Spectrum sesg, dyamc ose varace, margalzed adaptve partcle flterg, jot estmato. I. Itroducto Cogtve rado (CR), as a e ectve techology to solve spectrum scarcty problem, was frst proposed []. CR has a potetal to accomodate for the 5th geerato (5G) commucato system, sce t ca fully utlze all avalable o-cotguous spectrums flexbly ad e cetly 5G wreless etworks []. However, the ma challege of CR s to crcumvet ferece to prmary systems. Oe strategy for ths challege s that the secodary users (SUs) access to frequecy bads opportustcally whch are detected to be vacat. Ths flexble approach s defed as spectrum sesg (SS). It s mportat to ote that the pror kowledge of ose dstrbuto s crucal for SS. However, the SUs ofte eed to detect prmary sgals accurately wth mperfect kowledge of ose level whch s referred to as ose ucertaty whe mplemetg SS the 5G commucato system. I order to deal wth ose ucertaty, varous SS methods are vestgated []-[5]. Dog Che et al. propose a combato method of cooperatve SS wth adaptve multple thresholds []. Ad accordg to [4], Chuy Sog et al. preset a mult-atea based SS method usg the geeralzed lkelhood rato test (GLRT) paradgm to tackle ose ucertaty. These reports ca address the ose ucertaty ssue Copyrght (c) 5 IEEE. Persoal use of ths materal s permtted. However, permsso to use ths materal for ay other purposes must be obtaed from the IEEE by sedg a request to pubs-permssos@eee.org. M. W. Su, C. L. hao ad B L are wth the School of Iformato Scece ad Egeerg, Bejg Uversty of Posts ad Telecommucatos, Bejg 876, Cha (clzhao@bupt.edu.c; stoe 456@6.com). M. W. Su s wth the School of Egeerg ad Computg Sceces, Durham Uversty, Durham DH LE, UK (e-mal: megwe.su@durham.ac.uk). Su Ya s wth the State Rado Motorg Ceter Testg Ceter, Bejg 4, Cha. (e-mal: yasu@srtc.org.c). Ths work was supported by Natoal Natural Scece Foudato of Cha uder Grats 6796, Ph.D. Programs Foudato of the Educato Mstry of Cha 56 ad Foudato of Cha Scholarshp Coucl. but are mpractcal to be appled to sgle-ode sgle-atea (SNSA) systems due to the hgh complexty of commucato devces. I [5], Yoghog eg et al. preset a SS algorthm based o the d erece of statstcal covarace matrx betwee trasmtted sgals ad pure ose. Ths algorthm ca be appled to SNSA systems, evertheless, t requres hgh correlato of trasmtted sgals space or tme. I addto, the propertes of ose process are ofte o-statoary due to the varablty ad ucertaty of wreless or moble commucato evromet. But ufortuately, exstg methods are desged for ose process wth statc statstcal propertes ad the performace wll deterorate whe beg appled to CR systems wth dyamc ose propertes. To overcome the challege caused by o-statoary ose propertes ad also to allevate the d culty future flexble deploymets (e.g. DD commucatos), we propose a effectve SS method whch ca detect the PU states ad track the ose varace jotly based o Bayesa ferece framework. The proposed sesg algorthm s easy to be appled SNSA systems wth dyamc ose varace ad does t requre the correlato of trasmtted sgals. The ma cotrbutos of ths correspodece ca be summarzed to two aspects. Frstly, we formulate a dyamc state-space model (DSM) to depct SS system wth dyamc ose varace. The PU states ad ose varace are cosdered as hdde states ad oly the samplg observato of receved sgals s kow to SU, hece the SS s coverted to a bld estmato problem. Secodly, based o the formulated DSM, a sequetal estmato scheme s proposed whch ca motor PU states ad dyamc ose varace jotly ad real tme at the recever. Ths jot estmato framework s accomplshed by utlzg margalzed adaptve partcle flterg (MAPF) techology [6]. By trackg ose varace, the formato ucertaty ca be suppressed to the mmum, ad the mprovemet of sesg performace wll be acheved. Moreover, as a uexpected gft, the recovered ose varace wll go far towards further CR ehacemets especally power allocato for spectrum sharg ad s also helpful for SU to recogze the rado evromet. The rest of ths correspodece s orgazed as follows. I Secto II, we provde the DSM of SS system. The jot bld sesg algorthm s troduced detal Secto III. I Secto IV, umercal results ad performace aalyss are provded. Ad fally, coclusos are draw Secto V. The otatos used ths correspodece are defed as follows. Symbols for vectors ad matrces are lowercase boldface ad uppercase boldface respectvely. b c meas the floor value. E ( ) deotes the esemble average (c) 6 IEEE. Persoal use s permtted, but republcato/redstrbuto requres IEEE permsso. See for more formato.

