IMPACT OF LIMITED FEEDBACK ON MIMO- OFDM SYSTEMS USING JOINT BEAMFORMING

Transcription

1 IMPACT OF LIMITED FEEDBACK ON MIMO- OFDM SYSTEMS USING JOINT BEAMFORMING NAJOUA ACHOURA 1 AND RIDHA BOUALLEGUE 1 Department Natonal Engneerng School of Tuns, Tunsa najouaachoura@gmalcom SUP COM, 6 Tel Laboratory,Tunsa rdhabouallegue@supcomrnutn ABSTRACT In mult nput mult output antenna systems, beamformng s a technque for guardng aganst the negatve effects of fadng However, ths technque requres the transmtter to have perfect knowledge of the channel whch s often not avalable a pror A soluton to overcome ths problem s to desgn the beamformng vector usng a lmted number of feedback bts sent from the recever to the transmtter In the case of lmted feedback, the beamformng vector s lmted to le n a codebook that s known to both the transmtter and receverwhen the feedback s strctly lmted, mportant ssues are how to quantze the nformaton needed at the transmtter and how much mprovement n assocated performance can be obtaned as a functon of the amount of feedback avalablein ths paper channel quantzaton schema usng smple approach to codebook desgn (random vector quantzaton)s llustrated Performance results show that even wth a few bts of feedback, performance can be close to that wth perfect channel knowledge at the transmtter KEYWORDS MIMO, OFDM, Lnear precodng, CSIT, Random Vector Quantzaton 1 INTRODUCTION Multple-nput multple-output (MIMO) systems, whch use multple antennas at both transmtter and recever, provde spatal dversty that can be used to mtgate sgnal-level fluctuatons n fadng channels []When the channel s unknown to the transmtter, dversty can be obtaned by usng space-tme codes [3],[]When channel state nformaton (CSI) s avalable at the transmtter, however, dversty can be obtaned usng a smple approach known as transmt beamformng and receve combnng Compared wth space-tme codes, beamformng acheves the same dversty order as well as addtonal array gan, thus t can sgnfcantly mprove system performance Ths approach, however, requres knowledge of the transmt beamformng vector at the transmtter In practce, CSIT must be provded to the BS by some form of feedback CSIT feedback schemes are a very actve area of research (see for example [13] and the specal ssue [14] for a farly complete lst of references) In bref, we may dentfy three broad famles: 1) open-loop schemes based on channel recprocty and uplnk tranng symbols, applcable to Tme-Dvson Duplexng (TDD); ) closed-loop schemes based on feedng back the unquantzed channel coeffcents (analog feedback); 3) closed-loop schemes based on explct quantzaton of the channel vectors and on feedng back quantzaton bts, sutably channelencoded (dgtal feedback) When the uplnk and downlnk channels are not recprocal (as n a frequency dvson duplexng system), ths necesstates that the recever nforms the transmtter about the desred transmt beamformng vector through a feedback control channel The beamformng technques proposed DOI : 10511/jwmn

