Prediction of channel information in multi-user OFDM systems

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1 Prcon of channl nforaon n ul-usr OFD syss Ja-oon Jon an Yong-wan L School of Elcrcal Engnrng an INC Soul Naonal Unvrsy. Kwanak P. O. Box 34, Soul, Kora Absrac Channl nforaon s nspnsabl o ploy avanc channl awar chnologs such as pack schulng an aapv oulaon an cong (AC). In hs papr, w frs nvsga h lay ffc of nsananous sgnal o nrfrnc an nos powr rao (SINR) on h spcral ffcncy of ul-usr orhogonal frquncy vson ulplxng (OFD) syss ha ploy pack-bas channl awar chnologs. To allva h prforanc graaon u o lay channl nforaon, w consr h us of prc channl gan for lnk aapaon wh pack schulng. I s shown ha h us of prc channl gan can sgnfcanly nhanc h spcral ffcncy parcularly n hgh obly nvronns. For praccal ralzaon of an opu prcor, w propos a group nu an squar rror (SE) prcon sch, whch can subsanally ruc h plnaon coplxy whou nocabl prforanc graaon. Fnally, h propos sch s vrf by copur sulaon. Inx rs: channl sa nforaon, pack schulng, SE prcon, OFD I. INTRODUCTION I s known ha channl awar chnqus (.g., pack schulng, aapv oulaon an cong (AC), an hybr auoac rpa rqus (AR)) can sgnfcanly nhanc h avrag spcral ffcncy of ul-usr orhogonal frquncy vson ulplxng (OFD) syss [, ]. owvr, hs channl awar chnqus ns accura channl sa nforaon (CSI) (.g., nsananous sgnal o nrfrnc an nos powr rao (SINR)) n h ransr. Prvous sus ofn assu h us of prfc (or accura) CSI n h ransr [3, 4]. owvr, snc h ransr ofn acqurs h CSI fro h rcvr, ay suffr fro prforanc graaon u o unavoabl ranssson lay hrough a fback channl. Ths probl bcos srous as h obly ncrass. To allva hs probl, h us of prc CSI was suggs [5]. Rcnly, svral rsarchrs hav nvsga h ffc of channl (or nsananous SINR) prcon on h lnkaapaon n sngl-usr syss [6, 7]. owvr, o h auhor s bs knowlg, no rsul has bn rpor on h ffc of nsananous SINR prcon on ul-usr syss. In hs papr, w consr h us of prc channl gan (or nsananous SINR) for lnk-aapaon wh pack schulng n h ownlnk of a ul-usr OFD sys. To hs n, w consr h us of a lnar opu nu an squar rror (SE) prcor, call Wnr prcor, as h channl gan prcor. Alhough h opu Wnr prcor can prov appropra prforanc vn n hgh obly conon, ay no asly b applcabl u o hgh plnaon coplxy [8]. To allva hs probl, w ploy a group SE flrng sch ha can subsanally ruc h plnaon coplxy whou nocabl prforanc graaon. Th papr s organz as follows. Scon II scrbs a ul-usr OFD ownlnk sys. In Scon III, w nvsga h ffc of channl prcon on h channlawar chnqus. To allva h plnaon coplxy probl, w propos a group SE flrng sch n Scon IV. Fnally, conclusons ar suarz n Scon V. II. SYSTE FRAEWORK A. Sys ol Consr an OFD ownlnk sys, whr X ( nk, ) nos h h usr sgnal a h n h sybol an h k -h subcarrr, {0,,, } an k {0,,, K }. Th frquncy oan sybol s convr no a oan sgnal usng nvrs fas Fourr ransfor (FFT). A cyclc prfx (CP) s nsr o prsrv h orhogonaly bwn h subcarrrs an o lna h nrfrnc bwn h ajacn OFD sybols. W assu ha ach aa pack coprss N OFD sybols n h oan an N f subcarrrs n h frquncy oan, an ha plo sybols ar rgularly nsr n a rcangular parn (.., apar by an f sybols n h an frquncy gr, rspcvly). Afr h FFT n rcvr, h sgnal of usr slc by h pack schulr can b rprsn by Y ( nk, ) = ( nk, ) X ( nk, ) + Z ( nk, ), ()

