effect of correlated fading and in [2], only synchronous CDMA system has been considered. ABSTRACT

Transcription

1 Multuser Adaptve MMSE Recever usng Multple Antennas for Asynchronous CDMA Systems n Multpath Fadng Channels Adtya rved D. K. Mehra Electroncs and Computer Engg. Department Indan Insttute of echnology Rooree Inda emal: adtyat redffmal.com tr.ernet.n fax no.: ABSRAC he performance of multuser adaptve mnmum mean square error (MMSE) recever combned th multple antennas s nvestgated for deband code dvson multple access systems (CDMA) n multpath fadng channels. In the adaptve mplementaton of the recever performance of varous algorthms le least mean square (LMS) normalzed least mean square (LMS) recursve least square (RLS) and the nely proposed affne projecton adaptve (APA) flterng algorthm s consdered. th the use of spatal dversty (by havng multple antennas at the recever) sgnfcant mprovement can be acheved n the output sgnal tonterferenceandnose rato (SIR). he effect of fadng correlaton beteen antenna elements (hch s a functon of antenna spacng angle of arrval angle spread and carrer frequency) on the performance s evaluated usng smulaton. Index terms: CDMA systems multple access nterference multuser detecton multpath fadng dversty. I. IRODUCIO he capacty of reless CDMA systems s lmted by the nterference generated by the transmsson from other mobles non as multple access nterference (MAI) and by multpath fadng hch also causes ntersymbol nterference (ISI) []. Multuser detecton has been shon to be a very promsng method to ncrease the capacty of the CDMA systems. As an alternatve to optmal but exponentally complex maxmumlelhood sequence detector suboptmum lnear multuser detectors (le MMSE recevers) have been explored. hese tmedoman sgnal processng technques can be mproved upon by usng multple receve antennas and antenna array processng [] [] hch enhances the output SIR and offers dversty to mtgate the mparments caused by fadng [3]. he applcaton of adaptve spacetme multuser detecton s consdered n [] [] among others. In [] no attenton s pad to the effect of correlated fadng and n [] only synchronous CDMA system has been consdered. In ths paper e consder adaptve mplementaton of spacetme multuser detector based on MMSE crtera usng APA flterng algorthm [4] hose convergence performance s found to be superor to LMS algorthm th much less computatonal complexty as compared to the RLS algorthm. he APA flterng algorthm has not been used elsehere to the best of authors noledge for the adaptve mplementaton of MMSE recevers n multpath fadng channels. e also sho that by addng antennas at the recever SIR gan can be ncreased. e hghlght the addtonal dversty gan obtaned f ether angular spread s ncreased or ndependent fadng s assumed across antenna elements. In secton II e descrbe sgnal model. Descrpton of archtecture of spacetme multuser recever s gven n secton III ncludng APA flterng algorthm. Smulaton results are presented n secton IV. Conclusons are dran n secton V. II. SIGAL MODEL A standard model for an asynchronous bnary phase shft eyed (BPSK) drectsequence CDMA (DS/CDMA) system s used n ths paper [5]. In K user system the th actve users baseband transmsson can be rtten as x () t Ab [ ] s( t υ) here b [ ] nterval ( ) t duraton and b [ ] { } = () s the symbol transmtted durng th. s the symbol +. A and υ represent the th user s ampltude and delay respectvely. υ = ( d + δ) c here d s an nteger beteen and and δ les beteen [ ). s () t s the sgnature sequence assocated

