Codebook-Based Quantized MIMO Feedback for Closed-Loop Transmit Precoding

Transcription

1 MITSUISI ELECTRIC RESEARC LAORATORIES hp:// Codeook-ased Quanized MIMO Feedack for Closed-Loop Transmi Precoding Man-On Pun, Ron Pora, Phil Orlik, Jinyun Zhang, Toshiyuki Kuze TR Decemer 2009 Asrac Advanced quanizaion schemes are proposed for closed-loop ransmi precoding over correlaed muliple-inpu muliple-oupu (MIMO) channels in his work. Unlike he convenional schemes ha direcly quanize he MIMO channel covariance marix and feed ack each quanized marix elemen, he proposed schemes quanize he channel covariance marix y exploiing he common rank-one codeook shared y moile saions and ase saions. Compared o he convenional quanizaion schemes, he proposed quanizaion schemes can achieve comparale hroughpu performance wih more han 50% overhead reducion a he cos of affordale increase in compuaional complexiy. IEEE Asilomar Conference on Signals, Sysems, and Compuers This work may no e copied or reproduced in whole or in par for any commercial purpose. Permission o copy in whole or in par wihou paymen of fee is graned for nonprofi educaional and research purposes provided ha all such whole or parial copies include he following: a noice ha such copying is y permission of Misuishi Elecric Research Laoraories, Inc.; an acknowledgmen of he auhors and individual conriuions o he work; and all applicale porions of he copyrigh noice. Copying, reproducion, or repulishing for any oher purpose shall require a license wih paymen of fee o Misuishi Elecric Research Laoraories, Inc. All righs reserved. Copyrigh c Misuishi Elecric Research Laoraories, Inc., roadway, Camridge, Massachuses 02139

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3 CODEOOK-ASED QUANTIZED MIMO FEEDACK FOR CLOSED-LOOP TRANSMIT PRECODING Man-On Pun, Ron Pora, Philip Orlik, Jinyun Zhang and Toshiyuki Kuze ASTRACT Advanced quanizaion schemes are proposed for closedloop ransmi precoding over correlaed muliple-inpu muliple-oupu (MIMO) channels in his work. Unlike he convenional schemes ha direcly quanize he MIMO channel covariance marix and feed ack each quanized marix elemen, he proposed schemes quanize he channel covariance marix y exploiing he common rank-one codeook shared y moile saions and ase saions. Compared o he convenional quanizaion schemes, he proposed quanizaion schemes can achieve comparale hroughpu performance wih more han 50% overhead reducion a he cos of affordale increase in compuaional complexiy. Index Terms Quanized feedack, closed-loop ransmi precoding, MIMO. 1. INTRODUCTION Closed-loop (CL) ransmi precoding for muliple-inpu muliple oupu (MIMO) downlink (DL) ransmission has een well proven as an effecive and pracical capaciyachieving echnique [1]. Indeed, i has een sandardized in many emerging communicaions sysems such as IEEE m [2] and LTE [3]. In CL ransmi precoding, a moile saion (MS) firs esimaes he DL channel efore feeding ack he esimaed channel sae informaion (CSI) o he ase saion (S). Generally speaking, wo differen approaches are commonly employed in reurning he esimaed CSI o he S. Assuming ha he MS and S share a common codeook, he firs approach is designed o le he MS firs derive he opimal precoding codeword from he common codeook y exploiing he esimaed insananeous CSI. Afer ha, he MS feeds ack he opimal codeword index o he S. Upon receiving he feedack, he S precodes he DL daa wih he designaed codeword in he susequen DL Man-On Pun, Philip Orlik and Jinyun Zhang are wih Misuishi Elecric Research Laoraories, 201 roadway Camridge, MA 02139, U.S.A. ( s: {mpun, porlik, jzhang}@merl.com) Ron Pora, is wih InerDigial, 781 Third Avenue, King of Prussia, PA 19406, U.S.A. ( Ron.Pora@InerDigial.com) Toshiyuki Kuze is wih Misuishi Elecric Corporaion, Ofuna Kamakura, Kanagawa , Japan. ( Kuze.Toshiyuki@ah.MisuishiElecric.co.jp) ransmission unil i receives he nex precoding codeword from he MS. This approach has een demonsraed very effecive in improving sysem hroughpu over uncorrelaed MIMO channels. Fig. 1 Sysem schemaic of closed-loop ransmi precoding ased on long-erm channel covariance marix owever, he firs approach is handicapped y correlaed MIMO channels due o he fac ha exising codeooks are uniary and designed for uncorrelaed MIMO channels. To circumven his osacle, a second approach has een recenly proposed o feed ack he long-erm channel covariance marix o he S as illusraed in Fig. 1 [4]. Exploiing he long-erm channel covariance marix, oh S and MS adapively employ ransformed codeooks o opimize he DL precoding. In addiion o he performance improvemen, he second approach requires less frequen feedack due o he naure of he feedack as compared o he firs approach. Despie he aforemenioned advanages, unlike he firs approach in which he feedack informaion conains already quanized codeword indices, he MIMO channel covariance marix has o e firs quanized efore i can e pracically fed ack o he S. The convenional quanizaion mehod performs direc quanizaion on he covariance marix [2]. More specifically, i employs differen levels of quanizaion precision on he diagonal and upper-riangular elemens y exploiing he ermiian srucure of he covariance marix. Unforunaely, his simple scheme incurs large feedack overhead. In his work, we propose reduced-feedack quanizaion schemes y exploiing he common codeooks shared y he S and MS. Raher han direcly quanizing he MIMO channel covariance marix, quanizaion schemes are developed o represen he marix y using rank-one codewords eiher conained in he common codeooks or in a pre-defined seering vecor form. As a resul, he proposed

