Co-channel Interference Cancellation for Downlink Block Transmission with Cyclic Prefix

Transcription

1 o-cannel Interference ancellaton for ownlnk lock Transmsson wt yclc Prefx Kazunor ayas an eak Saka Grauate Scool Informatcs, Kyoto Unversty, Yosa onmac Sakyo-ku, Kyoto, -8, JAPAN e-mal: Abstract Ts paper proposes co-cannel nterference cancellaton / equalzaton metos for ownlnk block transmsson wt cyclc prefx n mult-cell envronments usng multple recevng antennas an teratve least-square (LS) nterference cancellaton ue to crculant structure cannel matrces n block transmsson emes wt cyclc prefx, pseuo nverse matrces, wc s requre n te teratve LS meto, can be obtane wt low computatonal complexty an s multple to te receve sgnal n an effcent manner omputer smulaton results sow tat te propose teratve LS nterference cancellaton an equalzaton meto can aceve almost te same bt error rate (ER) performance as an mnmum mean-squareerror (MMSE) approac wt lower computatonal complexty an wtout nose varance estmaton I INTROUTION lock transmsson emes wt cyclc prefx (P), suc as ortogonal frequency vson multplexng (OFM)[] an sngle-carrer block transmsson wt P (S-P)[]- [], ave been apple to moble communcatons systems, suc as WMAX system, were ortogonal frequency vson multple access (OFMA)[] s aopte for te pyscal layer /meum access control layer protocol One te most sgnfcant problems n suc moble communcatons envronments s te nterference from negborng cells, especally for te case wt frequency reuse factor In orer to cope wt te problem, we ave propose a ownlnk cannel estmaton eme for mult-cell block transmsson systems[], were not only a cannel response between a esre base staton (S) an a moble termnal (MT) but also responses between nterferng Ss an te MT are obtane smultaneously, by takng avantage te sgnal structure te block transmsson wt cyclc prefx In ts paper, assumng te avalablty te cannel state nformaton (SI) te esre an te nterference sgnals, we propose co-cannel nterference cancellaton / equalzaton metos for ownlnk block transmsson wt cyclc prefx usng multple recevng antennas an teratve least square (LS) nterference cancellaton, wc s also employe n [] ue to te crculant structure te cannel matrces n te block transmsson systems wt cyclc prefx, te pseuo nverse matrces, wc s requre n te teratve LS meto, can be obtane wt low computatonal complexty an s multple to te receve sgnal vector n an effcent manner omputer smulaton results sow tat te propose teratve LS nterference cancellaton an equalzaton meto can aceve almost te same bt error rate (ER) performance as an mnmum mean-square-error (MMSE) approac wt lower computatonal complexty an wtout nose varance estmaton II SIGNAL MOELING Te followng notatons are use for erbng te propose system K s te lengt te guar nterval, M s te FFT sze, an L s te cannel orer An M M entty matrx wll be enote as I M, an a rete Fourer transform (FT) matrx sze M M, wose (; j) element s p e ß()(j) j M M, as We wll use E[ ] to enote ensemble average, ( ) T for transpose, ( ) for ermtan transpose, ag[ ] for agonal matrx, an ( ) Λ for complex conjugate A OFMA Fg sows a system moel consere n ts paper, were sgnals from one esre base staton an U nterferng base statons are receve at a moble termnal, wc as Q antenna elements Assumng tat te FT wnow tmngs all te base statons are syncronze, an tat te lengt te cyclc prefx K s greater tan or equal to cannel orer L, te receve sgnal vector at te q-t antenna after te cyclc prefx removal can be wrtten as r (q) (q) s s n (q) ; were s [s ;:::;s M ]T enotes a transmtte sgnal block te esre base staton, s [s ;:::;s M ]T, ( ;:::;U) s a transmtte sgnal block from te -t nterferng base staton an n (q) s atve wte nose wt a covarance matrx ffn I M ere, note tat all te elements s wll be etecte n te moble termnal regarless subcarrer allocaton an, (q :::Q; :::;U) are M M crculant cannel matrces efne as ;q ::: ;q ::: ;q ; ()