2 Ths artcle has bee accepted for publcato a future ssue of ths joural, but has ot bee fully edted. Cotet may chage pror to fal publcato. Ctato formato: DOI.9/TVT , IEEE Trasactos o Vehcular Techology II. System Model We cosder the followg dscrete tme dyamc state-space model whch relates the hdde PU state S ad the ose varace to the observato y. [S, x ] = ([S, x ]) () = ( y = (x, v, : ) () ) () Here, S () deotes PU state ad comes to two forms: actve ad dormat, ad x represets the correspodg PU trasmtted sgal. The evoluto behavor of S s characterzed by TSMC [7] [8]. Ad the trasto probablty matrx (TPM) ca be wrtte as:!d!a X = 64 p a!d p a!a = p p p p 75 (4) I CR system, SU motors PU states ad trasmts ts ow sgal perodcally, ad ths tme frame structure s defed as sesg-trasmsso slot (STS) whch comprses two parts, amely sesg tme T s ad sgal trasmsso tme T s respectvely, ad T s +T s = T s [9]. It should be oted that the PU state remas the same oe STS. I sesg tme, the trasmtted sgals of PU x wll be sampled ad processed by SU. I ths correspodece, M s set to deote the samplg sze ad represets the STS dex. I (), s the actual ose varace at the -th STS, ad v = [v,, v,,...,,v,m ] () s a..d samplg ose sequece where v,m N(, ). It s well-kow that a statoary whte Gaussa assumpto of backgroud ose s oly a approxmato as t gores the dstrbutoal ucertaty []. Therefore, we assume that the recever ca arrow dow the ose process wth a set of dstrbutos deoted by W ", where " represets the amout of average sgal to ose rato (SNR) ucertaty,.e., there s at most " db ucertaty W " []. Sce the radometer oly sees eergy, the dstrbutoal ucertaty of actual ose varace ca be summarzed a terval = [(/ ), " ] where = ad represets the omal ose varace whch s assocated wth the ucertaty set W ". I addto, the ose varace s assumed to be slow varyg ths correspodece ad a thrd order TS-AR process s utlzed to model the dyamcs of ose varace vew of autoregressve (AR) model ca represet d eret types of radom process ad descrbe certa tmevaryg processes sgal processg []. Specfcally, the state trasform equato () s represeted by: = a + a + a + z, (5) where z s whte ose. deotes ose varace tme dex, the relatoshp betwee ad STS dex s wrtte as: = b/jc, J s a teger greater tha. Specfcally, the evoluto of ose varace s supposed to be slow varyg ad wll be statc over several STSs. Therefore, the STSs ca be classfed to two categores due to the d eret relatoshp wth ose varace coheret perod,.e., frst slot ad o-frst slot, ad ose varace chages oly the frst slots. There are two hypotheses: H deotes that the PU sgal does ot exst, whle H deotes that the PU sgal exsts. The observato uder these two hypotheses are gve by: y = 8 >< >: P Mm= v,m, H P Mm= (x,m + v,m ), H (6) III. Spectrum Sesg Algorthm The purpose of the proposed jot estmato algorthm s to detect hdde PU states S : together wth ukow ose varace :. We address ths problem by cocerg the jot posteror probablty of trasmtted sgal ad ose varace,.e., x : y : ). From Bayesa perspectve, the jot estmato could be acheved by maxmum a posteror probablty (MAP) crtero. (b :,bx :) MAP = arg max h :, x : y : ) (7) Followg the cocept of margalzed partcle flterg (MPF) [6], we decompose the jot posteror probablty (7) to codtoal destes as follows: :, x : y : ) = : x :, y : )x : y : ) (8) We ca coclude from (8) that the jot SS method cossts of three steps: estmate PU trasmtted sgal usg PF [], track ose varace based o margalzato cocept [4], ad detect