4 covariance marix quanizaion schemes can achieve good quanizaion accuracy wih susanially reduced feedack overhead a he cos of some affordale increase in compuaional complexiy. I should e emphasized ha he proposed quanized feedack schemes can e also employed for feeding ack he inerference covariance marix for applicaions such as inerference nulling and muli-user MIMO (MU-MIMO). Noaion: Vecors and marices are denoed y oldface leers. Furhermore, we use E {}, () * and () for expecaion, conjugae and ermiian ransposiion, respecively. 2. PROLEM FORMULATION We denoe y R he DL MIMO channel covariance marix. I should e emphasized ha R represens he channel covariance marix over a paricular sucarrier or resource lock in orhogonal frequency division modulaion (OFDM)-ased sysems. Exploiing he fac ha R is ermiian wih he real-valued diagonal elemens much larger han he asolue values of he complex-valued offdiagonal elemens, a simple direc quanizaion mehod has een proposed in IEEE m. More specifically, each diagonal elemen is quanized wih one i while each upper off-diagonal elemen wih four is, as shown in Fig. 2. As a resul, for N = 4, i requires oal 28 is or four yes o quanize R. In he sequel, his scheme is referred o as he direc quanizaion mehod (DQM). Fig. 2 Convenional direc quanizaion mehod proposed in IEEE m for for N = 4 [2]. Clearly, he amoun of overhead required y DQM grows in he order of N 2 for a marix of dimension N N. Furhermore, for OFDM sysems, he oal feedack overhead increases proporionally wih he numer of sucarriers or resource locks. Thus, i is desirale o reduce he quanized feedack overhead for each R. For presenaional simpliciy, we concenrae our following discussion on N = 4 while he discussion can e exended o oher values of N in a sraighforward manner. Alernaively, we oserve ha he covariance marix R can e decomposed ino he following form. R = UΛU (1) where U and Λ are 4 4 uniary and diagonal marices, respecively. Recall ha he MS and S share muliple common uniary codeooks of differen ranks. Inuiively speaking, if we can find a codeword V in he rank-4 common codeook such ha V U I, hen only he index of he chosen rank-4 codeword and four quanized real-valued { λ i; i = 1,2,3,4} are required o e reurned o he S, which sands for a susanial feedack overhead reducion compared o DQM. owever, wo prolems associaed wih his approach arise. Firs, he rank-4 codeook defined in he sandards is of a much smaller size compared o he lower-rank codeooks. As a resul, i is no guaraneed ha we can find a rank-4 codeword saisfying he requiremen of V U I. Second, considering a rank- 4 codeook of is, he compuaional complexiy involved in exhausively searching he opimal V is of he 3 order of O( 2 N ), which can e prohiiively expensive for a large N. In paricular, he second prolem ecomes more challenging for OFDM sysems wih a large numer sucarriers or resource locks. In he nex secion, we propose rank-one codeook-ased quanizaion schemes o cope wih hese wo prolems. 3. PROPOSED SCEMES We firs rewrie (1) ino he following form. P R = λp uu, (2) p= 1 where u p and λ p are he eigenvecors of lengh N 1 and real-valued eigenvalues of R wih rank ( R ) = P N. Wihou loss of generaliy, we assume λ1 λ2 λp. For correlaed channels under consideraion, we have P < N. Thus, for N = 4, we can safely assume ha P = 1 or P = 2 in pracice. Nex we assume ha he MS and S share a common rankone codeook of is, denoed y { v ; 1,2,,2 = }. Thus, if we can find wo rank-one codewords in he rankone codeook, { v1, v 2}, ha mach he firs wo principal vecors { u1, u 2}, hen only informaion aou he wo codeword indices and he raio eween heir corresponding eigenvalues is sufficien for he S o reconsruc R up o an unknown scalar. More specifically, if he common codeook is comprised of 2 rank-one codewords and he raio eween he wo eigenvalues is quanized wih is, he oal numer of feedack is is given y 2 +.

