Jurnal Teknologi. CRLB Analysis for Cognitive IR-UWB with Imperfect Sensing. Full paper

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1 Jurna enoog Fu aer CRB Anayss for Cogntve R-UWB wth merfet Sensng Haeh Hossen a* orshea Fsa a Sharfah Kamah Syed-Yusof a a Eetra Engneerng Deartment Unverst enoog aaysa 830 U Johor Bahru Johor aaysa *Corresondng author: haehs@fegraduate.utm.my Arte hstory Reeved :3 January 0 Reeved n revsed form :5 Otoer 0 Aeted :5 Deemer 0 Graha astrat Astrat Cogntve utra wdeand (UWB) tehnoogy has aty to sense the envronment and offers an adatve system wth ow transmsson ower and hgh throughut for wreess ommunatons. muse rado UWB (R-UWB) suorts fexe moduatons wth short mono-uses n whh hanne estmaton has a rta roe. However merfet sensng n ogntve R-UWB ntrodues the hanne estmaton errors assoated to the nterferng rmary users. wo man shemes of hanne arameters dentfaton are nown as ot-aded and nd methods. n ths aer the effet of rmary user nterferene s onsdered for hanne estmaton ased on maxmum-ehood () rteron. Cramer-Rao ower and (CRB) anayss s derved and erformane anayss s smuated to omare oth ot-aded and nd methods n ogntve R-UWB system. he resuts verfy the etter erformane of the ot-aded estmaton and aso show the negatve effet of nreasng the numer of rmary users and aths on the erformane. At SR=0 db for ot-aded method wth 0 users and 3 aths the CRB square root of gan s and that of deay s ess than nd method. Besdes when the numer of rmary users s 0 and the aths are 7 ths ga s for gan and for deay. Keywords: Cogntve rado; utra wdeand ommunatons; Cramer Rao ower and; hanne estmaton 0 Penert U Press. A rghts reserved..0 RODUCO Utra wdeand (UWB) ommunaton s a romsng tehnoogy for short or medum-range wreess ommunaton networs wth ow ost and ow ower mementaton n an extremey arge transmsson andwdth. UWB ommunaton s oerated as seondary user and oexst rmary users whh have exusve rght to use the setrum. For oexstene ogntve features enae the UWB user to sense the oued setrum y rmary users and adat the oortunst setrum and data rate aordngy [] []. UWB onssts of a varety of throughut otons nudng very hgh data rates wth aatons for wreess oa area networs (WA) and wreess ersona area networs (WPA). muse rado ased UWB (R-UWB) nown as arrer-ess short use and OFD ased UWB (OFD- UWB) are used for UWB mementaton. n ogntve R- UWB adataty s erformed y varyng the use duraton or waveform shae. When sensng mehansm s not erfet ogntve R-UWB needs to mtgate the marments from the rmary users nterferene. n ths aer the erformane of ogntve R-UWB s nvestgated n the resene of dfferent numer of rmary users and hanne ondtons. We emoy Rae reever wth maxmum rato omnng (RC) to exot mutath dversty. Channe trang s ursued n oth ot-aded and nd estmaton shemes. Pot-aded or data-aded (DA) method eroday retransmts the tranng sequene or n a deson-dreted (DD) manner. On the other hand nd estmaton or non-data-aded (DA) s hefu when new users enter the networ and tranng sequenes mede the transmtter [3]. Heren the Cramer-Rao ower ound (CRB) [4] [5] [6] s served as a enhmar for the hanne estmator n oth DA and DA ases. Usng errors redted y the CRB unnown symos are transmtted over a mutath hanne to erform DA estmaton. hen CRB of the varane of the deay and gan estmates s derved. n the resene of rmary users we anaye the standard devaton of ath gan and deay and omare the system erformane of ot-aded and nd estmaton methods. he rest of the aer s organed as foows. Seton desres the system desrton. Bnd hanne estmaton s dsussed n Seton 3. Seton 4 addresses CRBs for Channe estmaton. Smuaton resuts and dsusson are resented n Seton 5 foowed y onusons n Seton 6..0 SYSE DESCRPO One of the most sgnfant hanne modes for UWB systems s the mode roosed y Saeh-Vaenuea usng a Rayegh 60 (03) ess SS

