Performance Analysis of Iterative Multistage Detection Scheme for Overloaded DS-CDMA System

Transcription

1 Performance Analyss of Iteratve ultstage Detecton Scheme for Overloaded DS-CDA System Preetam Kumar,. Ramesh and Saswat Charaart G. S. Sanyal School of elecommuncatos, II Kharagpur Department of Electroncs and Electrcal Engneerng, II Kharagpur Astract: Overloaded Code Dvson ultple Access (CDA) system accommodates more numer of users an e spreadng factor,. One of e effcent schemes to overload a CDA system s to use two sets of orogonal sgnal waveforms (O/O). he frst set s assgned to e users and e second set s assgned to e addtonal users. An teratve multstage detecton technque s used to cancel nterference etween e two sets of users. At each stage of e detecton process, e est estmates of e multuser nterference s syneszed usng e decson avalale from e prevous stages, and s nterference s sutracted from e user sgnal of nterest efore enterng to a reshold detector. he nterference cancellaton recever uses hard decsons (HDIC) or soft decsons (SDIC) to estmate e nterference. In s paper, we have presented e analyss of s teratve multstage nterference cancellaton (ISD) recever for O/O overloaded DS-CDA system. A closed form expresson for e average Bt Error Rate (BER) s otaned, for each stage of HDIC recever. he analytcal results as otaned from e closed form expresson are compared w smulaton results for quas orogonal sequence (QOS) O/O overloadng scheme proposed for cdma000. I. IRODUCIO In a cellular system ased on CDA, e numer of sequences assgned to users n a cell s typcally less an e spreadng factor, and maes e cells underloaded. o mae a etter use of e rado spectrum, t s of consderale nterest to assgn more sequences an e spreadng factor,.e., to overload e channel. Overloaded CDA systems are of practcal nterest to e mole system operators, ecause ey can support more numer of users n a fxed andwd. hs nd of channel overloadng has een actually provsoned n rd generaton (3G) wreless standards []. Among e approaches descred n e lterature, e most effcent ones use multple sets of orogonal sgnal waveforms []. For nstance use, f we assgn orogonal sequnceces to e frst users and oer orogonal sequence to e addtonal users, we otan O/O overloadng scheme. In O/O overloadng scheme, e set users suffer from nterference of e set users only, whle set users suffer from nterference of e set users. he nterference etween users w resources from e dfferent sets can e handled usng maxmum lelhood (L) detecton or nterference cancellaton. As e computatonal complexty of L detecton s exponental w numer of users, teratve nterference cancellaton s preferred. he teratve multstage detecton (ISD) can use hard decson functon (HDIC) or soft decson functons (SDIC) to estmate e nterference form one set of users on oer sets. Specfc examples of O/O are scramled O/O (s-o/o) [3], hyrd DA/OCDA [4] and quas-orogonal sequences (QOS) [5] whch s a part of cdma000 standard. In random O/O (s-o/o), frst set of users are assgned Walsh-Hadamard (WH) orogonal codes overlad y e same P scramlng sequence. he second set of users are assgned e same Walsh-Hadamard sequence ut are scramled y a dfferent P sequence. In s way, we have two unque sets of orogonal codes. But n e case of QOS scheme, e scramlng sequence of set user s asent, whle e scramlng sequence of e set users s a fxed ent sequence. QOS are alance O/O sets, so at e correlaton etween any set and set user s equalzed,.e., ey are equcorrelated. Performance of a smlar type of equcorrelated overloadng scheme (O/s-O), has een evaluated y present auors n [6]. All ese schemes requre perfect tme algnment of e dfferent users, whch s generally acheved n e downln. Even n e upln, some systems le multcarrer-cda can mantan orogonalty y applcaton of approprate cyclc prefx and