On Space-Frequency Water-Filling Precoding for Multi-User MIMO Communications

Transcription

1 Proceedngs of the World ongress on Engneerng 05 Vol I WE 05, July - 3, 05, London, U.. On Space-Frequency Water-Fllng Precodng for Mult-User MIMO ommuncatons Yu-uan hang, Ye-Shun Shen, Fang-Bau Ueng and Shao-ua sa Abstract Multuser mult-nput mult-output (MU-MIMO) system has been wdely used n 4G communcaton system. MU-MIMO has hgh data rate and mproved capacty, however, t has multuser nterference (MUI) and multple access nterference (MAI). Block dagonalzaton (BD) s one of the methods to solve MUI and MAI, whch uses precodng algorthm to separate each user n the system. A generalzed zero-forcng channel nverson (GZI) algorthm s the smplest precodng method to mprove BD. owever, the BD/GZI algorthms use unform power dstrbuton. he water-fllng technology performs power allocaton based on channel envronment of each user. In ths paper, the BD/GZI algorthms are combned wth water-fllng technology to perform power allocaton and MUI/MAI cancellaton for the MU-MIMO systems. he proposed algorthms are wth space-frequency water-fllng. Some smulaton examples are gven to demonstrate the effectveness of the proposed algorthm. Index erms block dagonalzaton, water-fllng, optmal power allocaton, multuser mult-nput mult-output. I. IRODUIO E new generaton of wreless communcaton systems s provdng multmeda servces that requre very hgh data rates. he hgh spectral effcency can be acheved by usng multple antennas at both the transmtter and recever, so multple-nput multple-output (MIMO) systems have ganed popularty due to ther capablty n delverng hgh spectral effcency and ther robust performance aganst fadng. MIMO communcaton technologes have recently receved much nterest due to the promsng capacty gan when employng multple transmt and receve antennas. Informaton theoretc results show that MIMO systems can offer sgnfcant capacty gans over tradtonal sngle-nput sngle-output systems. hs capacty ncrease s enabled by the fact that the sgnals from each ndvdual transmtter appear hghly uncorrelated at each of the receve antennas n rch scatterng wreless envronments. he recever can explot these dfferences n spatal sgnatures to separate the sgnals orgnated from dfferent transmt antennas. In multpath channel, the receved sgnal n a MIMO recever s corrupted by the nter-symbol nterference (ISI), spatal nterference, and co-antenna nterference (AI). Sngle-user MIMO (SU-MIMO) consders only the dmensons of multple antennas for a sngle moble devce. owever, he authors are wth the Department of Electrcal Engneerng, atonal hung-sng Unversty, awan (e-mal: chungyukuan@hotmal.com; fbueng@nchu.edu.tw; c7643ohn@yahoo.com.tw). Ye-Shun Shen s wth the atonal Formosa Unversty (e-mal: ys.shen@msa.hnet.net). ISB: ISS: (Prnt); ISS: (Onlne) multuser MIMO (MU-MIMO) can deploy multple users as spatally dstrbuted transmsson resources at the cost of more complex sgnal processng, and s also known as spatal dvson multple access (SDMA). hus, multuser MIMO consders the overall capacty of network when several users are accessng the same lnk smultaneously. Due to transmsson array gan, dversty gan, spatal multplexng gan and nterference cancellaton gan, MIMO technques can ncrease system throughput and transmsson relablty wthout ncreasng the requred bandwdth that makes MIMO communcaton technologes become one of the most promsng ways for wreless communcaton by drty paper codng (DP) [-3]. he purpose of DP s to pre-cancel nterference at the transmtter usng know full channel state nformaton (SI). Block dagonalzaton (BD) s one of the well-known precodng algorthms near DP technques [4-5]. A generalzed zero-forcng channel nverson (GZI) algorthm s the smplest precodng method to mprove BD. Water-fllng technque has been proposed by [8] and has been used n MIMO system that uses each antenna SI to fnd maxmum egenvalue to do power allocaton as the spatal doman water fllng. In [5, 7, 9, 