2 esre sgnal s esre sgnal s Unesre sgnals s u, s u,u u, u, n n r r Unesre sgnals s u, s u,u u, u, n n r r Fg System Moel OFMA Fg System Moel S-P were f ;q ;:::; g enotes a cannel mpulse response between te esre base staton an te q-t antenna te termnal, an ;q ::: ;q ::: ;q ; () were f ;q ;:::; g, ( ;:::;U) enotes a cannel mpulse response between te -t nterferng base staton an te q-t antenna te termnal, respectvely After te FT at te recever, te receve sgnal vector s gven by R (q) r(q) s were N (q) n (q) an ag[ (q;) ag[(q;) s N (q) ; () ;:::; (q;m) ] ; () ;:::; (q;m) ] : () y stackng Q receve sgnal vectors R (q), (q :::Q), we obtan a receve sgnal vector sze QM as ef T R R T ::: R T were Λ N Λ Λ u; ::: Λ Λ Λ s Λ Λ u; ::: Λ N T :::N TΛ T s s u; s N N Λ s N; () T :::Λ, Λ T Λ :::Λ an S-P Fg sows te system moel consere n ts paper for te case te S-P transmsson Wt te same assumptons as n te OFMA case, te receve sgnal vector at te q-t antenna s gven by r (q) (q) s s n (q) : (8) Also, stackng Q receve sgnal vectors r (q), (q :::Q), we obtan a receve sgnal vector as r ef r T ::: r T T u; ::: s u; ::: were T ::: T s s u; s n n s n; (9) T ::: T T an n n T :::n TΛ T T, III O-ANNEL INTERFERENE ANELLATION / EQUALIZATION In ts secton, we conser MMSE base an teratve LS base co-cannel nterference cancellaton an equalzaton metos for bot te mult-carrer (OFMA) an te snglecarrer (S-P) cases A OFMA ) MMSE approac: Fg sows te confguraton te MMSE base approac for OFMA system enotng M QM matrx te MMSE nterference canceller / equalzer as F, te estmate s s obtane as ^s mmse F R ; F Λ s F Λ s F N: ()

3 Fg r r R F MMSE nterference canceller / equalzer: OFMA y solvng a mnmzaton problem cost functon J E jjs F R jj Λ ; () MMSE canceller / equalzer matrx F s obtane as X U F Λ Λ Λ Λ Λ ff n I QM ; () ff s were ffs enotes te varance s an s Note tat te nverse large non-agonal matrx, wc results n g computatonal complexty n general, s requre n orer to obtan F ) Iteratve LS approac: If we look on te secon an te tr terms n () as nose, we can smply obtan te LS estmate s as ^s Λy R ; () were Λ y s a pseuo nverse matrx Λ, wc s calculate as were Λ y Λ Λ Λ PQ q Λ(q) Λ ::: ; ()» (q;)λ P Qp j (p;) (q;m)λ P Qp : () j (p;m) j (q) ag ::: j In te same way, te LS estmate s s obtane as were ^s Λy R ; () Λ y Λ Λ Λ PQ q Λ(q) Λ (q) Λ ::: ; () an» u (q) ag (q;)λ P (q;m)λ Qp ::: P j (p;) j Qq : (8) j (p;m) j Note tat, altoug te estmaton accuracy ^s s worse tan ^s mmse, te pseuonverse matrces Λ y an Λy can be obtane wtout any g computatonal complexty an te multplcaton to te receve sgnal s also aceve effcently ue to te agonal structure Moreover, usng ^s, te estmaton s can be mprove as ^s Λy R Λ ^s an te estmaton s can be also mprove as ^s Λ ^s U X j j Λ u;j^s u;j ; (9) A : () enotng te estmate s an s at te k-t teraton ts process as ^s k an ^sk, respectvely, te teratve LS nterference cancellaton an equalzaton eme s gven as follows: ) k ) Intal estmaton s : ^s k Λy R ) Intal estmaton s, ( ;:::;U): ) k k ) Estmaton s : ^s k Λy ^s k Λy R R ) Estmaton s, ( ;:::;U): ^s k Λ ^s k Λ ^s k j j Λ u;j^s k u;j ) Go to step Te confguraton te teratve LS meto s sown n Fg, were te number nterferng base statons s set to be U for te smplcty Snce te matrces (q), Λ(q), (q), an Λ(q) are all agonal matrx, te teratve LS meto can be effcently realze by usng te same confguraton as one-tap frequency oman equalzers A S-P ) MMSE approac: For te case te S-P transmsson, te output te MMSE nterference canceller / equalzer s gven by ^s F r ; () were te M QM matrx F s obtane as F U X ff n I QM : () ffs

4 r r swtc Γ Γ Λ Λ Γ u, Γ u, Λ u, Λ u, u, r r swtc Γ Γ Λ Λ Γ u, Γ u, Λ u, Λ u, u, Fg Iteratve LS nterference canceller / equalzer: OFMA Fg Iteratve LS nterference canceller / equalzer: S-P Fg r r r F MMSE nterference canceller / equalzer: S-P ) Iteratve LS approac: omparng () wt (9), we can easly obtan te teratve LS nterference cancellaton an equalzaton meto for te S-P transmsson Te teratve algortm s gven as follows: ) k ) Intal estmaton s : ^s k y r ) Intal estmaton s, ( ;:::;U): ) k k ) Estmaton s : ^s k y r an Te pseuo nverse y an y can be smplfe as y PQ q (q) P Q q Λ(q) Q X q ::: Λ Λ ; () y ::: ; () were (q) an (q) are efne n () an (8), respectvely Usng te smplfe expressons te pseuo nverse matrces, te teratve LS nterference canceller / equalzer for te S-P also as a smple confguraton as sown n Fg ere, note tat no FT or nverse FT operaton s requre n te teratve process IV OMPUTER SIMULATION ^s k y r ^s k In orer to confrm te performance te propose metos, computer smulatons are conucte wt te followng system parameters; Mo/emo eme: QPSK coerent ) Estmaton s, ( ;:::;U): etecton, symbols per block: M 8, lengt cyclc prefx: K, number antennas: Q or, cannel ^s k ^s k u;j^s k u;j A orer: L, cannel moel: -pat frequency selectve j Rayleg fang cannel, number nterferng base statons: j U, cannel nose: atve wte Gaussan nose (AWGN) ) Go to step Te sgnal to nose power rato (SNR) per antenna s set to be [] Also, all te subcarrers or tme slots te sgnals

