MIMO Systems: Multiple Antenna Techniques

Transcription

1 ADVANCED MIMO SYSEMS MIMO Sytem: Multple Antenna echnque Yqng ZOU, Zhengang PAN, Ka-Kt WONG 1 1 Dr, Senor Member of IEEE, Aocate Edtor, IEEE Wrele, IEEE CL, and JoC (AP), Senor Lecturer, Department of EEE, Unverty College London, London, WC1E 7JE, Unted Kngdom el: +44-(0) , Fax: +44-(0) E-mal: yqzhou@atr.org, zgpan@atr.org, k.wong@ee.ucl.ac.uk

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3 1.1. Abtract h chapter revew mot known multple antenna technque for ngle-uer pont-to-pont ytem, from how multple antenna help provde dverty and multplexng to the detecton technque for thee ytem. Fnally, th chapter alo dcue the poblty of ung multple antenna for multuer ytem for patal multplexng. 1.. Lterature Revew he concept of multple antenna can be traced back long tme ago. In 1960, antenna array wa appled n mltary radar ytem for gnal copyng, drecton fndng and gnal eparaton [1,]. hee gnal parameter etmaton need hgh reoluton. Many algorthm have been propoed n th feld, uch a the maxmum lkelhood (ML) baed approach [3] and maxmum entropy (ME) baed approach [4]. he man lmtaton of thee approache are the ba and hgh entvty. hee problem were olved by Schmdt [5,6] and Benvenu [7] ndependently. Partcularly, Schmdt method known a MUSIC (Multple Sgnal Clafcaton), whch can provde ubtantal performance mprovement at the cot of hgh computatonal complexty and torage conumpton. hen, another cheme, ESPRI (Etmaton of Sgnal Parameter va Rotatonal Invarance echnque), propoed to acheve performance cloe to that of MUSIC but wth a gnfcantly reduced complexty [8]. In wrele communcaton ytem, due to the lmted phycal ze of moble devce, the applcaton of multple antenna ntally propoed for bae taton (BS) only. Invetgaton on thee multple antenna ytem focu on beamformng, etmaton of drecton of arrval (DOA), and patal dverty. he aforementoned algorthm lke MUSIC and ESPRI can be employed to realze the beamformng and the etmaton of DOA, where the receved/tranmtted gnal from/for dfferent antenna are coherently combned to pont at a pecfc drecton. In th way, the co-channel nterference from other moble taton (MS) can be reduced n the uplnk and the tranmon power can be focued to the dered MS n the downlnk. For example, n [9,10,11] and ome reference theren, multple antenna are deployed at BS to obtan receve dverty and/or co-channel nterference rejecton n the uplnk baed on the DOA. It demontrated that gnfcant capacty mprovement can be acheved. hen, n [10,1], the antenna at the BS are ued a a tranmt beamformer n downlnk. By focung the tranmt energy n the drecton of the dered MS, tranmt beamformng ncreae the gnal-to-noe rato (SNR) at the MS. Smlar to the ngle-nput ngle-output (SISO) ytem wth only one antenna at both de, the aforementoned receve dverty and tranmt dverty achevng ytem are called ngle-nput multple-output (SIMO) and multple-nput ngle-output (MISO) ytem, repectvely. Nowaday, multple-nput multple-output (MIMO) ytem have become one of the hottet reearch topc due to the magnfcent enhancement brought by multple antenna technque. he poblty to deploy multple antenna at both de of the communcaton lnk lay on the followng fact: 1) the development n hardware mnaturzaton and advance n antenna degn make the deployment of multple antenna at the mall MS more feable; ) wrele applcaton lke wrele local area network (WLAN) and fxed wrele acce (FWA) allow large phycal zed devce that can afford multple antenna, uch a laptop computer. he reearch on MIMO ytem tart from early elatar [13] found that ung MIMO ytem, there could be a dramatc mprovement n the ytem throughput whle no extra pectrum needed. In 1996, Fochn publhed the famou paper [14], where he propoed a Bell Lab Layered Space-me (BLAS) archtecture for MIMO ytem and t wa hown that hgh pectral effcence uch a 10 to 0 bt//z can be acheved. hen, an elegant pace tme block codng (SBC) archtecture wa propoed by Alamout [15], whch mple yet effectve n obtanng patal dverty. Alamout code ha led to a reearch fervor on SBC. In ummary, MIMO can be employed to acheve both tranmt and receve dverty, or make the ytem throughput ncreae lnearly wth the mnmum number of the tranmt and receve antenna Space-me Codng ranmtter dverty wa frtly propoed n [16,17] for BS mulcatng, where cope of the ame ymbol are tranmtted through multple antenna at dfferent tme, creatng an artfcal multpath dtorton at the recever. 3

