Cooperative Self Encoded Spread Spectrum in Fading Channels

Transcription

1 I. J. Communatons, etwork an Sstem Senes, 9,, 9-68 Publshe Onlne Ma 9 n SRes ( Cooperatve Self Enoe Sprea Spetrum n Fang Channels Kun HUA, Won Mee JAG, Lm GUYE Unverst of ebraska-lnoln, Omaha, E, USA Emal: {khua, wjang, nguenl}@unlnotes.unl.eu Reeve ovember 5, 8; revse Februar 6, 9; aepte Marh, 9 Abstrat Self-enoe sprea spetrum (SESS) s a unque realzaton of ranom sprea spetrum. SESS elmnates the nee for the tratonal transmttng an reevng P oe generators. Instea, the tme varng, ranom spreang sequene s obtane from the ata soure. Cooperatve verst (CD) has been attratng nreasng attenton as a novel an promsng verst tehnque. Ths paper analzes the ooperatve SESS for Amplf an Forwar CD lnks n Ralegh hannels. The results show that our ooperatve SESS mproves the sstem performane sgnfantl over MRC-base ooperatve sstems. Kewors: Cooperatve Dverst, Sprea Spetrum, Maxmum Rato Combner. Introuton Cooperatve verst reeves nreasng attenton as a verst enabler, whereb several partner termnals aroun a gven moble termnal form a strbute ooperatve network an transmt nformaton ollaboratvel []. The avantages of CD are smlar to exstng verst tehnque lke MIMO to ombat the etrmental effets of multpath fang. Senonars [,] has propose a user ooperaton moel that aheve an nrease n apat. As sprea spetrum an effetvel eal wth multpath fang, ret-sequene sprea spetrum transmssons have been onsere for mplementng a novel spetrall effent ooperatve protool [4]. SESS s a unque ranom sprea spetrum that elmnates the nee for tratonal transmt an reeve P oe generators [5]. In ths paper, we onser SESS ooperatve verst (SESS-CD) ommunaton over fang hannels an analze ts performane n fang hannels. Expressons for the average bt error rate (BER) are erve an the result s ompare wth the repetton sheme wth maxmum rato ombner (MRC). The moble rao hannel suffers from multpath fang, mplng that, wthn the uraton of an gven all, moble users oul experene severe varatons n sgnal attenuaton. Sprea spetrum an verst are methos for ombatng the etrmental effets of fang. Iteratve eteton wth SESS-CD reever s shown to aheve remarkable performane mprovement reung the BER sgnfantl. SESS-CD wth teratve eteton proves both temporal an spatal verst whle MRC explots onl spatal verst gan. In Seton, we esrbe the sstem moel. Seton analzes the performane of SESS-CD an MRC. The analtal an smulaton results base on SESS-CD shemes are presente n Seton 4. The onluson follows n Seton 5.. Sstem Moel Conser the ooperatve network where nformaton s ommunate between a soure (S=R ) an a estnaton (D=R ) over a omplex hannel wth fang parameter f. Two rela noes, R an R, are wllng to ooperate to prove repeate sgnals through the omplex hannels wth flat fang hannel parameters (f, f ) from (S) to (R, R ), an (f, f ) from (R, R ) to (D), respetvel. Wthout loss of generalt, we assume the relas an estnaton have the same atve whte Gaussan nose (AWG) power. We also assume that the values of ranom varables, f, f, f, f an f have been etermne at the reever ens b tranng. We onser the Coprght 9 SRes. I. J. Communatons, etwork an Sstem Senes, 9,, 9-68

2 9 K. HUA ET AL. Fgure. Cooperatve self-enoe sprea spetrum struture. Amplf an Forwar (AF) moel wth a onstant average power. The bas ea n our propose spatall ooperatve sprea spetrum s to mplement SESS aross a ooperatve rela network. Fgure shows the blok agram of SESS-CD sstem. At the transmtter, the ela regsters are onstantl upate from -tap seral ela of the ata to generate the spreang sequene of length. The urrent bt s sprea b the tme varng hp sequene that has been obtane from the prevous ata bts [6]. The SESS ata bt wll be transmtte through the ret an rela paths smultaneousl wth fferent fang oeffents as shown n Fgure. The self-enong operaton at the transmtter s reverse at the reever. The reovere ata are fe bak to the -tap ela regsters that prove an estmate of the transmtter spreang oe requre for sgnal e-spreang. The SESS-CD reever emplos teraton eson. The reever thus explots the atonal tme verst as well as the spatal verst nherent n rela sstems. The transmtte sgnal an be expresse as: x= S () where an S are the ata bt an the SESS spreang sequene, respetvel, urng -th bt uraton. In MRC sheme, x s a smple ata bt. Let the fang ampltue be f j wth the orresponng mean of K j. Then, the reeve sgnals an be expresse as: f x n () fa( fx nr ) n () fa( fxnr ) n (4) where n r s the nose at the rela, an n s the nose at the estnaton. n r an n are statstall nepenent Gaussan nose whh s strbute as (, ), where we assume the same nose power at relas an the estnaton. A an A are amplfaton fators to mantan onstant average power output of the relas: A ( Eb / o) /( f ( Eb / o) ) A ( E / ) /( f ( E / ) ) (5) b o b o Then, the output of the eorrelator at the reever s gven b r S S S (6) where S s the reovere spreang sequenes at the reever, whh ma be fferent from S ue to eteton errors., an are the normalzaton fators for fang an nose power: f / f A f /(( f A ) f A f /(( f A ) ) (7) ) Coprght 9 SRes. I. J. Communatons, etwork an Sstem Senes, 9,, 9-68