sngle-tap equalzaton. A hyrd overloadng scheme has een proposed y e present auors [7] where set users are assgned synchronous orogonal sequence ut e set users are assgned asynchronous P sequence to get etter BER performance. In s paper, we have analyzed e BER performance of teratve multstage nterference cancellaton recever for O/O overloadng scheme. he paper s organzed as follows: n secton II, e system model of ISD technque s presented. In Secton III, e BER expresson for HDIC scheme s otaned. Smulaton results are presented n secton -IV and compared e analytcal result. Fnally, secton-v summarzes e results and concludes e paper. II. IERAIVE ULISAGE DEECIO SCHEE In e sequel we wll consder e DS-CDA system w processng gan and e numer of users K (=+). We assume at e channel s a nondspersve addtve whte Gaussan nose (AWG) channel and at

2 e dfferent user sgnals are n perfect tme synchronsm. he dscrete-tme matrx model of e receved BPSK modulated CDA sgnal after demodulaton and chp samplng s gven y where = { } r=r +r = AS + AS + n (),... S s s s e orogonal sequences of set users of dmensons ( ) S = s,..., s s anoer orogonal sequences for set-users of dmenson ( ). he vector n s e sampled AWG nose w zero mean and varance equal to. A and A are e dagonal matrces of receved sgnal ampltudes of set and set users respectvely. and { } he receved demodulated and chp sampled sgnal () s despreaded and ntegrated over a t perod to get soft decsons output. hese outputs are fed to e teratve multstage detector (ISD). o explan e operaton e followng notatons are used: ˆ and ˆ are decsons aout set- and set- user data ts at e teraton, y and y are set- and set- matched flters output at teraton respectvely. At each teratve stage of e SD detector, e decson on e nformaton ts are made accordng to e followng expressons, ˆ ( ) ( ( -) = φ y = φ S r I ) () ˆ = φ ( y ) ( ) = φ S r I (3) where e reconstructed nterference for two groups n teraton s ˆ I = AS, ˆ I = AS. We assume at e reconstructed nterference for e frst group of users n e frst teraton s I 0 =0. atched flter outputs after nterference cancellaton form e decson statstcs vector y, l and y, l for set and set users data ts respectvely. In equaton and 3, φ ( x) s e decson functon. Accordng to e decson functon φ ( x), ISD can e classfed as hard decson nterference cancellaton (HDIC) and soft decson nterference cancellaton (SDIC). For e BER analyss we have consder e HDIC recever and e decson functon s defned as: x < 0 φ ( x) = sgn( x) =, (4) x > 0 III. BER EXPRESSIO OF HE HDIC RECEIVER We have assumed equal power, equal phase synchronous users n a sngle cell envronment over an AWG channel. he set- matched flters outputs n matrx form may e expressed as (- ) y = S ( r I ) (5) ˆ ( ) y = S ( AS + AS + n AS ) (6) y = + S S A ( ˆ ( ) ) + S n (7) In e case of AWG channel ampltude matrx s an dentty matrx,.e., A=I. For an artrary set- l user, e matched flter output s gven as ˆ (-),l,l,, y = + ( - +z (8) where l=,, 3, and z = [S n] l s e AWG for l user. he followng notatons have een used: s,l =set- l user sgnature,,l =set-, =set- user transmtted data-t, l user transmtted data-t, ˆ, =set- user tentatve decson on, at (-) teraton, ρ l, =ormalzed cross-correlaton value etween set- l user and set- output, l user sgnature. he matched flter y has ree components: ˆ (-) y, l =, l + (, -, l, + z { { desred AWG AI from set- users data otal ose Consderng Gaussan approxmaton for AI, to evaluate e BER performance we need to evaluate e varance of total nose term n (9),.e., (9) ˆ (-) (, -, + z (0) From e aove equaton, t s oserved at e varance s dependent on e set- transmtted data ts. Let s condtoned varance e,l/ = varance of set- l user matched flter output n teraton condtoned on set- users data and s expressed as: (-) / =Var( ( ˆ, -, +z)/,l ˆ(-) =E ( ( - +z)/,, ˆ( ) ˆ( ) ( ) ρ. ( ) ρ, m, m lm,, n, n ln, m= n= = E / ˆ( ) + + ( ) ρ. z,, l, =