4 A ML equence detecton or a mnmum mean quare error (MMSE) equalzer can be employed to reolve the multpath nterference and obtan dverty gan. h delay codng cheme can be taken a a repetton channel codng n patal doman. he dea of channel codng n pace and tme doman wa generalzed by arokh et al. n [18] and the o-called pace-tme codng (SC) wa ntroduced. here are everal knd of SC wth dfferent tructure Space-me Block Codng Alamout dcovered an elegant SBC cheme for MIMO ytem wth two tranmt antenna. A hown n Fgure 1.1, the nput ymbol to the SBC encoder are dvded nto group of two ymbol. In the frt ymbol duraton, two ymbol, 1 and, are tranmtted multaneouly from antenna #1 and #, repectvely. hen, n * the next ymbol duraton, the gnal and * 1 are tranmtted from antenna #1 and #, repectvely. Aumng that h 1,1 and h 1, are the fadng coeffcent correpondng to the frt and econd tranmt antenna to the receve antenna, repectvely, and are contant over two conecutve ymbol tme, the gnal receved over two conecutve ymbol perod are and y h, h n h h n 1 1 1,1 1, 1 1,1 1 1, 1 * * * y h, h h h n * 1 1,1 1, 1,1 1, 1 (1.1). (1.) hey can be rearranged nto a matrx form a follow y1 h1,1 h1, 1 n1 y * * * * y h 1, h 1,1 n eff (1.3) where eff the effectve channel matrx. Snce eff orthogonal, by a mple lnear operaton by 1 MISO ytem can be plt nto two eparate parallel SISO ytem a follow eff y, the * * 1 h1,1n1 h1, n z eff y h1,1 h1, (1.4) * * h1,n1 h1,1 n Fgure 1.1. Alamout code 4

5 Fgure 1.. A 4-tate pace tme trell code h orthogonal property can be extended to the cae where the recever ha multple antenna. It can be een that the Alamout cheme decouple the vector ML decodng problem nto calar problem. herefore, the cheme can realze full dverty whle reduce the recever complexty dramatcally. It wll be hown later that the Alamout code provde a performance gan mlar to that obtaned by ung one tranmt antenna and two receve antenna wth maxmum rato combner (MRC) except for a power reducton of (3 db). he Alamout cheme can be generalzed to an arbtrary number of antenna [19] and able to acheve the full dverty promed by the number of tranmt and receve antenna. Note that n the prevou example wth two tranmt antenna, two dfferent data ymbol are tranmtted n two ymbol duraton. hu the codng rate ymbol duraton 1, or the full rate. owever, for arbtrary number of antenna, full rate not alway achevable. Lettng the th row contan the data ymbol tranmtted at the th antenna n dfferent ymbol duraton, two SBC wth codng rate 3/4 and 1/ are gven by * * * * * * * * * * (1.5) and * * * * * * * * * * * * * * * * (1.6) repectvely Space-me rell Code (SC) 5