7], the spatal doman water-fllng wth BD algorthm s employed n multuser MIMO system to fnd maxmum sum capacty. he frequency doman water-fllng technque has been proposed by [3, 4] that the tme-doman sgnal s transferred to frequency doman and then each subcarrer s water- fllng processed. In ths paper, the BD/GZI algorthms are combned wth both spatal-doman and frequency-doman water-fllng technologes to perform power allocaton and MUI/MAI cancellaton for the MU-MIMO systems. he rest of ths paper s organzed as follows. In Secton, the BD precodng algorthm and GZI precodng algorthm for MU-MIMO downlnk system s descrbed. he proposed spatal-frequency water-fllng algorthm s descrbed n Secton 3. Smulaton results and conclusons are provded n Secton 4 and Secton 5, respectvely. otaton: Vectors and matrces are denoted by boldface letters; superscrpts of,,, and denote the complex conugate, transpose, ermtan transpose, and nverse, respectvely; stands for the ronecker product; and dag {} denotes a dagonal matrx; I s the dentty matrx; E{} denotes the statstcal expectaton. II. BLO DIAGOALIZAIO FOR MULIUSER MIMO SYSEM A. Block Dagonalzaton he multuser MIMO downlnk system wth WE 05

2 Proceedngs of the World ongress on Engneerng 05 Vol I WE 05, July - 3, 05, London, U.. ndependent users can be shown as Fgure. he transmtted sgnal goes through precodng matrx and then receved wth recever flter to decode the desred user sgnal. Block dagonalzaton (BD) s the well-known precodng method for the system [-5]. Defne the transmtted symbol vector x, nose w and the precodng matrx P as follows, x x w w x w... w P P P... P he receved sgnal can be descrbed as y y y... y Px w () where s the channel nformaton matrx and can be defned as... he receved sgnal can be rewrtten as follows, y P x... x P x k k, k k w Defne the receved flter M for all users as follows, M dagm M... M (4) he desred output sgnal x can be shown as () (3) x M P x M P x M w (5) k k, k he key dea of the BD s to desgn the precodng matrx that satsfes the followng condton, P 0 k,, k (6) So P should be n the null space of that s defned as follows, (7) he SVD of can be descrbed as ( ) (0) U Λ V V (8) where U and Λ denote the left sngular vector matrx and the matrx of ordered sngular values of, respectvely. he matrx () V and V (0) denote the rght sngular matrces each conssts of the sngular vectors correspondng to nonzero sngular values of and zero sngular values of. he desred user has non-nterferng block channel (0) V. In order to decouple ths block channel nto n parallel sub channels, the SVD of s computed as k (0) V ( 0) (0) (0) V V V b b b V (0) U Λ V U Λ V SVD (9) Employng (0) V V P and desred user s sgnal vector M U n (5), the x can be shown as follows, x Λ x U w (0) Fnally, we can fnd the precodng matrx P as follows, (0) (0) (0) P V V V V... V V () he all user s receved flter can be descrbed as follows, ISB: ISS: (Prnt); ISS: (Onlne) M dag U U... U () B. Generalzed Zero-Forcng hannel Inverson For the so-called Generalzed Zero-Forcng hannel Inverson (GZI) method [5], we need to perform the pseudo-nverse operaton of the channel matrx as follows,... (3) onsder the QR decomposton of matrx dmenson n as follows, t Ĥ wth Q R for,..., (4) where R s an n n upper trangular matrx and Q s an t n matrx whose columns form an orthonormal bass for Ĥ. In (3), due to 0, we have Q R 0. Snce R s nvertble, t follows that Q 0. As n the BD algorthm, n order to decouple ths block channel nto parallel sub channels, the SVD of Q s computed as follows, Q Q Q vp vp vp SVD Q U Λ V U Λ V (5) ( ) Employng vp P Q V and M U n (5), the desred user s sgnal vector x can be descrbed as follows, x Λ x U w (6) Fnally, we can fnd the precodng matrx P as follows, P QV QV... Q V (7) he all user s receved flter can be shown as M dagu U... U (8) For the BD and GZI algorthms, we assume that transmtter knows the channel staton nformaton perfectly. owever, due to the msmatch between the transmtter and recever, the