2 for narrowband channels can be easly extended to frequency selectve channels by employng orthogonal frequency dvson multplexng (OFDM) The combnaton of MIMO and OFDM (MIMO-OFDM), converts a broadband MIMO channel nto a set of parallel narrowband MIMO channels, one for each subcarrer [10] Transmt beamformng can be performed ndependently for each subcarrer of MIMO-OFDM In non-recprocal channels, ths means requres that the MIMO-OFDM recever calculates and sends back to the transmtter the optmal beamformng vector for every subcarrer Practcally, the feedback rate can be managed by usng lmted feedback technques where the beamformng vectors are quantzed usng a beamformng codebook desgned for narrowband MIMO channels [17] For MIMO-OFDM s structures dfferent approaches are possble In ths paper, jont beamformng, that conssts n the extenson to the transmtter sde of the classcal receve beamformng, s used We focused ths analyse on the mpact of lmted CSI on the transmtter on the performance of such system Ths paper s organzed as follows In Secton we present the basc system model n bref Secton 3 ntroduce channel quantzaton lmted feedback model, random vector quantzaton s presented n secton 4 Fnally n Secton 5 some smulaton results and conclusons are presented SYSTEM MODEL In adaptve Beamformng, an array of antennas s exploted to reach maxmum recepton n a specfed drecton: the dea s to estmate the sgnal arrval from the desred drecton (n the presence of nose) whle sgnals of the same frequency from other drectons are not accepted [] Ths can be acheved by varyng the weghts of each of the antennas used n the array Ths spatal separaton ams to separate the desred sgnal from the nterferng sgnals In adaptve beamformng the optmum weghts are computed usng complex algorthms based upon dfferent crtera The communcaton over a frequency selectve MIMO channel wth N T transmts and N R receve antenna can be represented n mult-carrer fashon as: y = H s + n 1 k N (1) k k k k n 1 Where k denotes the carrer ndex, N s the number of carrers, T s the transmtted nr nt n 1 vector, H k s the channel matrx, y R k s the receved sgnal vector, and n R 1 n k s a zero-mean crcularly symmetrc complex Gaussan nose vector wth arbtrary covarance matrx R k Snce transmt beamformng s used at each carrer, the transmtted sgnal s: s = b x 1 k N () k k k s k Where b k s the transmt beamvector and x k s the transmtted symbol at the k th carrer []The recever also uses beamformng: H xˆ = a y 1 k N (3) k k k n 1 Where a R k s the receve vector and x k s estmated symbol at the k th carrer The transmtted s constraned n ts average transmt power as: { } N N E s k = bk Pt k = 1 k = 1 where P T s the power per block-transmsson Employng lmted feedback n coherent MIMO- OFDM communcaton systems requres cooperaton between the transmtter and recever At (4) 40

3 the recepton, the estmate of the forward lnk channel matrx H s used to desgn feedback that the transmtter uses to adapt the transmtted sgnal to the channel There are two approaches to desgn feedback: quantzng the channel or quantzng propertes of the transmtted sgnal For most closed-loop schemes, ether method can be employed It wll be apparent, however, that channel quantzaton offers an ntutvely smple approach to closedloop MIMO, but lacks the performance of more specalzed feedback methods 3 CHANNEL QUANTIZATION The basc dea behnd closed-loop MIMO s to adapt the transmtted sgnal to the channel One approach to lmted feedback s to employ channel quantzaton, whch s llustrated n Fg 1 Ths problem s reformulated as a Vector Quantzaton problem (VQ) by stackng the columns of the channel matrx H nto a Mr Mt dmensonal complex vector h vec The vector h vec s then quantzed usng a VQ algorthm A vector quantzaton works by mappng a complex valued vector nto one of a fnte number of vector realzatons The mappng s usually desgned to mnmze some sort of dstorton functon such as the average mean squared error (MSE) between the nput vector and the quantzed vector s 1 [k] s M [k F[k] Recever Precoder matrx usng {F1, F B } Channel Quantzaton usng {F 1, F B } Fgure 1 Lmted feedback lnear precoded MIMO system Sendng a quantzed verson of the forward lnk channel from recever to transmtter gves the transmtter more flexblty to choose among dfferent space-tme sgnalng technques Intutvely, one mght expect that a random selecton of matrces n the codebook F s lkely to result n a large subspace dstance between any par of matrces n the codebook Ths ntuton s vald for a large number of antennas Mt, and s related to the fact that two vectors wth d components become orthogonal (wth probablty one) as the length becomes large In the case of a random MIMO channel wth d components, the columns of the optmal precodng matrx are egenvectors of the channel covarance matrx, whch are sotropcally dstrbuted These consderatons motvated the Random vector quantzaton (RVQ) scheme proposed n [7], n whch the elements of the codebook F are ndependently chosen random untary matrces (e, Fk*Fk = I for each k)when used for beamformng n a MISO channel, RVQ s asymptotcally optmal n the sense that t acheves the maxmum rate over any codebook Furthermore, the achevable rate can be computed for both MISO and MIMO channels [7] Here asymptotc means for a large system n whch the number of antennas Mr and Mt each go to nfnty wth fxed rato (or n the MISO case Mt goes to nfnty), whle also fxng B/MtM, the number of feedback bts per dmenson 41