PU state by Neyma-Pearso (N-P) detector. A. Estmato of PU Trasmtted Sgal The posteror dstrbutos of trasmtted sgal x s approxmated wth dscrete radom measures based o PF [5], [6], ad the, x s estmated by MAP crtero. bx arg max 64! (x x ) 75 (9) = Specfcally, the partcles are geerated from a mportat dstrbuto,.e. x (x x :, y :). Ad the, the mportat weghts ca be evaluated by [7]: e! / x, y x :, y : ) (x x : )! () where the margal dstrbuto x, y x :, y : ) ca be computed by tegratg out the ukow ose varace: x, y x :, y : ) = x, y, x :, y : ) x :, y : )d () The predctve dstrbuto x :, y : ) ca be smplfed as ) ad we ca rewrte () as: x, y x :, y : ) = x, y, x :, y : ) / y )d, x :, y : )x x : ) )d () Here, the pror probablty of PU sgal x x : ) s acheved by the TPM gve (4). Ad the lkelhood fucto follows Gaussa dstrbuto ad ca be obtaed by: (c) 6 IEEE. Persoal use s permtted, but republcato/redstrbuto requres IEEE permsso. See for more formato.

3 Ths artcle has bee accepted for publcato a future ssue of ths joural, but has ot bee fully edted. Cotet may chage pror to fal publcato. Ctato formato: DOI.9/TVT , IEEE Trasactos o Vehcular Techology y, x :, y : ) = q M exp B@ y P Mm= x,m CA M () The, the mportat weghts s ormalzed ad the trasmtted sgal s derved wth partcles ad assocated mportace weghts based o asymptotcal MAP crtero (9). B. Estmato of ose varace It should be oted that the evoluto of ose varace s characterzed by slow varyg, so t s d cult to get relable ad fxed estmato for the whole sesg process based o a refemet after several STSs. I order to overcome ths problem, we desged a adaptve estmato mechasm whch ca track the evoluto of ose varace real tme. More specfcally, the estmated result of ose varace b equals to the statstcal expectato of curret posteror probablty y : ) depedg o ubased estmato. Ad y : ) s approxmated by the margal posteror probablty x :, y :) ad the assocated mportace weghts!. Furthermore, the hyper-parameters of the margal posteror probablty are updated based o the the cocept of cojugacy pror ad the adaptve mechasm of forgettg factor desged ths correspodece. The cocrete calculated steps for ose varace are show as follows. For ose followg ormal dstrbuto wth kow mea ad ukow varace, the cojugate pror s defed as a verse Gamma (G) dstrbuto [4] ad the herarchcal Bayesa model ca be wrtte as: v,m G(, B@ ) / N(, ) (4) CA + exp B@ (5) where ad are the predctve hyper-parameters. Based o the dervato preseted (6), the posteror probablty of ose varace also follows G dstrbuto. Ad the hyper-parameters of the posteror dstrbuto ca be computed recursvely as follows: = + (7) = + y P Mm= x,m M (8) where the predctve hyper-parameters are updated as = ad =. Here, deotes forgettg factor whch specfes how quckly the flter reduces the fluece of past sample formato. I ths correspodece, we desg a adaptve mechasm of forgettg factor. I.e., = whe STS s the frst, ad = whe t s the ofrst, here, < <. Sce the ose varace stays the same o-frst slots ad more past sample formato ca be used to estmate the ose varace. Ths proposed mechasm ca take advatage of the slow varyg characterstc of ose varace ad ehace estmato accuracy. CA After ad are updated, the margal posteror of ca be computed relyg o margalzato cocept. y : ) = x :, y : )x : y : )dx : = x :, y :)! (9) Fally, depedg o ubased estmato, the estmated result of ose varace equals to the statstcal expectato. b = E( y : ) = =!, > () C. Detecto of PU State N-P decso polcy s a smple