2 whr X ( nk, ) s h aa sgnal, (, ) nk s h frquncy rspons of channl puls rspons (CIR) fro h ransr o a slc usr, an Z ( nk, ) s h backgroun nos plus nrfrnc r whch can b approxa as zro an av wh Gaussan nos (AWGN) wh varanc σ. r, h CIR can b rprsn as, Z L τ =, τ l δ τ, l l = 0 h (, ) h () ( ), () whr L s h nubr of ulpahs, δ () s Kronckr la funcon, τ, l an h, l () ar h lay an coplx-valu CIR a of h l-h pah, rspcvly. Snc h CIR can b sa accuraly by usng h rcv plo sybols, w assu prfc cohrn con n h rcvr. B. Pack schulng Th spcral ffcncy can sgnfcanly b prov by ployng an nllgn pack schulng sch akng h channl conon no accoun, so-call opporunsc pack schulng [9-]. Th axu SINR schulng an proporonal far (PF) schulng ar xapls of h opporunsc schulng. Th axu SINR schulng slcs a usr whos nsananous SINR s h largs as = arg ax ( n, k ), (3) {,, } whr ( nk, ) = ( nk, ) ar h avrag SINR an h channl gan of usr, rspcvly. Thus, ( nk, ) rprsns h nsananous SINR. Assung ha usrs ar alloca n ach subcarrr, w can o h subcarrr nx k whou loss of gnraly. Ths pls ha a ul-carrr sys wh an opporunsc schulr can b ra as a spl paralll xnson of a snglcarrr vson ulplxng sys [9]. Thrfor, w wll o h nx k n wha follows. Th axu SINR schulng axzs h spcral ffcncy by achvng h ul-usr vrsy (UD) gan. owvr, ay no guaran farnss f h avrag SINR of ach usr has a larg varaon. Ths farnss probl can b allva by ployng a PF schulng sch as n h cax EvDO sys [0]. Lng R ( n ) b a possbl ranssson aa ra a sybol n an R ( n ) b h avrag aa ra up o h sybol n, h PF schulr slcs a usr accorng o an ( ) R ( n) = arg ax. (4) {,, } R ( n) If w assu ha all h usrs xprnc h sa channl sascs an ha h obsrvaon s suffcnly long, (4) can b scrb as [] ( n) = arg ax = arg ax ( n) {,, } (5) {,, } C. Prcon of nsananous SINR Accura channl nforaon s nspnsabl for h ployn of channl awar chnqus. Th CIR of usr corrsponng o h plo sybol can b sa by a axu lklhoo (L) ho as ( n, k = Y( n, k/ X( n, k, (6) = ( n, k + Z ( n, k whr Z ( n, k nos h nos r. To allva h lay probl assoca wh h CSI, w consr h prcon of channl gan a ( n+ p). Th prc channl gan can b oban usng a convnonal on-nsonal Wnr prcor n h oan as ( ( n+ p) ) =wo, (7) whr [ ( ) (( ) ) (( ) )] T = n n n U+ nos U orylss L sas of h plo sybol, h suprscrp an T rspcvly no h ran an ranspos opraon, an w o s h Wnr flr coffcn rn as wo = R p. (8) r, R( = E[ ] ) s h ( U U ) auo-covaranc arx of h rcv plo sybol an p( = E [ ( ( n+ p ) )]) s h ( U ) cross-covaranc vcor of h sr an h rcv plo sybol. Thn, h corrsponng prcon SE can b rprsn as σ = σ wop p wo + wo Rwo (9) = σ p wo whr σ = E[ ( ( n+ p) ) ]. Th nsananous SINR can asly b prc fro h prc channl gan. Snc h avrag SINR can b sa accuraly by a long r avrag [], w can assu ha h avrag SINR can b sa vry accuraly. Th nsananous SINR a ( n+ p) can b prc as (( ) ) (( ) ) n+ p = n+ p. (0) III. Th avrag spcral ffcncy can b rprsn as [] Λ = E[ Λ ] = E[log ( + η)] () whr Λ nos h nsananous spcral ffcncy an η nos a sys loss facor u o plnaon. For as of analyss, w assu ha all h usrs xprnc h sa avrag SINR (.., = ). L Γ r b h r-h ln of h channl gan vcor OS, arrang n an ascnng orr, gvn by LINK ADAPTATION WIT PEDICTED SINR