3 ˆ( ) = E ρ /,, l, = ˆ( ) ˆ( ) + E ( ) ρ. ( ) ρ / +, m, m lm,, n, n ln, m= n= n m ˆ( ) + E ( ) ρ. z/ (),, l, = We have analyzed each term n aove expresson and e frst term s smplfed as : ˆ (-) E (, -, ) ρ / ˆ (-) E (,/ ) +E (, / ) = ρ (-) -E ˆ,, / ˆ (-),, ˆ (-),, = ρ +-E[ / ] = ρ -E[ / ] () (-) In e aove expresson E[ ˆ,, / ] s evaluated for all ( ) possle pars of.ˆ as follows:,, E[ ˆ(-) / ],, = ˆ( -) (.). P ( = / = ). P ( = ),,, ˆ( -) + (.-). P ( = -/ = ). P ( = ),,, ˆ( -) + (-.). P ( = / = -). P ( = -),,, ˆ( -) + (-.-). P ( = -/ = -). P ( = -),,, (-) =-P (3) e, (-) where e P represents e BER of set-, user. e, Susttuton of equaton (3) n () gves E ( - ) ρ / ˆ (-),, ˆ (-),, = ρ -E[ / ] (-) = ρ -(-P ] e, (-) = 4P ρ (4) e, hs s e term- n e condtonal varance expresson. We have furer smplfed nd and 4 term of equaton. he 3 rd term s e AWG w zero mean and varance. ow we summares e terms n e varance equaton as gven n equaton () n smplfed form for e set- users matched flters output n ale. We can derve e varance of e total nterference for set users n smlar way, and e results are gven n ale. Under e followng assumptons: ) he tentatve decsons of o set- and set- are uncorrelated and ) e tentatve decsons and e nose terms are uncorrelated, e second and four terms ecome zero. Under ese assumptons and usng e Gaussan approxmaton for e nterferng multuser sgnal, we can otan e expresson for BER of BPSK modulated users for e set-, l user (l=,, 3 ) and teraton > as: () P e,(,l) =Q (-) e,(, ) +4 P ρ (8) Smlarly for e set- ( l=,,3 ), e BER for e set-, l user (l=,, 3 ) for -e teraton ( > ) s gven y () P e,(,l) =Q () e,(,) +4 P ρ (9) For e frst teraton ( =) and e users n e frst group we do not have any nowledge of e data ts from second group of users and e expresson for BER n s case can e otaned y susttutng P =0.5 n equaton (8). 0 e,(, ) ABLE I Smplfed erms for e Varance of Set Users SE- matched flter output varance For artrary l user (l=,..) erm Expresson (-) 4P ρ e, (-),mˆ,n l,m l,n (-) (-) (-) m= n= + ˆ ˆ ˆ m n,n,m -,m,n - ρ ρ E / 3 4 (-) - ρ ˆ E(, z/ )

4 ABLE Smplfed erms for e Varance of Set Users SE- matched flter output varance expresson terms for e artrary l user (l=,..) erm Expresson () 4P ρ e, () () () () ˆ ˆ ˆ ˆ ρlm, ρln, E, m, n, n, m, m, n / m= n= m n ˆ (), - ρ E( z/ ) IV. SIULAIO RESULS onte-carlo smulaton has een carred out n A- La to compare e smulaton and analytcal BER performance of O/O overloadng schemes n an AWG channel. We have consdered QOS overloadng scheme for smulaton, n whch e frst set s WH sequences and e second set s otaned y scramlng e same WH codes w (quas) ent sequences [5]. We have assumed equal power and equal phase (zero phase users) synchronous users n o e sets. In e stuaton when users are synchronous and w equal phase, maxmum level of AI power results etween e sets. he spreadng factor, s 64. he overloadng percentage s defned as e rato of extra users and e spreadng factor expressed n percentage. Fgure compares e analytcal and smulaton BER performance curves at e st teraton for 6 % (4 extra set users) and 9% ( extra set users) overloadng for set- users. In e st teraton, ere s no nterference cancellaton for set user. It gves matched flter output for set user. It s oserved at for set- users analytcal and smulaton results are closely matchng at hgher overloadng of 9%. At lower overloadng of 6%, ere s a slght varaton at hgher E /o values. For a small numer of set users, e central lmt eorem may not hold, us e AI may not e well approxmated as a Gaussan process. So we oserve e dfference etween analytcal and smulaton results at lower overloadng. In fgure e analytcal and smulaton results of set users are compared for 6% and % overloadng at e st teraton. In e st