5 To reduce compuaional complexiy, we develop suopimal search algorihms o find he es-maching rankone codewords sequenially, raher han joinly. In he following, we will firs propose a Gram-Schmid-ased searching algorihm (GSSA) efore exploring differen variaions of he algorihm. The GSSA is summarized in he following seps. v, we firs find Sep 1: For a given rank-one codeook { } he codeword ha es maches he firs principal eigenvecor as m = arg max v Rv, (3) = 1,2,,2 wih λ 1 = vmrv. m Sep 2: Nex, we generae a new se of rank-one vecors { d } ha are orhogonal o v m y using he Gram- Schmid mehod: v ( vm v) vm d =, (4) v v v v for = 1,2,,2. ( m ) m Sep 3: Afer ha, we find a codeword in { d } ha es maches he second principal eigenvecor of as n = arg max d Rd, (5) = 1,2,,2 wih λ 2 = dn Rd. n Sep 4: Finally, we quanize he raio q = λ2 / λ1 ino a predefined se of hresholds. The feedack includes he wo indices of he winning eigenvecors { mn, } and he index of he quanized eigenvalue raio q. I is worhwhile o poin ou several ineresing properies relaed o he proposed rank-one quanizaion approach. Firs of all, ecause he rank-one common codeook is usually much larger han he higher-rank common codeooks, i is more likely for he proposed approach o find a good maching codeword for a given principle eigenvecor. Furhermore, he oal compuaional complexiy of GSSA is aou O( 2 N ) wih mos compuaion incurred in (3) and (5). This sands for a significan compuaional reducion compared o (1) of 3 O( 2 N ). ased on he aove Gram-Schmid algorihm, we can also derive algorihms wih differen variaions. For insance, raher han using he opimizaion ojecive funcion in Sep 3, we can employ he following opimizaion funcion. 2 n = arg min R λ ( v v + qd d ). (6) = 1,2,,2 1 m m 4. SIMULATION RESULTS In his secion, sysem-level simulaion resuls are provided o confirm he performance of he rank-one quanized feedack schemes proposed in he previous secion. We compare he performance of differen quanized feedack schemes in erms of he DL specral efficiency, assuming a minimum mean squared error (MMSE) receiver a he MS wih perfecly known inerference. We use he m 4- anenna codeooks (6i and 4i suse) and also examine he performance of a 4-i seering vecor given elow o quanize he srongly correced channels: 1 jπsin( θi ) 1 e sv i =, (7) j2πsin( θi ) 2 e j3πsin( θi ) e 1 π π where θ i = ( i ) wih i = 1,..., As shown in he simulaion, he seering-vecor approach is paricularly helpful in reducing compuaion and feedack overhead for correlaed anennas. We examine he performance of he following six quanized feedack schemes: 1. Perfec SV uses he sronges unquanized singular vecor of he average narrowand ransmi correlaion marix. The oal feedack overhead is infinie; 2. 4i+R uses he four-i codeook suse ransformed y he unquanized R. The oal feedack overhead is infinie; 3. 4i+VQ (6+6+1) uses he proposed vecor quanizaion scheme wih he 6-i rank-one codeook specified in he IEEE m. The oal feedack overhead is 13 is; 4. 4i+(4+4+1) uses he proposed 4-i seering-vecor quanizaion scheme as shown in (7). The oal feedack overhead is 9 is; 5. 4i+Quanized R uses he convenional scheme specified in he IEEE m o perform elemen-wise quanizaion. The oal feedack overhead is 28 is; 6. 6 i uses he m rank-1 6 is codeook only (no feedack of R ). Clearly, Perfec SV and 4i+R sand for he ideal feedack cases ha canno e realized in pracice. In he simulaion, he Macro and Uran Macro spaial channel models (SCM) wih an angular spread of 15 o are employed [2]. Two ypes of anennas configuraions are simulaed, namely he ULA wih four λ -spaced anennas 2 and wo λ -spaced cross-polarized array. We simulae an 2