3 Γ = OS {,,, }, () r r whr OSr {,,, } nos h oupu of an orr sasc flr wh rank r. As a spcal cas, can b sn ha Γ = ax. Thn, h cuulav srbuon {,, } funcon (c an probably nsy funcon (p of Γ r ar rspcvly rprsn as [3] k F ( x) = F ( x){ F ( x)} Γ r r (3) r r f ( x) = r F ( x){ F( x)} f ( x) Γ r r whr f ( x) an F ( x) no h pf an cf of h channl gan, rspcvly. r, w o h nx n an h usr nx for brvy. No ha h usr slc by a PF schulr s qual o Γ. f ( x) = x /( σ ) σ. (9) Afr h schulng wh h orr sasc flrng n (), h pf of ( p) can b wrn as f x = F x f x. (0) ( ) { ( )} ( ) Nglcng h las r n (8), w can approxa (0) as [9] x/ σ x( + )/( σ ) N f ( x) ( ). () 0 + σ ( σ ) Thus, h avrag spcral ffcncy wh h us of prc channl gan can b rprsn as Λ = E[log ( + η )] p σ ( + ) E(/( ) ) E( ) + ( σ ) η / ση ( + )/( σ ) η σ ρ η ( ) log 0 + σ ( σ) Whn h oua channl gan s us for h PF schulng, h avrag spcral ffcncy can b () rprsn n a clos for [9]. Slarly, w can analyz whr E( x) =. x h prforanc of PF schulng wh h us of prc channl gan. Assung ha usr s schul bas on To vrfy h rsul, h prforanc of avrag spcral h prc channl gan, w can rprsn h avrag ffcncy s valua by copur sulaon n rs of spcral ffcncy of h slc usr as h noralz lay f Tp s. Whn h prforanc loss facor η an avrag SINR ar -5B an 8B, rspcvly, E[ Λ ] = E log { + η (( ) ) n+ p }, (4) Fg. pcs h avrag spcral ffcncy wh h us of whr ( ) ( ) ( n+ p) ( ). = n+ p prc channl gan, whr h lgn nos h ap sz of h Wnr flr. Th sulaon parars ar Th CIR a ( n+ p) can b prc usng a suarz n Tabl, whr w assu ha h channl s Wnr prcor as unchang urng ach pack. For coparson, h (( n+ p) ) (( ) ) (( ) ) = n+ p + n+ p (5) prforanc wh h us of non-prc channl gan s pc as No prcon. For rfrnc, h prcon whr (( n+ p) ) nos h prcon rror. For SE s also pc. I can b sn ha h us of prc splcy of scrpon, w wll o h nx n an gan s qu ffcv n h prsnc of hgh obly an plo nrval n wha follows. Fro [ 0] ha h analyc rsuls agr wll wh h sulaon rsuls. E [ ( p ) ( )] p = σ Alhough (3) s rprsn n a clos for, s no (6) asly calcula. Insa, w consr an uppr boun of E [ ( p ) ( )] p = σ (3) usng Jnsn s nqualy an concavnss of h ( p ) n (6) can b rprsn as logarh funcon. Assung no fback lay (.., al cas), h avrag spcral ffcncy s boun as [9] ( p) = ( ) ( ) p + σ z p (7) whr σ nos h varanc of h prcon rror ( ) Λ p, al = E log { η (0) + } an ( p) an z( p) ar npnn zro-an coplx log { + η E[ (0)]} (3) Gaussan rano varabls wh un varanc. Thus, h channl gan of h schul usr can b rprsn as = log + η + = ( p) = ( ) ( ) R{ ( ) ( )} (8) p + σ z p + p z p whr E[ (0)] = Γ. No ha h scon r / = whr ( p) = ( ) an. p ( p) = ( ) p rprsns h ul-usr vrsy (UD) gan achv n Snc h CIR s ol as a zro an coplx Gaussan rano varabl, h prc channl gan h al conon. Assung h us of channl gan whou prcon, h ( p) can b ol as an npnn xponnal CIR a h srvc can b rprsn as rano varabl wh pf gvn by ( p) = ρ (0) + ρ z (4)