2 ... Detetor 36 Haeh Hossen orshea Fsa Sharfah Kamah Syed-Yusof / Jurna enoog (Senes & Engneerng) 60 (03) roaty densty funton for fadng hanne oeffent [7]. Refeton dffraton and satterng are the man reasons for mutath ourrene n UWB hannes [8]. Fgure reresents an -ray mutath hanne wth ndeendent deays and gans ( s of eah ath. Fgure utath hanne mode A rae reever s emoyed to resove and omne these reeved oes of the orgna sgna and tae advantage of mutath dversty rne. Fgure ustrates a rae reever omrsed of fngers to detet the strongest mutath omonents. n rate ror nowedge of the deays and the assoated gans s not avaae and needs to e estmated as and. ( r Fgure Bo dagram of the AWG Prmary sgna ranh Rae reever A-RAKE (A-RAKE) reever s an otma desgn wth enough numer of fngers and seetve-rake (S-RAKE) reever s suotma wth the mted numer of fngers whh are nvestgated n [9]. A ero forng (ZF) Rae reever an e omned wth ordered suessve nterferene aneaton (OSC) as roosed n [0]. R-UWB serves the same sread setrum onets as ode dvson mute-aess (CDA) wth DS-SS transever mementaton. he nformaton s moduated y use oston moduaton (PP) n whh ostons ndate the symos. n order to smooth the energy ses n the setrum aused y erodty of the use reetton a seudo-random sequene of deays tehnque nown as tme hong (H) s aed. H-PP format of the transmtted ogntve R-UWB sgna n our system s exressed as r ( s s ( t f a) () 0 where s ( s the ogntve user s sgna and ( 0 g( t f where g( s the monoye use wth duraton s the nformaton t ndex s the reetton ength frame nterva {0 } ) () f s the a s the -th nformaton t wth equa a ror roates s the addtona tme shft ntrodued when a s the tme-hong ode and s the h tme. he reeved sgna s oserved over an nterva of 0 t 0 n whh 0 s a mute of the symo erod f. We aso have E s E and E f dt. 0 he reeved sgna through aths at the outut of the ogntve reever antenna an e wrtten as r s ( t ) t (3) where and are attenuaton and the deay affetng -th ath resetvey and t ts rea traveng through the s therma nose us the nterferene aused y the rmary users wth tota ower setra densty.e. n( t where [ and t s ( t )] (4) s the numer of rmary users numer of rmary user aths and t ( t n denotes the (5) Assume s ) s determnst so [ E( ) E ( )] E (6) hen E t s [ E( ) E ( )] n (7) s

3 37 Haeh Hossen orshea Fsa Sharfah Kamah Syed-Yusof / Jurna enoog (Senes & Engneerng) 60 (03) BD CHAE ESAO n ths seton we onsder ogntve users and anaye nd (DA) hanne estmaton when the symos are unnown. As ndated n [7] we an get rd of these unnown nformaton y frst omutng the ehood funton a ) for ( a a a... a )... ] and ( 0 [... [ ] and then averagng over the roaty densty of â. hs rodues the margna ehood funton for ( ) as ( ) ( a ) () a d( a) (8) from whh the hanne estmates are derved. Sne there s no sef nowedge of the data symos exet for ndeendent ero or one vaues wth the same roaty we mode (a ) as ( a) [ ( a ) ( a )] 0 where (a) s the Dra funton. herefore (8) and (9) yed og[ ( )] og[ ex{ ( 0)} 0 ex{ ( )}] E (0) where ( a ) [ r( ( ] t f a () hus og[ ( ] s maxmed as a funton of( ). he frst ste rovdes () J ( ) E (9) F og[ ( )] 0 E( ) G 3 0 (5a) 0 og[ ( )] E( ) (5) [ H ] 0 og[ ( )] og[ ( )] E( ) E( ) 0 (5) where E /( ) s the sgna-to-nterferene-usenose rato (SR) and t (6) when J ( ) 0 ( 0) ( ) (3) then the roem redues to oong for the oaton of the extrema of ). J ( and sefy the vaue of 4.0 CRB FOR CHAE ESAO H a R tanhh( x) e ( xa R) R.[ R ( xa (7) R)] dx (8) n ths seton we auate the CRB of the ath deay and amtude estmaton errors as a funton of the arameters of the transmtted sgnas. We defne hanne arameter vetor as (4) [ ] R se h ( x) e ( xa R) R dx (9) hus from [0] we have