6 OFDM sysem similar o ha in he IEEE m sandard [2]. We se he DL andwidh o four physical resource locks (equivalen o 800Kz), assuming one precoder per and. To model he fading environmen and sysem feedack delay, we se he MS moile speed o 3kmph while he delay equal o 5ms. Furhermore, we assume ha he DL channel esimaion is perfec. Finally, up o four users are seleced from a 4-user pool y exhausive selecion such ha he oal hroughpu is maximized. To invesigae he performance of he proposed schemes, we adop he IEEE m rank-one codeook in our simulaion. The raio of he second o firs eigenvalues is quanized o he neares poin o eiher 0.25 or 0.5, which requires only one-i feedack. The plos show he specral efficiency raio of a sysem employing various feedack schemes as compared o a feedack of he 4i codeook suse only (wihou R). (6+6+1) and 4i+VQ (4+4+1), ouperform he convenional DQM 4i+Quanized R y aou 5% wih 50% less feedack overhead. Fig. 4 DL specral efficiency raio as a funcion of SNR in Uran Macro SCM channel wih uniform linear array. Fig. 3 DL specral efficiency raio as a funcion of SNR in Uran Macro SCM channel wih cross polarized anennas. Fig. 3 shows he DL specral efficiency raio as a funcion of SNR in Uran Marco SCM channel wih cross polarized anennas. Inspecion of Fig. 3 suggess ha he proposed 4i+VQ (6+6+1) scheme achieves comparale performance as he convenional DQM 4 i + Quanized R wih less han 50% feedack overhead. Compared o he ideal Perfec SV, he proposed scheme has aou 20% loss of DL specral efficiency. Fig. 4 depics he DL specral efficiency in he Uran Marco SCM channel wih ULA. We can oserve he similar performance rend as shown in Fig. 3. Finally, we examine he performance of he quanized feedack schemes in he Suuran Marco SCM channel wih ULA. Ineresingly, Fig. 5 indicaes ha he wo proposed quanized feedack schemes, namely, 4i+VQ Fig. 5. DL specral efficiency raio as a funcion of SNR in Suuran Macro SCM channel wih uniform linear array. 5. APPLICATION TO EAMFORMING AND NULLING eamforming and nulling is a well known echnique for reducing inerference o adjacen cell co-channel users while a he same ime improving he SINR of he served user. This is more easily faciliaed in TDD sysems using sounding signals wherey each S esimaes is own user channel and he inerference correlaion marix and forms a

7 eamforming soluion which is a radeoff eween gain delivered o is user and leakage energy delivered o adjacen cell co-channel users. The soluion ypically adoped is 1 V = P{( Ri + α NoI) RS} where he operaor P{} i denoes he principal eigenvecor, Ri is he spaial correlaion of oher-cell users exchanged eween he Ss, R S is he spaial correlaion of he serving S user, α is a regularizaion facor, No is an esimae of he user s oal noise plus inerfering power and I is an ideniy marix. The same echnique can e faciliaed in FDD sysems y explicily esimaing he inerference correlaion marix, quanizing i using he echniques descried efore and feeding i ack o he S. Simulaion resuls of various quanizaion echniques are eyond he scope of his paper. 6. CONCLUSION Quanized feedack schemes have een devised for closed-loop ransmi precoding over correlaed MIMO channels y exploiing he common rank-one codeooks shared y he S and MS or predefined seering-vecor codeooks. Simulaion resuls have confirmed ha he proposed schemes can achieve comparale hroughpu performance wih more han 50% less feedack overhead, compared o he direc quanizaion mehod in he curren 16m specificaion. REFERENCES [1]. Sampah, P. Soica and A. Paulraj, Generalized linear precoder and decoder design for MIMO channels using he weighed MMSE crierion, IEEE Trans. Comm., Vol. 49, pp , Decemer [2] S. amii, The Draf IEEE m Sysem Descripion Documen, IEEE m-08/003r6. [3] 3GPP TR V7.2.0, Requiremens for Evolved UTRA (E-UTRA) and Evolved UTRAN (E-UTRAN), [4] V. Raghavan, R.W. eah and M. Sayeed, Sysemaic Codeook Designs for Quanized eamforming in Correlaed MIMO Channels, IEEE Journal on Seleced Areas in Communicaions, Vol. 25, pp , Sepemer 2007.