threshold polcy that oly depeds o the comparso of the observato at the curret slot wth the calculated threshold. Specfcally, after the ose varace s estmated real tme, the threshold at the curret slot # ca be calculated for a target probablty of false alarm whch s defed as p f = H H ). # = p Mb erf ( p f ) () The detecto result of PU state bs ca be acheved usg N-P polcy descrbed as: H y Q # () H Ad the, the detecto probablty whch s defed as = H H ) ca be calculated. IV. Smulato Results The actual SNR s set as SNR ad t ca be calculated by: SNR = log E P N P Mm= x MN = x m, = log () E N P N = Ad the omal SNR s deoted by SNR. As metoed earler, whe the ose ucertaty exsts practce, the actual ose varace s dstrbuted radomly aroud ts omal value,.e., = [(/ ), ], >. As far as the SNR s cocered (), t wll be radomly raged [SNR ", SNR + "] db. Here, " = log. I ths secto, we llustrate the sesg performace of the proposed SS method compared wth covarace absolute value (CAV) detecto algorthm proposed [5] ad tradtoal eergy detecto (ED) method wth dyamc ose varace. Ad the, we evaluate the e ects to estmato performace caused by d eret system parameters. A. Comparso of sesg performace ) The detecto performace s frstly descrbed through ROC curves Fg.,.e., = H H ) versus p f = H H ). Here, SNR s set to be db ad " = db. It s obvous that the proposed algorthm ca acheve hgher detecto probablty uder the same probablty of false alarm. The specfc causes may be grouped uder two heads. Frstly, based o the accurate real-tme estmato of ose varace, (c) 6 IEEE. Persoal use s permtted, but republcato/redstrbuto requres IEEE permsso. See for more formato.

4 Ths artcle has bee accepted for publcato a future ssue of ths joural, but has ot bee fully edted. Cotet may chage pror to fal publcato. Ctato formato: DOI.9/TVT , IEEE Trasactos o Vehcular Techology 4 x :, y :) = y, x :, y : )x, x :, y : ) x :, y : ) y x :, y : )x x :, y : ) / y, x :, y : ) /! + + exp 64 y, x : =, y : ) x :, y : ) R y, x :, y : ) x :, y : )d P y Mm= x,m B@ M CA! + exp B@ CA + P y Mm= x,m / (M) 75 ) / p exp M (6) a accurate real-tme threshold ca be obtaed whch ca be used for N-P decso polcy. By cotrast, the threshold for ED method s obtaed relyg o the omal ose varace ad t ca t be accurate. Secodly, CAV method ca suppress the formato ucertaty whe there s hgh correlato of trasmtted sgals space or tme. The correlato of trasmtted sgals set ths correspodece does exst but s ot hgh eough, so the sesg performace of CAV method s beyod ED method but stll behd the proposed method ED method db ED method db.4 ED method 5dB CAV method db. CAV method db CAV method 5dB proposed method db. proposed method db proposed method 5dB Fg.. Detecto performace comparso uder d eret ose ucertaty ED Method CAV method proposed method.75 p f Fg.. ROC curves of the proposed algorthm compared wth CAV ad ED ) Next, we set the target p f =., ad the detecto probabltes of d eret ucertaty parameters " uder creasg SNR are compared Fg. (The correspodg actual average value of p f s show Table I). Here, " =,, ad 5dB due to the parameter setup [5] ad []. Ad the x-axs Fg. deotes the true value of SNR,.e, SNR. B. Estmato performace wth d eret parameters ) I ths secto, we frstly evaluate the e ects of chagg forgettg factors to the estmato performace of ose varace as show Fg.. The estmato results are provded for two realzatos,.e., realzato { =.98, =.985} ad realzato { =.96, =.965}. Oe ca observe from the results that