4 38 Haeh Hossen orshea Fsa Sharfah Kamah Syed-Yusof / Jurna enoog (Senes & Engneerng) 60 (03) f ( "( dt 0 where 0 and a E f sgn( a ) R ' E dt. Based on [5] the Fsher nformaton matrx s B C ( ) (0) C D where G 3.. F.. F B G F G 0 0 () C dag{0... 0} () 0 0 D dag{ [ H ]... [ 0 H ]... [ H ]} (3) he CRB of the deay estmaton and amtude estmaton for -th ath are defned as: var( var( ) [ ) [ ( )] [( B CD C) ] ( )] [( hen we an otan CRBs of estmates for he CRB for estmaton of s (4) D CB C) ] [ ( )] the -th dagona eement of the nverse matrx CRB for estmaton of (5).... whh s and the s / [ H ]. t s ovous that the CRBs 0 for estmatons deend on a ( 0.. ) (... ) SR and the same se. 5.0 SUAO RESUS AD DSCUSSO he foowng use wave form s adoted n these smuatons: t t ( ) [ 6 ( ) ]ex[ 8 ( g t ) ] (6) Parameters of () and () are susttuted as f 40 and f / 0. he h s and random symos are n the nterva of [0 9]. asynhronous rmary users are onsdered the numer of aths 3 R=. and the ath deay of a users are 5. he ath gans are and whe the other gans vary from user to user wth the Rayegh dstruton and ther exetatons are roortona to ex( / 4). Oservaton ength of 00 symos (=00) and SR of 0 db to 60 db ( assumed. SR E / n ) are Fgure 3 shows the CRBs of nd and ot-aded methods for ( ) as the numer of rmary users vares at dfferent vaues of SR wth 3. n ths fgure s the effetve numer of the aths that has een used for the roessng. t has een shown that nd estmator s oorer than ot-aded method for oth gan and deay. n Fgure 4 the vaue of SR s equa to 0 db and t omares the derved CRBs for nd and ot-aded of the standard devatons as the numer of rmary users vares for -th ath of tota aths 3. Fgure 5 shows ovous gas etween nd and ot-aded urves n the derved CRBs at SR=0 db whh nreases wth arge numer of rmary users. Fgure 6 and Fgure 7 are the CRBs of nd and otaded methods for and as the numer of rmary users vares at dfferent numers of = [357] whh the ath gans are and hese fgures show that the CRBs nreases wth nreasng of the numer of tota aths. n the revous wor [4] the standard devaton urves of gan and deay are derved ony for dataaded method. Besdes the authors dd not omare the otaded and nd methods whe ther system s a non-ogntve UWB.

5 39 Haeh Hossen orshea Fsa Sharfah Kamah Syed-Yusof / Jurna enoog (Senes & Engneerng) 60 (03) Fgure 6 he CRBs of DA and DA methods for gan of numer of rmary users versus Fgure 3 he CRBs of DA and DA methods for ( ) at dfferent vaues of SR wth 3 Fgure 7 he CRBs of DA and DA methods for deay of versus numer of rmary users. 6.0 COCUSO Fgure 4 he square root of CRBs for estmaton of fo -th ath when 3 and 3 and SR=0 db n ths arte CRBs of ot-aded and nd hanne dentfaton are rovded for ogntve R-UWB ommunaton. umera nvestgaton has verfed that nondata-aded method s oorer than data-aded method and there exst ovous gas etween DA and DA urves n the derved CRBs. he urves ustrate that the CRBs nrease wth the tota numer of rmary users and aths. As a future wor the merfet sensng errors an e nvestgated for C-C4 standard of UWB hanne modes. Referenes Fgure 5 he ga etween CRBs of DA and DA methods for ( ) at SR=0 db [] J. R. Fernandes D. Wentoff. 00. Reent Advanes n R-UWB ransevers: An Overvew. EEE nternatona Symosum on Cruts and Systems (SCAS). son Portuga [] E. Hossan V. K. Bhargava Cogntve Wreess Communaton etwors. Srnger Sene. [3] B. Shen et a. 00. on-data-aded Weghted on-oherent Reever for R-UWB PP Sgnas. ER Journa. 3(3). [4]. Huang and C. C. Ko Performane of axmum ehood Channe Estmator for UWB Communatons. EEE Commun. etter. 8(6). [5] Y. Chen. C. Beaueu CRB for DA Estmaton of UWB Channes. EEE Communaton etters. 9(8). [6]. Ye. Wash P. Hagh J. Barton A. athewson B. O Fynn. 0. Exermenta muse Rado EEE a UWB ased Wreess Sensor oaaton ehnoogy: Charateraton Reaty and Rangng. he 3 rd E rsh Sgnas and Systems Conferene (SSC) rnty Coege Dun.

6 40 Haeh Hossen orshea Fsa Sharfah Kamah Syed-Yusof / Jurna enoog (Senes & Engneerng) 60 (03) [7] A. A.. Saeh and R. A. Vaenuea A Statsta ode for ndoor utath Proagaton. EEE J. Seet. Areas Commun. 5(8 37). [8] K. S. Chatanya P. uradhar C. B. R. Rao mementaton of CORDC ased RAKE Reever Arhteture. nd EEE nternatona Conferene on Comuter Sene and nformaton ehnoogy [9] Q. Zhang; J. H. Cho On RAKE Reevers for Utra-wdeand Bnary Bo-oded PP n Dense utath Channes. EEE ransatons on Vehuar ehnoogy. 56(4)Part: : [0] J. An and S. Km An Ordered Suessve nterferene Caneaton Sheme n UWB O Systems. ER Journa. 3(4):