6 Although SBC can acheve a near optmal dverty gan wth a very mple decodng algorthm, t codng gan lmted. arokh [18] developed another SC approach known a pace tme trell code (SC) to acheve both dverty and codng gan. In SC, ymbol are encoded accordng to the number of antenna at whch they are multaneouly tranmtted and decoded ung a ML equence detector at the recever. Gven the number of tranmt antenna, the code degn of SC am to contruct the larget poble codebook wth dverty and codng gan. he degn crtera n dfferent cenaro have been developed by arokh et al., and a number of hand-crafted SC wth full dverty gan were gven [18]. Fgure 1. how the encoder and decoder of a 4-tate SC wth quadrature phae hft keyng (QPSK) modulaton and two tranmt antenna. A hown n the fgure, there are 4 tate of 0, 1, and 3. he ntal tate 0. If the nput ymbol, the output wll be two ymbol,.e., 0 and, and the tate tranformed to. he two output ymbol are tranmtted from antenna #1 and #, repectvely. Next, a econd data ymbol 1 nput, then the output wll be 1 and, and the tate become 1. Ung the trell tructure, at the recever, a ML equence detecton can be carred out. In the SC cheme, dverty gan acheved nce the encoded data arrve over uncorrelated faded branche. Moreover, SC can provde codng gan becaue of the trell tructure whch create a code relatonhp n the tme and pace doman. hee pace-tme trell tructure can be realzed by hft regter wth generator coeffcent determnng the multple output ymbol that are fed to dfferent tranmt antenna. SC perform better than SBC at the cot of addtonal encodng/decodng complexty. Full dverty code wth greater codng gan were ubequently preented [0], where code were found by a ytematc way through exhautve computer earche over a feed-forward convolutonal codng generator. SC code can alo be generated by earchng for the code wth the bet dtance pectrum properte [1]. SC effectve due to the combnaton of forward error correcton (FEC) codng and dverty tranmon. owever, becaue of the ML decodng, the complexty of SC grow exponentally wth the number of tranmt antenna. Increang tranmt antenna could become a bg ue for hgh-peed real tme decodng and the earch for the optmum SC code tll an open problem n order to reduce the decodng complexty Space-me urbo/ldpc Code S-urbo code and S-LDPC combne the turbo and low denty party check (LDPC) code wth pace-tme codng. Unlke the clacal SC code wth degnng rule lke SC and SBC, there lack of ytematc way to degn good S-urbo code and S-LDPC. Mot reearche try to extend the urbo-code and LDPC degned for tradtonal SISO ytem to MIMO ytem. Although lmted analy ha been done, S-urbo and S-LDPC have hown attractve ytem performance due to the powerful teratve decodng method. Fgure 1.3 llutrate two typcal encoder tructure of S-urbo code, one parallel concatenated tructure and one eral concatenated tructure. In the parallel tructure, SC can be employed a the conttuent code, whle the eral S-urbo a concatenaton of block/convolutonal code wth SC/SBC. Moreover, Fgure 1.4 depct a typcal encoder tructure of S-LDPC whch a eral concatenaton of one conventonal LDPC and one SC/SBC. S-urbo/LDPC code can acheve both codng gan and patal dverty gan. owever, a hown n Fgure 1.3, for parallel tructured S-urbo code, the number of tranmt antenna are lmted by the turbo code tructure. At the receve de, for parallel S-urbo, SC decodng needed, whle for the eral tructure, conventonal eral turbo decodng algorthm can be employed. Detal of thee code cheme can be found n [] and [3] and the reference theren Dfferental SC he coherent decodng algorthm of above codng cheme requre the channel tate nformaton (CSI) at the receve de. owever, n many cae, t dffcult to acqure the CSI, for example, n cae of hgh fadng rate or low complexty recever tructure. In thee cae, non-coherent decodng would be a good choce. o th end, a 6

7 Fgure 1.3. Parallel and eral concatenated S-turbo code Fgure 1.4. Encoder tructure of S-LDPC new cla of dfferental SC propoed n [4], an example of whch hown n Fgure 1.5 wth two tranmt antenna. At tme +, the nput ymbol vector dfferentally proceed by the matrx C, whch + c + generated from the SBC encoder output at tme. he reultant ymbol are denoted a, gven by c c C c c * 1, 1,, 1 + * c +, c, c 1, + (1.7) Fgure 1.5. Encoder tructure for dfferental SC 7

8 Aumng one receve antenna and gnorng the background noe, the receved gnal at tme and +1 can be wrtten a y y h h c 1,1 1, 1, * * * y h 1 1, h1,1 c, Smlarly, the receved gnal at tme + and +3 are gven by y y h h c h h c c * 1,1 1, 1, 1,1 1, 1,, 1 * * * * * * y h 3 1, h 1,1 c h, 1, h 1,1 c, c 1, + y y 1 1 * * y1 y + herefore, the gnal tranmtted at + can be mply recovered by 1 y y y y 1 1 * * y 1 1 y + y (1.8) (1.9) (1.10) 1.4. SIMO A hown n the prevou ub-ecton, multple tranmt antenna are requred to apply pace-tme codng. When there only one antenna at the tranmt de, SIMO can be ued to acheve receve dverty. he capacty of SIMO ytem ncreae logarthmcally to the antenna number. An llutraton of SIMO ytem hown n Fgure 1.6 wth n R receve antenna, where a gnal tranmtted from one antenna. After pang through the multple antenna channel h h 1,1, h,1,, h n,1, the receved gnal can be wrtten nto a vector a R y y,, 1 y, where h tand for the channel factor from the tranmt antenna to the receve antenna #, n R,1 and y the receved gnal at antenna # (=1,,, n ). he relatonhp between y and h gven by R y h n (1.11) where n n 1,, n n the noe vector wth a covarance matrx of I n n R R. Accordng to the electro-magnetc property of antenna, the antenna hould be uffcently paced o that the channel fadng at df- R ferent antenna ndependent to each other. Aume that the CSI known at the recever, whch can be realzed by channel etmaton. In the followng, two algorthm are ntroduced to obtan receve dverty. Fgure 1.6. A SIMO ytem 8