4 whr z an (0) rspcvly no zro an coplx Gaussan rano varabls wh un varanc, an ρ = E [ (0) ( p)]. Th xpc channl gan a ( n+ p) can b rprsn as. (5) [ ( )] = ρ [ (0)] ( )= ( ) ( ) + ρ ρ + + ρ E p E Thus, can b shown ha h corrsponng spcral ffcncy s boun as Snc Λ log + [ ( )] { η E p } np = + + N log η ρ / E[ ( p)] = E[ ( p) + σ z( p) + R{ ( p) z ( p)} ] ( σ) / σ, = = + (6) (7) can b shown ha Λp log { + η E[ ( p)] } = log + η + ( σ ) (8) Copar o (3), (6) suggss ha h UD gan s affc by a facor of ρ whn h schulng s prfor bas on h prc channl gan. If h channl corrlaon ρ s zro, no UD gan s achvabl. On h ohr han, (8) suggss ha h UD gan s affc by a facor of ( σ ) wh h us of prc channl gan, whr 0 σ. I can b sn n Fg. ha ρ raply crass as h obly ncrass, whras ( σ ) os no. Fg. pcs h avrag spcral ffcncy n rs of h prcon SE. For rfrnc, h spcral ffcncy s also shown whn hr s no UD gan. I can b sn ha h us of prc channl gan s qu ffcv unlss h prcon naccuracy s oo larg. Noc ha no UD gan s achvabl f h prcon SE σ s largr han as non bfor. IV. A COPLEXITY REDUCED CANNEL PREDICTOR Th us of prc channl gan can sgnfcanly prov h prforanc of cannl awar chnqus. owvr, h us of a Wnr yp prcor ay no asly b applcabl anly u o h plnaon coplxy [8, ]. To allva hs coplxy probl, s ofn consr h us of a spl ovng avrag (A) or Lagrang nrpolaon flr as h prcor. owvr, hs flrs ay no prov sr prforanc bcaus hy o no ffcnly ulz h channl corrlaon proprs []. To allva hs ssus, w propos a so-call group SE flrng chnqu. If h flr coffcns ar no uch chang bwn h ajacn plo sybols, can b possbl for h flrng procss o us ajacn plo sybols n a group bass rahr han a sybol by sybol bass. As llusra n Fg. 3, G conscuv plo sybols ar cobn for h group SE prcon of orr U, whr ( u) nos h su of CIR sas corrsponng o G plo sybol, rprsn as G 0 ( u) = ( ug ) = w, u = 0,,,, U +, (9) ug whr w nos a ( U ) unary vcor an [ ( ) ( + )] T ug = ug ug G. Lng = [ (0) ( U+ )] T, h opu coffcn of hs group SE flr can b rprsn as w ( ) [ 0 U ] T o = R p = w w w + (30) whr R ( = E [ ]) an ( p = E[ ( p) ] ) rspcvly rprsn h auo-covaranc arx an h crosscovaranc vcor of h group SE flr. Thn, h channl can b prc as ( ) ( ) p = w o (3) an h corrsponng prcon SE s gvn by σ = σ p w o. In orr o proprly ploy h propos grop prcon chnqu, s ncssary o rn h nubr G consrng h channl corrlaon bwn h plo sybols. W cobn h plo sybols n a group, whos corrlaon valus ar largr han a hrshol lvl λ. Sulaon rsuls show ha h opu hrshol s n a rang of 0.95 o Alhough h opu corrlaon hrshol sowha crass as h axu Dopplr frquncy ncrass, ay b praccal o us a consan hrshol (.g., λ =0.95). To valua h prforanc of h propos prcon sch, Fg. 4 pcs h avrag spcral ffcncy n rs of h noralz group lay whn h propos group SE prcor s ploy wh λ =0.95. For coparson, h prforanc of h Wnr prcon wh U=5 an 5 s also pc. I can b sn ha h propos sch s qu