4 31 Dgtal Channel Feedback Model At the begnnng, each recever quantzes ts channel to B bts and feeds back the bts perfectly to the access pont When each moble has a sngle antenna (N=1), vector quantzaton s performed usng a codebook C that conssts of B M-dmensonal unt norm vectors C { w, L w B }Each recever quantzes ts channel vector to the quantzaton vector that 1 forms the mnmum angle to t [4] [5] Thus, user ι quantzes ts channel to h ˆ, chosen accordng to: ˆ arg mn sn h = ( ( h, w )) w= w1, L, w B and feeds the quantzaton ndex back to the transmtter In ths work we use random vector quantzaton (RVQ), n whch each of the B quantzaton vectors s ndependently chosen from the sotropc dstrbuton on the M-dmensonal unt sphere [6] Each recever s assumed to use a dfferent and ndependently generated codebook, and we analyze performance averaged over the dstrbuton of random codebooks When Ν > 1, the quantzaton codebook conssts of matrces and the dstance metrc can be approprately defned Furthermore, random quantzaton corresponds to choosng the quantzaton matrces ndependently from the set of all untary matrces 3 Lnear Precodng After recevng the quantzaton ndces from each of the mobles, the AP uses lnear precodng to transmt data to the mobles When N = 1, we consder the smple strategy of zero-forcng beamformng (ZFBF) Snce the transmtter does not have perfect CSI, ZFBF s performed based on the quantzatons nstead of the channel realzatons When ZFBF s used, the transmt M vector s defned as x = v s where each σι s a scalar (chosen complex Gaussan wth = 1 power P/M) ntended for the ι-th recever, and and vι CΜ s the beamformng vector for the ι-th recever The beamformng vectors v1,, v M are chosen as the normalzed rows of the matrx hˆ,, ˆ K h M 1, and thus they satsfy v j = 1 for all ˆ H h v j = 0 for all ϕ 6= ι The resultng SINR at the ι-th moble s [8]: S IN R = 1 + P H h v M P H j h v M j The achevable long-term average rate s the expectaton of log (1+ΣΙΝΡι) over the dstrbuton of the fadng and RVQ When Ν > 1, ZFBF can be generalzed to block dagonalzaton [9] 4 RANDOM VECTOR QUANTIZATION In [1], authors analyzed, wth lmted channel knowledge at the transmtter, the channel capacty wth perfect channel knowledge at the recever, Specfcally, the optmal beamformer s quantzed at the recever, and the quantzed verson s relayed back to the transmtter Gven the quantzaton codebook C = { w1, L w } B, whch s also known a pror at the transmtter, and the channel H, the recever selects the quantzed beamformng vector to maxmze the nstantaneous rate, [11] 4

5 { ρ Hw j } w( H ) = arg max log(1 + ) ν j V where ρ = 1 σ n s the background sgnal-to-nose rato (SNR) The (uncoded) ndex for the ratemaxmzng beamformng vector s relayed to the transmtter va an error-free feedback lnk The capacty depends on the beamformng codebook V and B Wth unlmted feedback (B ) the w(h) that maxmzes the capacty s the egenvector of H*H, whch corresponds to the maxmum egenvalue We wll assume that the codebook vectors are ndependent and sotropcally dstrbuted over the unt sphere It s shown n [1], that ths RVQ scheme s optmal (e, maxmzes the achevable rate) n the large system lmt n whch (B,Nt,Nr) wth fxed normalzed feedback B = B/Nt and Nr = Nr/Nt (For the MISO channel Nr = 1) Furthermore, the correspondng capacty grows as log(ρnt), whch s the same order-growth as wth perfect channel knowledge at the transmtter Although strctly speakng, RVQ s suboptmal for a fnte sze system, numercal results ndcate that the average performance s often ndstngushable from the performance wth optmzed codebooks [1], [14] 5 SIMULATIONS RESULTS: In ths secton, we evaluate the mpact of workng wth lmted feedback; wtch s more practcal, on system s performance, especally on the bt error rate We consder only the case of one user (mono-user system) That means there s no need to user selecton algorthms and the s no nterference Fg shows the system s performance when there s two antenna n the transmtter and only one antenna on the recepton (MISO system) perfect cst -1 quantzed cst 10 - bt error rate SINR(dB) Fgure Nt=, Nr=1 (wth perfect channel knowledge) Results show that for Nt = and Nr=1, the Bt error rate wth perfect channel knowledge at both the transmtter and recever s larger than the rate wth random vector quantfed feedback And ths s perfectly expected so the blue curve s consdered as the deal case 43