3 COOPERATIVE SELF ECODED SPREAD SPECTRUM I FADIG CHAELS 9 We an wrte SESS sgnals as S S S S sprea sequene rkk k blok S S [( ) ] (8) where are the ata bts elae to form the SESS spreang sequenes. Sne the urrent bt s sprea b prevous bts, we an observe that urrent etetng bt s also relate to prevous nformaton bts, whh are store n the ela shft regster +,,. B norporatng prevous etete bts, we expet to mprove the performane. Therefore sgnal energ an be retreve from prevous estmate bts( ) as (9) an the bt eson an be mae base on Y () r For MRC sheme, we obtan () Y at the reever for bt eteton. We assume that eah rela path an ret path are solate. The solaton an be aheve b tme vson multplexng.. Performane ) BER for Rela Channel (MRC): As shown n Fgure, f, f, f, f an f are the fangs on the rela an ret paths. Let the mean an the seon moment (power) of the fang, f j are equal to K j an ζ j, respetvel. Then, the sgnal-to-nose rato (SR) at fferent noes an be alulate as: Px j j () where P x / o s the reeve SR n AWG hannels wthout fang. The SR at reever wth verst an be erve from [] as k k () z whh s reue to k k k k k (4) z k k k k o k k at hgh SR. In MRC ooperatve sheme, nformaton bts are repeate n rela paths. We assume bnar phase-shft keng moulaton (BPSK) over Ralegh fang hannels. Therefore, the bt error rate wth M rela branhes s []: M )( K ) Pe M k M M ( ) m m m (5) where K enotes the fator n non-entral Ch-square strbuton, an K= for exponental strbuton. The onstant k epens on the tpe of moulaton, an k = for phase shft keng. M) an be obtane as M ) M If the rela noes number M=, then (k ) k (6) ( M )! P 5 e ( ) ( )( ) E / (7) b o We observe that the error probablt P e s the funton of (E b / o ) -(M+) where M s the number of rela noes. Therefore, the ooperatve network an aheve the full verst orer of M +. ) BER for Self-enoe Sprea Spetrum Cooperatve Dverst (SESS-CD): The performane of SESS- CD wth teratve eteton an be onsere as P Q( k ) p ( ) (8) e z z z z where p ( z ) s the probablt enst funton of z z. In ths ooperatve SESS-CD performane analss, we o not onser the self-nterferene that omes from the erroneous espreang sequenes ue to the norret bt eson at the reever. The self-nterferene was shown to be omnant at low SR or wth small spreang fators [7]. The reeve energ n eah path an be onsere as for =,..., s an exponental ranom var- where able (r.v) wth parameter (9) /,.e., ) exp{ / } () ( p where s the hp energ to nose rato wth fang. The s an exponental r.v. wth parameter /. The frst term n Equaton (9) s the output of the urrent bt espreang an the seon term s the teratve eteton output. We appl the entral lmt theorem to fn the approxmate probablt enst funton (pf) of. Sne the mean an varane of, for =,, Coprght 9 SRes. I. J. Communatons, etwork an Sstem Senes, 9,, 9-68

4 94 K. HUA ET AL. s an, respetvel, we an approxmate the mean an varane of n Equaton (9) as m ( ) () () Therefore, the approxmate pf of the r.v. an be obtane as p ( ) exp{ ( m ) /( )} () Sne the frst term n Equaton (9) s a omnant term, Equaton () ma not be the best approxmaton. However, we wll fn that the result an prove a useful nsght regarng the SESS-CD verst gan. For hgh SR, p () tens to be zero. Therefore, we wll fn the p() / to be apple to the ntal value theorem of Laplae Transforms [] as p( ) m exp{-m / } (4) exp{ } exp{ }, for large (5) where b s the bt energ to nose rato wth fang. The SR at the fferent noes an be represente as j. Wth M ooperatng branhes, the probablt of bt error wth BPSK an be obtane as where M )( K ) Pe ( M ) k a ( M ) M M ( r b ) r (6) a ( / exp( )) from Equaton (5). M) In Fgure, we an see that the performane of SESS- CD s superor to MRC. The result an be prete from Equatons (5) an (6). The BER fferene between SESS-CD smulaton an analss omes from the gaussan approxmaton of the reeve sgnal power. The exat pf an ts gaussan approxmaton of the reeve sgnal power over ranom fang hannels are shown n Fgure. We an observe that the gaussan approxmaton shfts the probablt of low reeve sgnal power to hgh reeve sgnal power at both E b / o equal to 5 B an B, whle mantanng the same mean an varane as the exat pf. However the slope of SESS-CD smulaton BER an analtal BER agrees well. The verst gan etermnes the slope of the BER versus average SR urve, at hgh SR, n a log-log sale. On the other han, ong gan (n ebels) etermnes the shft of urve n SR relatve to the benhmark BER urve n unoe ommunaton over a ranom fang hannel [8]. We see that the Gaussan approxmaton exhbts a rather aurate verst gan but not ong gan. The verst gan n Fgure portras well the square term of the SR enhanement n SESS-CD n Equaton (6). Fgure 4 shows the performane of Fgure. Smulaton BER, SESS-CD (64 hps/bt) an MRC, K =K = =, K =K =. an be obtane as ( M ) (k ) k M ) (7) (( M ))! Comparng Equatons (5) an (6), we fn that the effetve SR n SESS-CD wth teratve eteton s the square of the atual SR. 4. Smulatons an umeral Results Fgure. Probablt enst funton of exat pf an gaussan approxmaton, 64 hps/bt, E b / o =5 an B. Coprght 9 SRes. I. J. Communatons, etwork an Sstem Senes, 9,, 9-68