9 Selecton Combnng At the receve de, the ntant gnal to noe rato at antenna # gven by where P E SNR E h,1 h,1 P E n (1.1) the gnal power. Snce the channel experenced by receve antenna are dfferent, the receve SNR vare from antenna to antenna. Ung electon combnng, the receved gnal at the antenna wth the larget SNR choen a the output Maxmum Rato Combnng Dfferent to electon combnng, whoe output jut one of the n R receved gnal, maxmum rato combnng (MRC) make ue of all receved gnal. he bac dea that the receved gnal wth hgher SNR hould have a more mportant role n the fnal gnal. herefore, the weghtng vector of gan combnng gven by After gan combnng, the gnal become * * * 1,1,1 R,1 w h, h,, h n h (1.13) y wr h h n h h n where tand for the Eucldean norm of a vector and. he SNR at the output of gan combnng then gven by h n R 1 E h 4 h P h P P SNR,1 E h n h 1 h n R (1.14),1 h (1.15) Compared to electon combnng, MRC can produce a gnal wth hgher SNR nce for any n 1, R. Moreover, a receve dverty of order n R can be acheved. h n R 1 h h,1,1 Fgure 1.7. A MISO ytem 9

10 1.5. MISO he tructure of a MISO ytem hown n Fgure 1.7, where the ame data wll be radated from n tranmt antenna. Smlar to SIMO ytem, the tranmt antenna hould be uffcently paced to enure that the channel fadng at dfferent antenna ndependent to each other. In SIMO ytem, channel nformaton etmated at the recever. hu, electon combnng and MRC can be employed to acheve receve dverty. But n MISO ytem, there no channel nformaton at the tranmtter. here are two dfferent way to obtan tranmt dverty n MISO ytem. If channel nformaton fed back from the recever, precodng cheme lke tranmt MRC can be employed. On the other hand, f there no channel nformaton at the tranmtter, preproceng algorthm can be employed, uch a pace tme codng ranmt MRC o obtan the channel nformaton needed n tranmt MRC, channel etmaton hould be carred out frt. Plot ymbol could be ent from dfferent tranmt antenna n dfferent tme lot, o that the channel fadng factor from the tranmt antenna #j to the receve antenna, h 1,j, can be etmated. hen the recever feed the channel nformaton h h 1,1, h 1,,, h 1, n back to the tranmtter. When tranmt MRC employed, the weghtng vector at the tranmtter gven by 1 * * * 1 h1,1, h1,,, h1, n w h h h (1.16) 1 h ntroduced to normalze the total tranmt gnal power to P. So the tranmt gnal vector be- w and the receved gnal gven by where come whoe SNR can be calculated a 1 y hwn h hh n h n (1.17) E h n h P P j 1 SNR h E n 1, j (1.18) herefore, a tranmt dverty of order n can be acheved. It can be een that when the number of tranmt and receve antenna are the ame,.e., n nr, the MISO ytem wth tranmt MRC can provde the dverty gan a that of the SIMO ytem wth MRC Space me Codng Even f channel nformaton not avalable at the tranmtter, MISO ytem can tll acheve tranmt dverty by ung pace tme codng. For example, an Alamout code can be employed n a MISO ytem wth two tranmt antenna, a hown n Fgure 1.. he receved gnal vector y proceed by a matched flter eff, and the reultant gnal gven by (1.4) * * 1 h1,1n1 h1,n z h1,1 h1, * * h1,n1 h1,1n o keep the total tranmon power to P, the gnal power of 1 and are et to E E P. 1 It can be calculated that the SNR for each element at the output of the SBC decoder are the ame and gven by 10

11 E h1,1 h1, 1 h1 h P SNR E h n h n * * 1,1 1 1, (1.19) Compared to the SNR obtaned by tranmt MRC (1.18), t can be een that there are 3dB lo n the SNR provded by Alamout code, due to the lack of channel nformaton at the tranmt de. Aumng two tranmt antenna, QPSK modulaton, and..d. raylegh fadng channel, the bt error rate (BER) llutrated n Fgure 1.8 a a functon of SNR when tranmt MRC and Alamout code are employed. Perfect channel nformaton avalable at both tranmtter and recever. A a comparon, the performance of ytem wth ngle antenna alo hown. It can be een that wth more tranmt antenna and proper gnal proceng technque, the ytem acheve better performance. Furthermore, the performance of tranmt MRC better than that of Alamout code, at the cot of more complexty nce channel nformaton need to be fed back to the tranmtter for tranmt MRC. Fgure 1.8. Performance of a MISO ytem wth two tranmt antenna Fgure 1.9. A MIMO ytem 11