2 th the th user. e consder short code CDMA here same sgnature sequence s employed for each symbol nterval. () = ( ) ψ ( c) () j= s t a j t j here c s the chp nterval and the processng gan s here = / c. ψ (t) s the chp aveform and a ( ) j { } ± s normalzed so that s () t s havng unt energy and duraton. Receved sgnal correspondng to the th user at m th antenna s gven by L P r () t = h t x t τ (3) () ( ) m l m l l= here hlm () t s the channel coeffcent correspondng to the th user s l th multpath for m th antenna and τ l s the path delay assocated th the th user s l th multpath. L P s total number of multpaths. e have modfed de sense statonary uncorrelated scatterng channel model [6] to nclude drectonal dependence to smulate the fadng multpath channel. A hghly frequency selectve tapped delay lne channel model s consdered here multpaths arrve at c nterval length follong the arrval of the frst path.e. τl = τ + ( l ) c here l = 3.. L P.hs stuaton arses here the delay profle s more or less contnuous. Correlated fadng channel coeffcents beteen recevng antenna elements are gven as d hlm = hl exp jπ ( m) snθl (4) λ here m =.. M. h l s the channel coeffcent at the frst antenna. θ l s azmuthal angle of arrval of th user s l th path and d s antenna spacng. For ndependent fadng all channel coeffcents correspondng to dfferent antennas are generated ndependently assumng that antenna elements are ept suffcently apart. he recever s assumed to be synchronzed th the man path (hch s taen to be the frst path) of the th desred user.e. τ + υ = and the receved sgnal s passed through a chp matched flter and sampled at the chp rate. e next + defne matrces P and P ± ± ± ± P =... p p p LP (5) + here p l. and p l K and l LP are the vectors of chp matched flter sampled outputs durng th symbol duraton correspondng to the nputs s ( t υ τ l) and s( t ( ) υ τ l) respectvely [5]. If e run one chp matched flter per user to trac the frst ray of each user then receved sgnal vector at the m th antenna correspondng to j th users (chp matched flter) ould be (durng th symbol duraton) K m j j j j j m m = j + + [] = b [] A [] + [ b [] A [] + b[ ] A Ph m[ ] ] + nm[ ] (6) here h m [ ] = [ h m h m... hl ] P m (7) superscrpt denotes transpose. n [ ] s the r Ph Ph vector of zeromean complex (crcularly symmetrc) Gaussan nose samples havng varance σ at m th antenna n the th nterval and..d. across antenna elements. In all e collect K samples per antenna and for M antennas e aggregate KM samples. Let r m [ ] be a K length vector at the m th antenna m ( rm[] = m [] m []... m K [] r r r ) and r [ ] be the overall data vector of length KM obtaned by stacng the M antenna outputs durng th nterval [] [] M [] = r[ ] r r... r (8) A. Archtecture : III. ADAPIVE SPACE IME MMSE MULIUSER DEECIO Space tme multuser detecton presented here s sutable for centralzed (at the base staton) processng. Recever archtecture for users and sngle antenna case s shon n fg. Receved sgnals from other antennas are processed usng smlar structure and then added to the last summer for each user as shon. Sampled output at nterval denotes soft estmates ˆb. Let jqm [ n ] be the n th tap (flter coeffcent) of j th user s chp matched flter output gong to q th users summer n the m th

3 m = ν Chp matched flter C C bˆ ~ b ν Chp matched flter C C C From other antennas bˆ ~ b Fg.. Spacetme multuser detector. antenna here j q K m M and n. All s are adapted accordng to MMSE crtera. he output SIR of an MMSE detector depends on ts ablty to capture the receved energy of the desred user hle suppressng MAI and ISI. Choosng KM samples hch are shared by all the users based on MMSE crtera the detector acheves the optmum tradeoff beteen RAKE matched flterng and nterference mtgaton and maxmzes the output SIR []. For obtanng synchronsm beteen all detected data symbols of all users e can delay the sgnal at the nput to the th user s chp matched flter by c υ here c s the smallest nteger that results n postve delay. o e defne KM length flter coeffcents for the th user n th symbol duraton as [ ] [ ] [ ]... [ ] = M (9) here K length vector [ ] [ ] [ ]... [ ] m = m m Km and length vector jqm = jqm jqm jqm [ ] [] []... [ ] e choose [ ] to mnmze the meansquareerror (MSE) beteen the th data symbol and ts soft estmate From other antennas { [] ˆ [] } = E b b MSE H H H = + Γ v v () here e have defned autocorrelaton matrx of data vector Γ and cross correlaton vector v as { [ ] H [ ]} Γ = E r r and v = E r b () * {[] [] } E H and * are expectaton Hermtan transpose and complex conjugate operatons respectvely. Mnmum MSE s acheved by solvng ener Hopf equaton [4]..e. = Γ v () Groupng the coeffcent vector for the K users e have the MMSE multuser coeffcent matrx... = K = Γ V (3) here multuser crosscorrelaton matrx V of dmenson KM K s gven as V= [ v v... v K ] SIR can be expressed n terms of MSE as σ b MSE SIR = (4) MSE here σ s the varance of nput symbols. b B. Multuser APA algorthm: In the adaptve mplementaton flter coeffcent can be computed teratvely by transmttng tranng symbols. APA flterng can be veed as multple constrants optmzaton crteron th number of constrants L s called as the order of the APA flter. e may ve the APA flter as