transmtter can not accurately know SI. Defne err as the channel estmaton error, the SI can be descrbed as follows, est err (9) where and est are the true SI and the estmated SI, respectvely. We assume that err s uncorrelated wth est and x. err has..d. elements wth zero mean and estmaton error varance e,h. So the receved sgnal n () can be rewrtten as y s estpsx s errpsx s w s (0) where the errpsx s s the estmaton error term, and we defne the total error term s e errpsx s w s. he total error varance e can be shown as follows, e t e, h rp s Ps r w e () For the BD algorthm, equaton (7) can be rewrtten as est,... est, est,... est, () For the GZI algorthm, equaton (3) can be rewrtten as WE 05

3 Proceedngs of the World ongress on Engneerng 05 Vol I WE 05, July - 3, 05, London, U..... est, est, est, est, est, est, est, III. E PROPOSED WAER-FILLIG ALGORIM (3) A. Spatal-Doman Water-Fllng Please check wth your edtor on whether to submt your manuscrpt as hard copy or electroncally for revew. If hard copy, submt photocopes such that only one column appears per page. hs wll gve your referees plenty of room to wrte comments. Send the number of copes specfed by your edtor (typcally four). If submtted electroncally, fnd out f your edtor prefers submssons on dsk or as e-mal attachments. onsder the system shown as n Fgure 3, the capacty for complex AWG MIMO channel when s perfectly known at the recever can be expressed as follows [7, 8], Q fxed max p( x) I( X ; Y ) loga det I (4) n he capacty under ergodcty condtons when s perfectly known at the recever can be descrbed as where ergodc E n loga det I Q n (5) s the nose covarance, E n t ) n ( t ). n ( k l he transmtter correlaton matrx Q can be dagonalsed as Q V D P (6) D Q 0 0 We can obtan the result that the capacty s the sum of the capacty of the parallel channels, that s fxed _ log a det I mn( M, ) Q V U Λ V V D V V Λ U Λ Φ loga n Q n (7) he sum rate R BD for the BD algorthm can be wrtten n terms of the followng maxmzaton [5,6], R BD max Φ subect to log r( Φ Λ deti ) P w total Φ (8) he optmal power loadng matrx Φ can be calculated from the sum rate (8) by usng the water-fllng method [9-], n Φ wth μ such that Φ P (9) Λ Usng (3) and (5), the optmal capacty can then be descrbed as n such that Λ ( b Λ loga n ) (30) Fnally, we can fnd the block dagonalzaton precodng BD matrx P as (0) (0) (0) V V V V... V V Φ P BD (3) he all user s receved flter can be shown as BD M dag U U... U (3) Smlarly, the GZI precodng matrx P GZI GZI P s as follows, Q V Q V... Q V Φ he all user s receved flter s GZI (33) M dag U U... U (34) B. Spatal-Frequency Doman Water-Fllng he multuser MIMO downlnk system wth space-frequency doman water fllng can be shown as Fg. 4. he transmtted sgnal goes through precodng matrx and water fllng and then receved wth recever flter to decode the desred user s sgnal. If the GZI method s employed to perform space- doman water fllng, the sgnal before FF operaton can be descrbed as follows, xs x S xs... xs (35) P S Q V x PS Q V x... PSQ V x hen after -pont FF operaton, the frequency-doman sgnal of the th user s as follows, X X X... X F P Q V x (36) ollectng the all user sgnal we obtan X F P X X... X vp vp vp vp Q V x... F P Q V x S S S (37) Let be the number of subcarrer, f be the -th sub-channel, P [] be the transmtted power of the -th subchannel. he capacty of the k-th subchannel s gven[4,5], k (38) f f log [ 0 Where f, [, P [ and 0 denote the subcarrer spacng, frequency response, transmsson power and nose varance of the k-th subchannel. he total channel capacty s gven by the sum of the capacty for ndvdual subcarrers, f k (39) k 0 Gven the SR for each subcarrer, we may allocate dfferent powers to dfferent subcarrers so as to maxmze the total system capacty, that s ISB: ISS: (Prnt); ISS: (Onlne) WE 05