6 perfect cst - quantzed cst 10 - bt error rate SINR(dB) Fgure 3 Nt=, Nr= In Fgure 3, we consder MIMO system wth two antennas both n the transmtter and the recever, usng the same parameters Results are better here so red curve wtch represents quantfed feedback s more close to the deal case In other hand, we consder the case where we use channel estmaton n fgure 4, we consder the case when all tranng sequences are dedcated for estmaton e there s no data blocs We show estmaton s result for orthogonal phase shft sequences, In fact we can easly remark degradaton of performance between the two fgures, ths of course can be explaned by the addton of two types of error: error due to channel estmaton transmtted by feedback and the second error called quantzaton error perfect cst -1 quantzed cst 10-1 bt error rate SINR(dB) 3 CONCLUSIONS Fgure 4 Nt=, Nr=1 (wth channel estmaton) Ths paper outlnes a general framework for enablng lmted feedback n closed-loop MIMO- OFDM systems We revew the applcaton of lmted feedback to MIMO communcaton Numercal examples llustrate that relatvely lttle feedback can provde substantal performance mprovements 44

7 Channel estmaton error and channel evoluton wll defntely compromse expected performance mprovements, but smulatons and expermental results are requred to determne how recent the feedback bts must be to mantan satsfactory performance More work s also needed n the area of lmted feedback applcatons n MIMO-OFDM systems In fact, a more practcal technque s to feed back nformaton on a select subset of tones and then use nterpolaton technques Other applcatons of lmted feedback such as for mult-user MIMO channels are promsng areas for nvestgaton REFERENCES [1] D J Love, R Heath, W Santpach, and M L Hong, What s the value of lmted feedback for MIMO channels IEEE Commun Mag, vol 4, no 10, pp 54 59, Oct 004 [] S M Alamout, A smple transmt dversty technque for wreless communcatons, IEEE J Select Areas Commun, vol 16, pp , Oct 1998 [3] A Iserte, A Perez-Nera, D Palomar, and M Lagunas, Power allocaton technques for jont beamformng n OFDM-MIMO channels, Proceedngs EUSIPCO 00, (France), September 00 [4] DJ Love, R Heath, and T Strohmer, Grassmannan beamformng for mmo wreless systems, IEEE Trans Inform Theory, vol 49, no 10, Oct 003 [5] C Au-Yeung and D Love, On the Performance of Random Vector Quantzaton Lmted Feedback Beamformng n a MISO System, IEEE Transactons on Wreless Communcatons, vol 6, pp , Feb 007 [6] W Santpach and ML Hong, Asymptotc capacty of beamformng wth lmted feedback, n Proceedngs of Int Symp Inform Theory, July 004, p 90 [7] RFrancsco and T M Slock, An Optmzed Untary Beamformng Technque for MIMO Broadcast Channels», IEEE transacton on wreless communcatons, vol9, no 3, march 010 [8] N Ravndran, and N Jndal, Mult-User Dversty vs Accurate Channel State Informaton n MIMO Downlnk Channels, IEEE Trans Communcatons, July 009 [9] N Jndal, MIMO Broadcast Channels wth Dgtal Channel Feedback, Aslomar Conference on Sgnals, Systems, and Computers, Aslomar, CA, Oct 006 [10] H Bolcske, M Borgmann, and A Paulraj, Impact of the propagaton envronment on the performance of space-frequency coded MIMO-OFDM, IEEE J Select Areas Commun, vol 1, pp , Apr 003 [11] W Santpach, M Hong Optmzaton of Tranng and Feedback Overhead for Beamformng over Block Fadng Channels IEEE Trans Info Theory, August 009 [1] W Santpach and M L Hong, Capacty of multple-antenna fadng channel wth quantzed precodng matrx, IEEE Trans Info Theory, vol 55, no 3, pp , Mar 009 [13] G Care, N Jndal, and N Ravndran, Multuser MIMO Downlnk Made Practcal: Achevable Rates wth Smple Channel State Estmaton and Feedback Schemes, Submtted to IEEE Trans Informaton Theory, Nov 007, Arxv preprnt csit/071164v1 [14] IEEE Journal on Selected Areas on Communcatons (Specal Issue on Lmted Feedback), Nov