12 1.6. MIMO Fgure 1.9 llutrate the tructure of a MIMO ytem, where n and n R antenna are deployed at the tranmtter and recever, repectvely. MIMO can be degned to explot the dverty gan. In th cae, the ame data ymbol tranmtted on all n tranmt antenna. he total dverty gan not larger than n nr. MIMO can alo be ued for patal multplexng to ncreae the ytem throughput, when dfferent data ymbol are ent on dfferent tranmt antenna. In th cae, the throughput can be ncreaed lnearly wth the mnmum number of tranmt and receve antenna n the large SNR regme. here alway a tradeoff between the dverty gan and the throughput gan [5] Background Knowledge Defne a matrx of ze nr n. It can be ngular value decompoed (SVD) nto three matrx a follow =U V (1.0) where U and V are nr nr and n n untary matrx contraned by UU I and VV I, repectvely, and a n R n matrx wth ngular value of a t dagonal element. A non-negatve real number a ngular value for f and only f there ext unt-length vector u of ze n 1 an d v of ze n R 1, uch that v u and u v. he vector u and v are called left-ngular and rght-ngular vector for, repectvely Domnant Egenmode When channel nformaton avalable at the tranmtter, the domnant egenmode algorthm can be employed to maxmze the patal dverty gan. In th cheme, the ame data ymbol wll be frtly weghted by a vector w, then the j th t wt,1,, wt, n weghted copy of, w, radated from the tranmt antenna #j. Denote t, j a the MIMO channel matrx of ze nr n, whoe element h, j tand for the channel fadng factor from the tranmt antenna #j to the receve antenna #. hen, the receve gnal vector gven by y w n (1.1) t where n a n 1 noe vector wth a covarance matrx of R weghted by a vector r wr,1,, wr, n w a follow R I. he receved gnal wll be further he SNR of z can be calculated a E SNR z w y w w w n (1.) r r t r w r wt wr wt E wr n wr P (1.3) Let max max 1,,, r repreent the maxmum ngular value of, where r the rank of. he receve SNR can be maxmzed when w and w are choen a the left and rght ngular vector of correpondng to r t max max, repectvely. he reultant SNR gven by P SNR. 1

13 Space me Codng A n MISO ytem, when there no channel nformaton at the tranmtter, pace tme codng can be employed n MIMO ytem to acheve dverty gan. Agan, Alamout code taken a an example and a MIMO ytem wth two tranmt antenna and two receve antenna condered. At the frt and econd tme lot, the tranmt gnal vector are 1, and * *, 1, repectvely, whch the ame a that n MISO ytem. But there are two receve antenna now, and the correpondng receved gnal vector are gven by and eff h1,1 h n 1, 1 y1 h h n 1,1,1,, 1 * h1,1 h1, n1, y h *,1 h, n. (1.5) 1, hee gnal vector can be rearranged nto a new vector a follow h 1,1 1,1 h1, n y1 h,1 h, 1 n1, y * * n * * h 1, h 1,1 n eff y,1 * * h *, h,1 n, eff Smlarly, y wll pa through a matched flter of orthogonal,.e., eff (1.4) (1.6) eff. It can be proved that the equvalent channel matrx I. herefore, the output of the matched flter gven by eff z eff y eff eff eff n eff eff n (1.7) hu, the receve SNR can be calculated a SNR= E eff 1/ eff P eff P E eff n eff (1.8) Conder a by MIMO ytem wth QPSK modulaton and..d. raylegh fadng channel. Perfect channel nformaton aumed at both the tranmtter and recever. he performance of the ytem ung domnant egenmode and Alamout codng are hown n Fgure It can be een that ung domnant egenmode, the ytem obtan a 3dB gan n SNR compared to that ung Alamout cheme Multple Egenmode ranmon When channel nformaton avalable at the tranmt de, the multple egenmode can be employed to maxmze the throughput gan (or patal multplexng gan). A hown n Fgure 1.11, n dfferent data ymbol 1,, n are frtly weghted by a matrx Wt, then radated from dfferent tranmt antenna. After pang through the MIMO channel, the receved gnal vector further weghted by another matrx W r. Aume that the SVD of gven by =U V. hen, V and U are choe n a the tranmt and re- 13

14 ceve weghtng matrx, W t and W, repectvely. At the rece ve de, the weghted output gven by r r t r r z W WW n U UV VW n= n' (1.9) Fgure Performance of domnant egenmode and Alamout cheme Fgure Multple egenmode tranmon 14