5 OFMA, SNR/antenna S-P, SNR/antenna MMSE (-antenna) Iteratve LS (-antenna, ar) Iteratve LS (-antenna, st) Iteratve LS (-antenna, st) Iteratve LS (-antenna, ar) t Error Rate e- MMSE (-antenna) Iteratve LS (-antenna, ar) Iteratve LS (-antenna, st) t Error Rate e- Iteratve LS (-antenna, ar) Iteratve LS (-antenna, st) MMSE (-antenna) e- e- MMSE (-antenna) e- # Iteratons e- # Iteratons Fg t Error Rate Performance: OFMA Fg 8 t Error Rate Performance: S-P from te esre base staton are assume to be use for te ata transmsson te moble termnal Fg sows te ER versus te number teratons te propose teratve LS nterference cancellaton an equalzaton meto for te OFMA system In te fgure, st means st ecson, wc correspons to te algortm sown n Sec III-A, an ar means an ntroucton ar ecson for eac estmate s or s Te performance te MMSE approac s also plotte n te same fgure From te fgure, we can see tat teratve LS approac wt st ecson can aceve comparable performance as te MMSE approac wt aroun teratons, wle te performance te MMSE approac s te best among te tree metos We can also see tat te ntroucton te ar ecson egraes te performance for te case te OFMA system Fg 8 sows te ER versus te number teratons te propose teratve LS nterference cancellaton an equalzaton meto for te S-P system We can also see tat te teratve LS approac wt st ecson can aceve almost te same performance as te MMSE meto wt only teratons For te case S-P system, te ntroucton te ar ecson coul mprove te ER performance, wle t ncreases te computatonal complexty ue to te FFT an IFFT operaton n te teratve process So far, we on t ave analytcal explanatons for ts penomenon, owever, te prncple turbo sgnal processng use n te MMSEbase turbo equalzer[],[8] may gve us an nsgt nto te penomenon emes omputer smulaton results sow tat te teratve LS base approac can aceve comparable performance to tat te MMSE approac wt only teratons Moreover, for te case te S-P transmsson, te teratve LS wt te ar ecson coul outperform te MMSE meto Future stuy wll nclue te analytcal reasonng te fference n performance between te ar an st ecsons, an te ntroucton error correctng coe or belef propagaton base teratve sgnal processng REFERENES [] S ara an P Prasa, Overvew multcarrer MA, IEEE ommun Mag, vol, pp, ec 99 [] Sar, G Karam an I Jeanclaue, Transmsson tecnques for gtal terrestral TV broacastng, IEEE ommun Mag, vol, pp 9, Feb 99 [] Falconer, S L Aryavstakul, A enyamn-seeyar an Eson, Frequency oman equalzaton for sngle-carrer broaban wreless system, IEEE ommun Mag, vol, pp8, Apr [] Z Wang an G Gannaks, Wreless multcarrer communcatons, IEEE Sgnal Processng Mag, vol, pp98, May [] IEEE St 8e, Ar nterface for fxe an moble broaban wreless access systems amenment for pyscal an meum access control layers for combne fxe an moble operaton n lcense bans, IEEE, [] K ayas an Saka, ownlnk cannel estmaton for multcell block transmsson systems wt cyclc prefx, Proc VT Sprng, pp -8, Apr [] Reynols an X Wang, Low complexty turbo-equalzaton for versty cannels, Sgnal Processng, vol 8, no, pp 98999, May [8] M Tucler, R Koetter an A Snger, Turbo equalzaton: Prncples an new results, IEEE Trans ommun, vol, no, pp, May V ONLUSION We ave propose co-cannel nterference cancellaton an equalzaton metos for ownlnk block transmsson wt cyclc prefx n mult-cell envronments, assumng te avalablty te cannel state nformaton not only te esre base staton an te moble termnal, but also te nterferng base statons an te termnal We ave consere te MMSE base meto as a performance bencmark an te smple teratve LS base approac for bot te OFMA an te S-P