4 Proceedngs of the World ongress on Engneerng 05 Vol I WE 05, July - 3, 05, London, U.. max P0,..., P k 0 f k subect to max log k P P [ ] 0,..., k 0 0 used k 0 P (40) where P s the average power for each subcarrer avalable n the transmtter. Employng the Lagrange multpler method for optmzaton wth equalty constrant n Equaton (40), the followng soluton s obtaned. We can fnd the optmum soluton by maxmzng the Lagrange functon defned by [6], P k used [ ] L log [ P (4) k 0 0 k 0 hat s (4) L [ ] P k used log [ ] [ ] k 0 P k P k 0 k 0 0 L used k 0 [ he soluton s 0 P [ [ [ P , [ f 0 [ otherwse (43) (44) where s the Lagrange multpler that s chosen to meet the power constrant n Equaton (44). Each frequency-doman user sgnal s then multpled frequency-doman water-fllng operaton and can be express as follows, X X... X vp vp vp vp FP Q V x... P FP Q V x X f (45) Pf S f S he total transmt sgnal can be descrbed as S S S... St (46) X X... X... X X... X t IV. SIMULAIO RESULS In ths secton, we provde some smulaton examples to demonstrate the performance of the proposed method. he results wll be verfed by Monte arlo smulaton method, and the adopted channel model s the OS 07 RA/U/BU envronments. We compare the BER performance of our proposed algorthm wth that wthout water-fllng. he smulated modulated sgnal format s QPS. he smulated number of actve users s =. For the U channel model, the number of paths L s equal to. For the BU channel model, the number of paths L s equal to. For the smulatons, two precodng algorthms, BD and GZI algorthms, are employed to combned wth spatal-doman and frequency-doman water-fllng technology for the MU-MIMO system. For the MU- MIMO system, the base staton s equpped wth four antennas and the moble staton s equpped wth two antennas. In Fg. 5, we compare the bt error rate (BER) ISB: ISS: (Prnt); ISS: (Onlne) performances of the MU-MIMO systems wth and wthout BD algorthm, an further compare the BER performances wth -D (spatal-doman) water-fllng and -D (spatal-doman and frequency-doman) water-fllng. Fg. 5 shows that the proposed -D water-fllng BD algorthm has superor performance compared wth -D BD algorthm and conventonal BD algorthm. In Fgs. 6-7, we show the performance degradaton of the conventonal BD/GZI precodng algorthms and the water-fllng BD/GZI algorthm n the stuaton of channel msmatch, respectvely. he proposed water-fllng BD/GZI algorthm outperforms the conventonal BD/GZI algorthm, especally n the low sgnal-to-nose rato condton. In Fgs. 8-9, we compare the BER performances of the GZI algorthm wth and wthout water-fllng technology n OS-07 U and BU channels, respectvely. Fgs. 8-9 show that -D water-fllng GZI precodng algorthm outperforms -D or conventonal GZI, even though the transmsson power s one half of that of conventonal GZI. In Fgs. 0-, we show the performance degradaton of the proposed -D water-fllng GZI precodng algorthms n the stuaton of channel msmatch n OS-07 U and BU channels, respectvely. he proposed -D water-fllng GZI algorthm has BER 0.00 at SR 5 db even though channel msmatch exsts. V. OLUSIO he water-fllng technology performs power allocaton based on channel envronment of each user and has been used n MIMO system that uses each antenna SI to fnd maxmum egenvalue to do power allocaton as the spatal doman water fllng. In ths paper, the BD/GZI algorthms are combned wth water-fllng technology to perform power allocaton and MUI/MAI cancellaton for the MU-MIMO systems. he proposed algorthms are wth space-frequency water-fllng. Some smulaton examples are gven to demonstrate the effectveness of the proposed algorthm. REFEREES []. Jafarkhan, SPAE-IME ODIG: EORY AD PRAIE, ambrdge unversty press, 005. [].-J. Lee,. Sung, and I. Lee, Lnear Precoder Desgns for ogntve Rado Multuser MIMO Downlnk Systems, n Proc. of IEEE onference ommuncatons, June 0. [3] S. Bose, D. Zhu and B. ataraan, Multuser MIMO apacty wth Lmted Feedback rells Exploraton Based Precoder, n Proc. Internatonal onference on omputng, etworkng and ommuncatons, Jan. 0. [4] J. Zhang, Y. Wu, S. Zhou and J. Wang, Jont lnear transmtter and recever desgn for the downlnk of multuser MIMO systems, IEEE ommuncatons Letters, Vol. 9, no., pp , ov [5] S. S. Shm, J. S. wak, R. W. eath and J. G. Andrews, Block dagonalzaton for mult-user MIMO wth other-cell nterference, IEEE ranscatons on Wreless ommuncatons, Vol. 7. no. 7, pp , July 008. [6]. Sung, S.