15 Snce a n R n matrx wth ngular value of a t dagonal element, n R mut be equal to or larger than n o that the tranmtted gnal vector can be recovered. Denote the n ngular value of a,, 1, n ) element of vector z expreed a 1. he th ( n z n ' (1.30) It can be een that ung multple egenmode, the MIMO ytem wth channel can be tranformed nto n parallel SISO ytem, a hown n Fgure Sgnal Detecton n MIMO Sytem When channel nformaton not known at the tranmtter, but can be obtaned by mean of channel etmaton at the recever, multple egenmode not applcable. Wthout pre-proceng at the tranmtter, the receved gnal become y n (1.31) Varou gnal detecton algorthm have been propoed t o recover the tranmtted gnal vector. A. Lnear Detecton Lnear detecton provde low-complexty oluton to the MIMO gnal detecton problem. wo popular lnear detecton algorthm are zero-forcng (ZF) (alo known a leat quare (LS)) and MMSE detecton. ZF detecton degned to mnmze the quare error between the receved gnal vector y and the recovered tranmtted gnal vector, aumng that element of take contnuou value. he objectve functon gven by ZF arg mn y for contn uouly valued 1,, 1,, n n (1.3) It wll be hown later that f By relaxng ettng the dervaton of 1,, n take dcrete value, the LS problem become a ML detecton problem.,, to be contnuouly valued, the oluton of the LS problem can be obtaned by mply 1 n y wth repect to ZF ZF to zero y ZF 1 0 ZF y ZF y y ZF (1.33) where the peudo nvere of the nr by n channel matrx. o enure that nvertble, t requred that the rank of hould be n. herefo re, to apply ZF detecton, the number of receve antenna n R requred to be equal to or larger than the number of tranmt antenna n,.e., nr n. Aumng a by MIMO ytem wth QPSK modulaton,..d. raylegh fadng channel and practcal channel etmaton at the recever [6], the performance of ZF detecton hown n Fgure 1.1 wth that of a SISO ytem. It can be een that the BER of MIMO wth ZF the ame a that of SISO. owever, t hould be noted that ung the ame pectrum, data nformaton conveyed by the MIMO ytem doubled compared to that of the SISO ytem. So ZF detecton can only provde throughput gan but not dverty gan. MMSE detecton am to degn a weghtng matrx W e to mnmze the mean quare error between the tranmtted gnal vector and the weghted receved gnal vector We y, gven by W arg mn E W y (1.34) e W Aume that the covarance matrx of gnal and noe vector are E P n I and E repectvely. It can be derved that nn I, 15

16 Fgure 1.1. Performance of MIMO ytem wth ZF detecton Fgure Performance comparon between ZF and MMSE detecton 16

17 1 E E E E En n W yy y e 1 Pn I 1 1 (1.35) Generally, MMSE detecton can provde better performance than ZF detecton. owever, MMSE detecton alo need more nformaton than ZF, uch a the channel noe varance and tranmt gnal power. Moreover, at hgh SNR, Pn 1 approache zero and MMSE detecton reduce to ZF detecton. A performance comparon betw een the ZF and MMSE detecton gven n Fgure B. Nonlnear Detecton: Interference Cancellaton MIMO ytem can be taken a a pecal mult-uer ytem. At the receve de, each antenna receve a combned gnal contanng data gnal tranmtted from dfferent antenna. Conder the gnal from the tranmt antenna #. Other data gnal become nterference to. he nterference cancellaton technque can be appled n the gnal detecton of MIMO ytem. he bac dea to frtly ue lnear detecton to recover the data gnal n from tranmt antenna # n. hen the nterference caued by n can be cancelled out from the receved gnal. After nterference cancellaton, lnear detecton are ued agan to recover the data gnal n 1. h lnear detecton and ucceve nterference cancellaton (SIC) proce goe on untl 1 obtaned. W hen ZF or MMSE detecton appled wth SIC, the cheme known a ZF-SIC or MMSE-SI C. Aumng a by MIMO ytem, the ZF/MMSE-SIC algorthm llutrated n Fgure Ung QR decompoton, the ZF/MMSE-SIC algorthm can be realzed n a mple way. Frtly, the QR decompoton of the channel matrx gven by QR, where Q an nr nr orthogonal matrx and R an nr n upper trangular matrx. After mult plyng the receved gnal ve ctor y wth the hermtan of Q, the reult gven by z Q y Q Q n RQ n (1.36) Lettng z, r, j, and n ' tand for the element of z, R, and Q n, repectvely, the prevou equaton can be expreed n an elemen tal format a follow Fgure Illutraton of ZF/MMSE-SIC 17