the fluctuato of estmato are more turbulet for smaller but ca track chages of the ose varace more rapdly. O the other had, smoother estmato ca be obtaed by larger, however, t wll lead to a slower respose to chages. The reaso s that larger forgettg factor meas that the formato of curret observato accouts for a lower proporto of the whole utlzed formato, so t s more d cult to track chages rapdly. TABLE I Probabltes of false alarm " method db db 5dB ED CAV... proposed method the value of ose varace true value realzato realzato From Table I ad Fg., we ca see that p f of ED exceeds the target false alarm probablty ad of ED s lower tha other methods ad very sestve to ose ucertaty whle p f ad of the CAV ad proposed methods are ot very sestve to ose ucertaty. Sce the formato ucertaty of ose ca be suppressed to the mmum by trackg the ose varace accurately wth the proposed algorthm. Ad the valdty of the CAV algorthm oly reles o the assumpto that the sgal samples are correlated. 5 5 sesg trasmsso slot dex Fg.. Estmated ose varace for d eret forgettg factors ) Ad the mea-square error (MSE) performace of estmated ose varace uder d eret forgettg factors s show Fg.4. Fve sets of forgettg factors are cosdered,.e., realzato { =.94, =.945}, realzato { =.96, =.965}, realzato { =.98, =.985}, realzato4 { =.99, =.995} ad realzato5 { =, (c) 6 IEEE. Persoal use s permtted, but republcato/redstrbuto requres IEEE permsso. See for more formato.

5 Ths artcle has bee accepted for publcato a future ssue of ths joural, but has ot bee fully edted. Cotet may chage pror to fal publcato. Ctato formato: DOI.9/TVT , IEEE Trasactos o Vehcular Techology 5 = }. It s see that alog wth the crease of forgettg factors, the MSE of realzato s less tha realzato ad realzato. Ths s because the fluctuato of actual ose varace set ths vestgato s ot sharp, the fluctuato of estmato caused by smaller forgettg factors wll crease the estmato error. However, whe the forgettg factors are large eough such as the sets of realzato4 ad realzato5, the estmato performace wll become less satsfactory sce t ca t track the chages of ose varace. MSE of estmated ose varace realzato realzato realzato realzato4 realzato Fg. 4. Estmato performace of ose varace uder d eret ED method M=. ED method M= CAV method M= CAV method M=. proposed method M= proposed method M= Fg. 5. Sesg performace of the proposed algorthm uder d eret M ) The, we study the e ects o detecto performace caused by d eret samplg sze M. Ad two typcal cofguratos of M are cosdered,.e., M = ad [7], [8]. It s observed from Fg.5 that creasg samplg sze s a e ectve way to ehace detecto performace of all detecto methods. I addto, compared wth ED method, the superor detecto performace of the proposed algorthm stll mataes eve though the samplg sze creases. C. Aalyss of Computatoal Complexty The CAV method requres about M multplcatos whe computg the autocorrelatos of receved sgal, whch s why ts complexty s about O(M ) [5]. I cotrast, ED method has a lower complexty tha O(M), sce the decso threshold ca be mplemeted usg a lookup table for Q ( ) fucto ad be reused [9]. Whle the proposed detecto algorthm s depedet of samplg sze M ad, therefore, we could measure t by O(E) whch s related to partcle sze P. To sum up, the complexty of the proposed algorthm ad ED method ca be regarded as the same order of magtude ad much smaller tha CAV whe the samplg sze M s large eough. V. Coclusos I ths correspodece, we develop a ovel SS