-R. Lee and I. Lee, Generalzed channel nverson methods for multuser MIMO systems, IEEE ransactons on ommuncatons, Vol. 57, no., pp , ov [7] P. e, L. Zhao, S. Zhou and Z. u, Water-Fllng: A Geometrc Approach and ts Applcaton to Solve Generalzed Rado Resource Allocaton Problems, IEEE ransactons on Wreless ommuncatons, Vol., o. 7, pp , July 03. [8] Q.. Spencer, A. L. Swndlehurst and M. aardt, Zero-Forcng Methods for Downlnk Spatal Multplexng n Multuser MIMO hannels, IEEE ransactons on Sgnal Processng, Vol. 5, no., pp , Feb. 004 WE 05

5 Proceedngs of the World ongress on Engneerng 05 Vol I WE 05, July - 3, 05, London, U.. [9] P. Patcharamaneepakorn, A. Doufex and S. M. D. Armour, Weghted Sum apacty Maxmzaton Usng a Modfed Leakage-Based ransmt Flter Desgn, IEEE ransactons on Vehcular echnology, Vol. 6, o. 3, pp , March 03. [0]. L, X. Yuan, X. Ln and L. Png, "On Water-Fllng Precodng for oded Sngle-arrer Systems," IEEE ommuncatons Letters, Vol. 3, o., pp , January 009. [] Y. R. Zheng, M. Wang, W. Zeng and. Xao, "Practcal lnear precoder desgn for fnte alphabet multple-nput multple-output orthogonal frequency dvson multplexng wth experment valdaton," IE ommuncatons, pp , August 03. [] B. Enzo and B. Mauro, A water-fllng based approach for power allocaton for multple-antenna Raylegh flat fadng systems wth partally coherent detecton, n Proc. of IEEE Vehcular echnology onference, 00. [3]. Jndal, W. Rhee, S. Vshwanath and S. A. Jafar, Sum power teratve water-fllng for mult-antenna Gaussan broadcast channels, IEEE ransactons on Informaton heory, Vol. 5, no. 4, pp , Aprl 005. [4] Y.-. u and G.-S. uo, Space-me-Frequency Doman Water-Fllng n MIMO-OFDM Fadng System, n Proc. of IEEE Vehcular echnology onference, Aprl 007. [5] Y. S. ho, J. m, W. Y. Yang and. G. ang, MIMO-OFDM wreless communcatons wth Matlab, John Wley & Sons, Ltd, 00. [6] X. hen, L. Zhang, L. Song, Y. Zhao and B. Jao, "Feedback ompresson for me-orrelated MIMO Block-Fadng hannels Usng uffman odng," n proc. IEEE Internatonal onference on ommuncaton echnology, pp. 4-45, Sept. 0. [7] L. Zhao, Y. Wang and. Pascal, Effcent Power Allocaton Strategy n Multuser MIMO Broadcast hannels, n proc. IEEE Internatonal Personal Indoor and Moble Rado ommuncatons, pp , Sept. 03. Fg. 5: BER performance comparsons of the proposed D water-fllng algorthm and some exstng algorthms: 4 transmt antenna, receve antenna, users. Fg. : Block dagonalzaton algorthm for multuser MIMO downlnk system. Fg. 6: BER performance comparsons of the BD/GZI algorthms (wthout water-fllng) wth channel msmatch: 4 transmt antenna, receve antenna, users. Fg. : GZI algorthm for multuser MIMO downlnk system. Fg. 3: GZI wth D-water fllng multuser MIMO downlnk system. Fg. 7: BER performance comparsons of the BD/GZI algorthms (wth D water-fllng) wth channel msmatch: 4 transmt antenna, receve antenna, users. Fg. 4: GZI wth D-water fllng multuser MIMO downlnk system. ISB: ISS: (Prnt); ISS: (Onlne) WE 05

6 Proceedngs of the World ongress on Engneerng 05 Vol I WE 05, July - 3, 05, London, U.. Fg. 8: BER performance comparsons of the proposed GZI water-fllng algorthm wth dfferent power: 4 transmt antenna, receve antenna, users and U channel. Fg. : BER performance comparsons of the proposed GZI D water-fllng algorthm wth channel msmatch: 4 transmt antenna, receve antenna, users and BU channel. Fg. 9: BER performance comparsons of the proposed GZI water-fllng algorthm wth dfferent power: 4 transmt antenna, receve antenna, users and BU channel. Fg. 0: BER performance comparsons of the proposed GZI D water-fllng algorthm wth channel msmatch: 4 transmt antenna, receve antenna, users and U channel. ISB: ISS: (Prnt); ISS: (Onlne) WE 05