18 z1 r1,11 r1, r1, n 1n 1 r1, n n n' 1 z r, r, n 1 1, ' n r n n n zn 1 r 1, 1 1 1, ' n n n r n n n n n zn r n, ' n n n n Ung ZF crtera, can be mply recovered a n dec zn rn, n n 1 (1.37), where dec the decon operaton choong the gn al contellaton that the nearet to z r,. hen, the nterference caued by can be cancelled out by ubtractng recovered a n d n r n n n ˆ n,, rn 1 n ˆ n from z1,, z 1, repectvely. Next, 1 can be 1, n, 1 n 1 n 1, n n, n ec z r r, and o on. MMSE-SIC can alo be mplemented n a mlar way. Gven a by MIMO ytem, the performance of ZF/MMSE-SIC demontrated n Fgure 1.15 wth comparon to ZF/MMSE detecton. It can be een that by ung SIC baed detecton, the ytem performance mproved. Moreover, MMSE provde better performance than ZF, ether wth or wthout SIC. It well-known that n mult-uer SIC, the gnal wth larger SNR hould be recovered frt. Smlarly, n ZF/MMSE-SIC of MIMO ytem, the gnal hould be detected n an approprate order. Generally, the pot-zf/mmse detecton SNR choen a the crteron. hat mean, f 1,, n are recovered ung ZF/MMSE detecton, SNR can be calculated for each data decon varable at t he output of detecton. Suppoe that ha the hghet SNR, then hould be the frt data gnal to be recovered. After the nterference caued by cancelled out, the pot-zf/mmse detecton SNR can be calculated for the ret gnal, and the one wth th e hghet SNR hould be the econd gnal to be recovered. At the cot of addtonal complexty caued by the orderng, the ordered ZF/MMSE-SIC cheme can provde better performance than the non-ordered one. n n n Fgure Sytem performance wth ZF/MMSE-SIC 18

19 Fgure BLAS ytem hgh-level block dagram Fgure V-BLAS he ordered ZF-SIC wa frtly employed n Bell Lab Layered Space-me (BLAS) or layered pace tme codng [14]. BLAS a bandwdth-effcent approach to wrele communcaton whch take advantage of the patal dmenon by tranmttng and detectng a number of ndependent co-channel data tream ung multple, eentally co-located, antenna. he central dea behnd BLAS the explotaton, rather than the mtgaton, of multpath effect n order to acheve very hgh pectral effcence (bt/ec/z), when multpath vewed a an adverary rather than an ally. Fgure 1.16 how a typcal ytem tructure of a BLAS ytem. At the tranmt de, the orgnal ymbol tream dvded nto everal ub-tream, each to be tranmtted by one antenna. At the recever, an array of antenna ued to pck up the multple tranmtted ubtream and ther cattered mage. Under the wdely ued theoretcal aumpton of ndependent Raylegh catterng, the theoretcal capacty of the BLAS archtecture grow roughly lnearly wth the number of antenna, even when the total tranmtted power held contant [7]. Dependng on the mappng method between parallel ymbol tream and tranmt antenna, there are two cheme: V-BLAS, D-BLAS. he mappng method of V-BLAS depcted n Fgure 1.17 where each ub-tream wll alway be tranmtted by the ame antenna over the whole block, whle the mappng method of D-BLAS depcted n Fgure 1.18 where each ub-tream wll be tranmtted from one antenna to another for each ndvdual ymbol. he performance of V-BLAS code n low fadng envronment nferor to that of D-BLAS code. For V-BLAS, the average parwe error probablty of the bottommot row nverely proportonal to the n th R n 1 power of SNR. In contrat, n D-BLAS, the average parwe dagonal error probablty between two dagonal c and e nverely proportonal to the n umdc,e th R power of SNR. herefore, f 19

20 Fgure D-BLAS conttuent code of equvalent data rate and complexty are deployed, the error probablty of a D-BLAS code n a low fadng envronment can be much lower than that of a V-BLAS code. In cae of fat fadng channel, they wll perform almot the ame. C. Nonlnear Detecton: Maxmum Lkelhood (ML) Detecton Among all gnal detecton algorthm, ML the optmum detecton provdng the bet performance at the cot of the hghet complexty, whch ncreae exponentally wth the number of tranmt antenna and the ze of the gnal contellaton. he objectve of ML to fnd a gnal vector that mnmze the Eucldean d- tance between y and arg mn y (1.38) Aumng that all tranmtted data ymbol are taken from the ame gnal contellaton wth ze C, the ML n detecton mut earch over C poble gnal vector to ob tan. G ven a mple by MIMO ytem wth QPSK modulaton, the ytem performance wth ML detecton llutrated n Fgure A a comparon, the performance of other detecton alo hown. It can be een that ZF detecton preent the hghet BER, whle MMSE, ZF-SIC and MMSE-SIC provde better and better performance. Yet the BER curve of ZF, MMSE, ZF-SIC and MMSE-SIC have mlar lope. Remember that ZF detecton cannot provde dverty gan. So the dverty order of ZF, MMSE, ZF-SIC and MMSE-SIC are bacally the ame. But the BER of ML detecton decreae much more rapdly compared to thoe of lnear detecton and nterference cancellaton cheme. herefore, bede the throughput gan, ML detecton can alo provde a dverty gan. Although ML detecton can be mplemented n mple ytem, t complexty become unmanageable wth ncreaed number of antenna and hgh-level modulaton. For example, ung 64QAM modulaton and four n 4 7 tranmt antenna, there are totally C t gnal vector to be earched. Due to t hgh complexty, ML not applcable n practcal ytem. Some ub-optmum algorthm have been propoed, amng to acheve near optmum performance wth lmted complexty. I. QR-MLD Gven the QR decompoton of the channel matrx,.e., Q R, the objectve functon of ML can be expreed a [8] arg mn y arg mn y y arg mn Q yq Q yq arg mn Q yr (1.39) Lettng y ', r, j and be further wrtten a Q y objectve functon can tand for the element of, R, and, repectvely, the 0