teraton, nterference form set users are estmated from e set users detected ts and sutracted efore tang decson aout set users. It s oserved at for set- users analytcal and smulaton results closely matches at an overloadng of 6%. At hgher overloadng of 9%, ere s a dfference etween analytcal and smulaton results. Fgure 3 shows e analytcal and smulaton BER performance curves at e 3 rd teraton of ISD recever for 6% and 9% of overloadng for set- users. It s oserved at e analytcal and smulaton results closely match at 6% overloadng. At hgher over loadng of 9% smulaton result starts devatng from e analytcal result after 6 db and an error floor s reached. Fgure 4 shows e analytcal and smulaton BER performance curves at e 3 rd teraton of ISD recever for set- users. It s oserved at for set- users analytcal and smulaton results closely matches for 6% over loadng. For hgher overloadng smulaton results devates and an error floor s reached. W e aove dscusson t s clear at e analytcal BER expressons at are derved w e assumptons of uncorrelated tentatve decsons and uncorrelated nose and tentatve decsons are not vald at hgher overloadng. here s a correlaton etween e tentatve data decsons and e nose and data decson at dfferent stages, when nterference s cancelled n multstage teratvely. At lower overloadng, e AI s small and e Gaussan nose ecomes domnant, so we can assume ese terms to e zero. But ese terms ecome sgnfcant at hgher overloadng. So we need to refne e varance calculaton of e decson varale y consderng e correlaton etween e multple access nterference and Gaussan nose. hs approach needs e evaluaton of e covarance at nvolves e non-lnear hard decsons on detected ts made n e prevous stages. V. COCLUSIO In s paper, we have analyzed e performance of teratve multstage nterference cancellaton recever for O/O overloadng scheme. We have compared e smulatons and analytcal BER performance of QOS cell overloadng scheme for HDIC technque. It s oserved at w lower overloadng analytcal and smulatons results matches closely. But at hgher overloadng t s found analytcal and smulatons results are dfferent at hgher values of E/o. hs shows at at hgher overloadng, e tentatve data decsons and nose samples ecome correlated n e process of teratve nterference cancellaton n multstage detecton. REFERECES [] F. Adach,. Sawahash and H. Suda, Wdeand DS-CDA for ext- Generaton ole Communcaton Systems, IEEE Commun. ag., vol.36, pp , Sept.998. [] H. Sar, F. Vanhaveree and. oeneclaey, Extendng e Capacty of ultple access Channels, IEEE Communcaton agazne, pp-74-8, Jan [3] F. Vanhaveree,. oeneclaey and H. Sar, DS/CDA w wo Sets of Orogonal Sequences and Iteratve - Detecton, IEEE Commun. Lett., vol. 4, pp. 89-9, Sept [4] H. Sar, F. Vanhaveree and. oeneclaey, ultple access usng two sets of orogonal sgnal waveforms, IEEE Commun. Lett., vol. 4, no., pp. 4-6, Jan [5] K. Yang, Y.K. Km and P. V. Kumar, Quas-orogonal sequences for code-dvson multple-access Systems, IEEE rans. Inform. heory, vol. 46, pp , ay 000. [6] P. Kumar,. Ramesh and S. Charaart, Performance evaluaton of Orogonal/scramled-Orogonal overloaded DS-CDA system, n Proc. of IFIP Internatonal Conference on Wreless and optcal communcaton networ (WOC), pp. -5, Sngapore, July 007 [7] P. Kumar and S. Charaart, A new overloadng Scheme for DS- CDASystem, n Proc. of atonal Conference on Communcaton, pp , Jan. 007, II Kanpur.

5 Avg.BER(set-,teraton-) %-sm 9%-sm 9%-ana Avg.BER(set-,teraton-3) %-sm 9%-sm 9%-ana Fgure. BER performance of Set- users versus E/o at st teraton (matched flter output) Fgure 3. BER performance of set- users versus E/o at 3rd teraton Avg.BER(set-,teraton-) %-sm 9%-sm 9%-ana Avg.BER(set-,teraton-3) %-sm 9%-sm 9%-ana Fgure. BER performance of set- users versus E/o at st teraton Fgure 4. BER performance of set- users versus E/o at 3rd teraton