ffcv n hgh obly nvronns an ha provs nar opu prforanc copar o h us of Wnr prcors. Th copuaonal coplxy s also copar n Tabl, whr h sapl corrlaon ncas whhr h channl corrlaon s calcula bas on a sybol-by-sybol or group-sybol bass. I can b sn ha h propos sch sgnfcanly rucs h plnaon coplxy copar o h Wnr flrs. V. CONCLUSION In hs papr, w hav consr h us of prc channl gan for h ployn of channl-awar chnqus n ul-usr OFD syss. Whn a Wnryp opu prcor s appl o h prcon of

5 channl gan, h prforanc of PF schulng s analyz an vrf by copur sulaon. I has bn shown ha h us of prc channl gan can sgnfcanly nhanc h prforanc of channl-awar chnqus n hgh obly nvronns unlss h channl prcon s svrly naccura. To allva h plnaon probl wh h us of Wnr prcors, w hav propos a group SE prcon sch. Th sulaon rsuls show ha h propos sch can prov nar opu prforanc whou plnaon coplxy probl. REFERENCES [] S. Aba,. Aarash an. Sawahash, Broaban Pack Wrlss Accss Incorporang gh-sp IP Pack Transsson, n Proc. of PIRC 00, pp , Sp. 00. [] A. J. Golsh an S.-G. Chua, Varabl-ra varabl-powr A for fang channls, IEEE Trans. on Cou., vol. 45, pp. 8-30, Oc [3] G. E. On,. ol, an K. J. ol, Aapv co oulaon wh prfc channl sa nforaon, n Proc. ISWC-00, pp. 9-0, 00. [4] G. E. On,. ol an K. J. ol,, Ipac of channl prcon on aapv co oulaon prforanc n Raylgh fang. IEEE Trans. on Vhcular Tch., vol. 3, pp , ay 004. [5] I. C. Wong, A. Fornza, R. W. ah, an B. L. Evans;, Long rang channl prcon for aapv OFD syss, n Proc. ACSSC 004., pp , Nov [6] A. Dul-alln, S. u an -alln, Long rang prcon aks aapv oulaon fasbl for ralsc obl rao channls, n Proc. CISS 000., pp. -6, 000. [7] P. ohr, S. Kasran an P. Robrson, Two-nsonal plosybol-a channl saon by Wnr flrng, n Proc. IEEE ASSP Conf., vol. 3, pp. -4, Apr [8] J. oon an Y.-. L, Prforanc analyss of opporunsc schulng wh paral channl nforaon, IEEE Trans. on Wrlss Coun., sub, 005. [9] F. Brggrn an R. Jann, Asypocally far schulng on fang channls, n Proc. IEEE Vhcular Tch. Conf., vol. 4, pp , Sp. 00. [0] S. Zhou an Gorgos B., ow accura channl prcon ns o b for rans-baforng wh aapv oulaon ovr Raylgh IO channls, IEEE Trans. on Wrlss Coun., vol. 3, pp , July 004. [] J.-W. Cho, Dsgn of aapv OFD wrlss ranscvrs, Ph. D. ssraon, Soul Naonal Unvrsy, Aug [] T.. Covr an J. A. Thoas, Elns of nforaon hory, John Wly & Son, 99. [3]. A. Dav, Orr sascs, Nw York: cgraw-ll, 98. Tabl. Sulaon conon. Spcral ffcncy (bps/z) =3, p = Ial cas No prcon (sulaon) 0.85 No prcon (analyss) x Wnr prcon (sulaon) x Wnr prcon (analyss) ρ ( σ ) Noalz lay ( ftp s ) Fg.. Spcral ffcncy wh prc channl gan whn = 8B. Spcral ffcncy =3, p =64 Avg. SINR 0B Avg. SINR 4B Avg. SINR 8B Avg. SINR B Avg. SINR -4B E-3 0. ( UG+ ) Prcon SE Fg.. Spcral ffcncy u o prcon rror. + ( U ) ( UG+ G) ( G+ ) (0) ( ) (0) No UD gan w U + w ( p) Fg. 3. Block agra of h group SE prcon sch. Tabl. Copuaonal coplxy. Spcral ffcncy (bps/z) =3, p =64 Ial cas No prcon 5x Wnr prcon 5x Wnr prcon 5x groupng Wnr prcon Noalz lay ( ftp ) s Fg. 4. Prforanc wh h us of h group SE prcor whn = 8B.