5 COOPERATIVE SELF ECODED SPREAD SPECTRUM I FADIG CHAELS 95 Fgure 4. Smulaton BER of SESS-CD, 64 hps/bt. Fgure 6. Smulaton BER of MRC an SESS-CD (64 hps/ bt) wth K =K =K =.5, K =K =.5, uner fferent bt loss perentage. square term of the SR whle the MRC BER s nversel proportonal to the SR onl. We observe that SESS-CD s ver stable n hghl orrelate hannels as well as n severel fang hannels. SESS ombne wth CD s obvousl a promsng CD tehnque for the future generaton of wreless ommunatons. 6. Aknowlegment Ths work was supporte n part b ontrat awar FA from the U.S. Ar Fore Offe of Sentf Researh. Thanks are ue to Dr. J. Sjogren whose support has allowe the authors to nvestgate the fel of ooperatve self enoe sprea spetrum. Fgure 5. Smulaton BER of MRC an SESS-CD (64 hps/bt) wth K = K = K =.5, K = K =.5, for varous orrelaton values of orrelate hannel. SESS-CD wth fferent rela loatons. The rela loaton n the mle of the soure an estnaton (K =.5, K =.5) exhbts a better BER than the rela loaton near to the soure (K =.9,K =.). We an also see n Fgure 5 that SESS-CD s stable n orrelate hannels but MRC egraes rapl as the hannel orrelaton nreases. A smlar effet an be observe n hostle hannels wth bt losses n Fgure 6 where SESS-CD splas muh stable BER performane ompare to the MRC. 5. Conlusons We norporate SESS wth CD n ths paper. SESS-CD verst gan s lnke to the square of the reeve SR. The SESS-CD BER s nversel proportonal to the 7. Referenes [] A. Rbero, C. X. Ca, an G. B. Gannaks, Smbol error probabltes for general ooperatve lnks, IEEE Transatons on Wreless Communatons, Vol. 4, o., pp. 64-7, Ma 5. [] A. Senonars, E. Erkp, an B. Aazhang, User ooperaton verst-part I: Sstem esrpton, IEEE Transatons on Communatons, Vol. 5, o., pp , ovember. [] A. Senonars, E. Erkp, an B. Aazhang, User ooperaton verst part II: Implementaton aspets an performane analss, IEEE Transatons on Communatons, Vol. 5, o., pp , ovember. [4] A. Rbero, X. Ca, an G. B. Gannaks, Opportunst multpath for banwth-effent ooperatve networkng, IEEE Internatonal Conferene on Aousts Speeh an Sgnal Proessng, Montreal, Canaa, Ma 4. [5] L. guen, Self-enoe sprea spetrum an multple Coprght 9 SRes. I. J. Communatons, etwork an Sstem Senes, 9,, 9-68

6 96 K. HUA ET AL. aess ommunaton, IEEE 6th Internatonal. Smposum on Sprea-Spetrum Tehnques & Applatons, ew Jerse, September. [6] K. Hua, L. guen, W. M. Jang, Self-enoe sprea spetrum snhronzaton wth genet algorthm an markov han analss, IEEE 4th Conferene on Informaton Sene an Sstems, Prneton, ew Jerse, Marh 8. [7] Y. Kong, L. guen, an W. M. Jang, On the BER of self-enoe sprea spetrum ommunaton sstems, Proeengs of the IASTED Internatonal Conferene, Wreless an Optal Communatons, Banff, Alberta, Canaa, June 7-9,. [8] Z. Wang an G. B. Gannaks, A smple an general parameterzaton quantfng performane n fang hannels, IEEE Transatons on Communatons, Vol. 5, o. 8, pp.89-98, August. Coprght 9 SRes. I. J. Communatons, etwork an Sstem Senes, 9,, 9-68