4 ABLE I. COMPUAIOAL COMPLEXIY FOR VARIOUS ADAPIVE ALGORIHMS an ntermedate adaptve flter beteen the LMS flter and RLS flter n terms of both computatonal complexty and performance. If L= then APA flter reduces to LMS flter and f L= KM APA algorthm reduces to RLS algorthm. In APA flter cost functon for update eght vector for th user s gven as [4] = + + C Computatonal complexty Complex Complex Algorthm Addton / Multplcaton / Subtracton Dvson L M S + L M S Regularzed APA Algorthm (L + L + )+ L (L + L)+ L + L+ ( L ) R L S [] [ ] [] H ( b [ j] [ + ] r[ j] ) L * Re λ j (5) j= λ j are the Lagrange multplers pertanng to multple constrants. Solvng the above problem e get the follong APA algorthm [4] A H [] = [r [] r []. r [L+] ] B [] = [b[] b[] b[l+] ] E [] = B [] A[] [] [+] = []+ µ A H [].(A[]A H []+δi) E[] (6) here b ˆ[ ] = H []r[] b[ ] = sgn( real( b ˆ [ ] )) b = b here durng tranng [ ] [ ] b [] b [] b []... b [] = K. µ s step sze hch controls the adaptaton rate. δ s small postve constant used for regularzaton and I s dentty matrx of order L. Computatonal complexty nvolved for varous algorthms s gven n table I here = KM. IV SIMULAIO RESULS In our smulaton e used Gold sequences of length 3 chps (.e. =3). Data rate consdered s 3 Kbps (to eep smulaton tme small) hch corresponds to chp rate of 4.96Mchps/sec. Multpath spread s taen to be.5 µsec. causng a multpath span of c. e consder 4 user (K=4) system th nterferers at db poer advantage as compared to the desred user to llustrate the advantage of MMSE recever n nearfar stuaton. Input SR of the desred user s taen to be 8 db. In smulaton of asynchronous CDMA system e consder that tme delay of ntal path of the users are unformly dstrbuted beteen [). Exponental poer delay profle s assumed and channel s consdered statc n each ndependent tral. Mean angle of arrval (AOA) s unformly dstrbuted beteen [π) for each user. Around ths mean AOA Laplacan dstrbuted angular spread [7] s taen as 5 degrees except hen addtonal dversty gan obtaned by ncreasng angular spread s consdered. Order four (L=4) APA flter s used. Smulaton runs are carred over a large number of ndependent trals and ther mean s plotted. In fg. e demonstrate the superorty of APA flterng algorthm over LMS and smple LMS for sngle antenna case. For a far comparson n convergence characterstcs e ept the resdual MSE same for all the three cases. As seen from the fgure APA flterng algorthm clearly outperforms LMS algorthm convergng n about 8 teratons as aganst 354 teratons taen by LMS algorthm. RLS algorthm converges n about 67 teratons but the computatonal complexty nvolved s much hgher as seen from the table I. Fg.3 hghlghts the dversty gan obtaned by usng multple antennas at the recever end. e see from the fgure that by doublng the antenna elements e get roughly 3 db advantage n MSE (or correspondngly n SIR as per eq. (4). Results obtaned are n agreement th [3]. In fg.4 e sho that by havng uncorrelated fadng at the antenna elements addtonal dversty gan of roughly db can be acheved for four antennas case. In correlated fadng th antenna spacng of half avelength and angular spread of 5 degrees correlaton n excess of.98 s observed beteen adjacent antenna elements and around.8 beteen frst and fourth antenna. hrough smulaton e have also obtaned mprovement of.5 db f angular spread s ncreased from 5 degrees to 5 degrees.

5 V COCLUSIOS In ths paper performance of adaptve MMSE multuser detector combned th multple antennas for the detecton of asynchronous CDMA sgnals n multpath MSE n db RLS APA LMS LMS umber of teratons Fgure. Convergence characterstcs of APA RLS LMS and LMS flterng algorthms MSE n db umber of teratons Fgure 3. Dversty gan obtaned by multple antennas n correlated fadng MSE n db Four antennas to antenn as sngle antenna ndependent fadng umber of teratons correlated fadn g Fgure 4. Addtonal dversty gan obtaned th ndependent fadng at the antenna elements (four antenna case) Raylegh fadng channel s obtaned n terms of resdual MSE. th the use of APA flterng algorthm sgnfcant mprovement can be obtaned over LMS adaptve algorthm n convergence characterstcs. e have also demonstrated that usng multple antennas at the recever enhances the performance of the temporal processng (multuser detecton) even f the correlaton beteen antenna elements s hgh. Roughly 3 db advantage s obtaned by doublng the antenna elements. e have also hghlghted that addtonal dversty gan can be acheved f the antennas are placed dely apart so that ndependent fadng occurs at each antenna element. REFERECES [] John E. Smee and Stuart C. Schartz Adaptve spacetme feedforard/feedbac detecton for hgh data rate CDMA n frequencyselectve fadng IEEE rans. Commun. vol. 49 no. pp Feb.. [] Constantnos B. Papadas and Hoard Huang Lnear spacetme multuser detecton for multpath CDMA channels IEEE J. Select. Areas Commun. vol. 9 no. pp Feb.. [3] G. J. Foschn and M. J. Gans On lmts of reless communcatons n a fadng envronment hen usng multple antennas reless Personal Commun. vol. 6 no. 3 pp 3335 March 998. [4] Smon Hayn Adaptve Flter heory 4 th ed. Pearson Educaton Inc.. [5] Mchael L. Honng Scott L. Mller Mar J. Shensa and Larence B. Mlsten Performance of adaptve lnear nterference suppresson n the presence of dynamc fadng IEEE rans. Commun. vol. 49 no. 4 pp Aprl. [6] Kunah Yp and ungsang g Effcent smulaton of dgtal transmsson over SSUS channels IEEE rans. Commun. vol. 43 no. pp. 979 Dec [7] Rchard B. Ertel Paulo Carder Kevn. Soerby heodore S. Rappaport and Jeffrey H. Reed Overve of Spatal Channel Models for Antenna Array Communcaton Systems IEEE Personal Comm. Mag. vol. 5 no. pp Feb.998.