algorthm for CR systems wth dyamc ose varace. By fully explotg the dyamc propertes of PU state ad ose varace, a DSM s formulated ad a sequetal spectrum scheme s desged by trackg the dyamc ose varace ad PU states jotly. Smulato results have bee provded to valdate the satsfactory sesg performace of the proposed algorthm. Refereces [] Federal Commucato Commsso, Spectrum Polcy Task Force Report, ET Docket o. -55, Nov.. [] Huawe, 5G: A Techology Vso, Huawe Europe, Ja. 4. [] D. Che, J. L, ad J. Ma, Cooperatve spectrum sesg uder ose ucertaty cogtve rado, Proc. Wreless Commucatos, Networkg ad Moble Computg, Dala, Cha, Oct. 8, pp. -4. [4] C. Sog, Y. D. Alemseged, H. N. Tra, et al, Adaptve two thresholds based eergy detecto for cooperatve spectrum sesg, Proc. Cosumer Commucatos ad Networkg, Las Vegas, USA, Ja., pp. -6. [5] Y. eg, ad Y. C. Lag, Spectrum-sesg algorthms for cogtve rado based o statstcal covaraces, IEEE Tras. Veh. Techol., vol. 58, o. 4, pp , May. 9. [6] E. Ozkaa, V. Smdlb, S. Sahaa, et al, Margalzed adaptve partcle flterg for olear models wth ukow tme-varyg ose parameters, Automatca, vol. 49, o. 6, pp , Ju.. [7] B. L, C. L. hao, M. W. Su, et al, Spectrum sesg for cogtve rados tme-varat flat fadg chaels: A jot estmato approach, IEEE Tras. Commu., vol. 6, o. 8, pp , Aug. 4. [8] B. L, J. Hou, X. L, et al, Deep Sesg for Space-Tme Doubly Selectve Chaels: Whe a Prmary User s Moble ad the Chael s Flat Raylegh Fadg, IEEE Tras. Sgal Process., vol. 64, o., pp. 6-75, Ja 6. [9] M. W. Su, S. H. L, B. L, et al, Spectrum Sesg for Self-Orgazg Network the Presece of Tme-Varat Multpath Flat Fadg Chaels ad Ukow Nose Varace, Moble Netw Appl., vol., o. 4, pp , Aug. 5. [] R. Tadra ad A. Saha, SNR Walls for Sgal Detecto, IEEE J. Sel. Topcs Sgal Process, vol., o., pp. 4-7, Feb. 8. [] R. Tadra ad A. Saha, Fudametal lmts o detecto low SNR uder ose ucertaty, Proc. 5 Iteratoal Coferece o Wreless Networks, Commucatos ad Moble Computg, Mau, HI, Ju. 5, pp [] L. Jackso, J. Huag, ad K. Rchards, AR, ARMA, ad AR-ose modelg by fttg wdowed correlato data, Proc. Acoustcs, Speech, ad Sgal Processg, IEEE Iteratoal Coferece o ICASSP, Texas, USA, Apr. 987, pp [] B. L, S. H. L, A. Nallaatha, et al, Deep Sesg for Future Spectrum ad Locato Awareess 5G Commucatos, IEEE J. Sel. Areas Commu., vol., o. 7, pp.-44, July. 5. [4] S. Saha, E. Ozka, F. Gustafsso, et al, Margalzed partcle flters for Bayesa estmato of Gaussa ose parameters, Proc. th Coferece o Iformato Fuso (FUSION), Edburgh, UK, Jul., pp. -8. [5] B. L, M. W. Su, X. F. L, et al, Eergy Detecto Based Spectrum Sesg for Cogtve Rados Over Tme-Frequecy Doubly Selectve Fadg Chaels, IEEE Sgal Process., vol. 6, o., pp. 4-47, Ja. 5. [6] M. W. Su, B. L, Q.. Sog, et al, Jot detecto scheme for spectrum sesg over tme-varat flat fadg chaels, IET Commu., vol. 8, o., pp. 64-7, Aug. 4. [7] J. Mguez ad P. M. Djurc, Bld equalzato by sequetal mportace samplg, Proc. IEEE Iteratoal Symposum o Crcuts ad Systems (ISCAS), Arzoa, Scottsdale, May., pp. I-845-I-848. [8] B. L, S. H. L, A. Nallaatha, et al, Deep Sesg for Next-Geerato Dyamc Spectrum Sharg: More Tha Detectg the Occupacy State of Prmary Spectrum, IEEE Tras. Commu., vol. 6, o. 7, pp , Jul. 5. [9] W. L. Ch, J. M. L, ad H. H. Che, Low-Complexty Eergy Detecto for Spectrum Sesg Wth Radom Arrvals of Prmary Users, IEEE Tra. Veh Techol., vol. 65, o., pp , Feb (c) 6 IEEE. Persoal use s permtted, but republcato/redstrbuto requres IEEE permsso. See for more formato.