21 Fgure Performance of ML detecton Fgure 1.0. ree Structure of ML detecton y' 1r1,1 r1, r1, n 1 nt t d1 arg mn y' r r arg mn d d d (1.40),, n n t t 1 1,, nt 1,, nt d y' n r, nt t nt n t dn t h expreon ndcate that ML algorthm can be realzed n a tree tructure, a hown n Fgure 1.0. Start nt 1

22 from the root of n. Snce n ha C dfferent value, C branche can be generated wth, n a d y' r the weg ht on each branch. So there are C canddate of n n n n for each branch of ub-branch weght layer, there wll be mply the equence n at the frt layer. hen, n, C ub-branc he are generated accordng to the value of n 1 wth dn a the 1 dn a reult, C canddate of n 1, th n are obtaned at the econd layer. Fnally, at the n. A n C canddate of,, 1 n wth 1,, n d1 d n wth the mnmum branch weght. a the branch weght. he ML oluton o reduce the complexty of ML detecton, the number of canddate at each layer can be decreaed. For example, at the frt layer, ntead of keepng all C branche/canddate, only the C 1 ( C1 C ) branche wth maller weght are kept and the other branche are deleted. herefore, at the econd layer, there wll be d n C1 C branche. Smlarly, only C out of C 1 C branche are kept for the next layer. Aumng C0 1, t can be hown that the total number of branche vted by th ub-optmum ML detecton n 1 CC1CCC Cn 1 C C C be m, whle for full ML detecton, the number wll m0 n n 1 CC C C C C1. By choong dfferent value for C m, the ub-optmum algorthm can provde varou ytem performanc e wth dfferent level of complexty. II. Sphere Decodng he phere decodng algorthm add a condton to the objectve functon of ML detecton,.e., Q y R, where d r d r a preet value [9]. Snce Q y a pont n a n -dmenonal vector pace, the condtonal ML problem equ valent to fnd a pont R n a phere of radu r d centered at Q y that ha the mnmum dtance to Q y. Snce the earchng lmted n the phere, the number of vector that, n n n d hould be vted reduced compared to that of the full ML algorthm. hu, the complexty decreaed. Baed on the tree tructure, the phere decodng algorthm can be decrbed a follow. Smlar to QR-MLD, the algorthm begn wth the element n. Frtly, fnd all poble value of n that atfy y ' r n r. hen, chooe one value of n and fnd all canddate of n 1 that atfy the followng expreon n 1 ' n y n ' n 1 n 1, n 1 n 1, n n n, n d y r r r r (1.41) If there no uch canddate of n 1, chooe another value of n untl the oluton et of the nequalty not null. Next, gven n 1, n, all poble value of n can be obtaned by olvng the nequalty n n y' m rm, n r n d mn nm. h earchng goe n untl the canddate of 1 provdng oluton ',, 1 n to the nequalty o are generated g ven,, n, Q y R rd. Calculate the dtance between R ' ˆ and Q y, and chooe the one wth the mnmum dtance ŝ '. h not the fnal oluton nce only

23 one poble canddate of,, n condered. But th oluton can be ued to update the radu r d nce the dtance between R ' ˆ and Q y hould be le than the ntal radu wth hgh probablty. hen the earchng goe on n a maller phere wth the updated radu rd untl all pont n the phere are vted. In phere decodng, t mportant to et an approprate value for the ntal radu. If the ntal radu too mall, there may be no pont n the phere and the oluton of the condtonal ML problem null. On the other hand, f a large ntal radu et to enure that the ML oluton ncluded n the phere, there wll be many pont n the phere and the complexty hgh. Generally, the ntal radu can be et accordng to th e qualty of the channel,.e., the noe varance. When the noe large, the channel n bad condton and t lkely that the ML oluton far from the center of the phere. hu, a large radu needed. On the contrary, f there lttle noe, the ML oluton hould be cloe to the center of the phere and a mall radu hould be choen to reduce the complexty. Another way to et the ntal radu that a mple lnear detecton carred out frt to fnd a canddate of tranmtted gnal vector. hen the dtance between the oluton of lnear detecton and t he receved gnal vector can be taken a the radu. h method enure to nclude the ML oluton n the phere. Ung the tree tructure of ML problem, t can be een that n QR-MLD, at each layer of the tree, ome branche are deleted baed on the current weght. Snce the deletng not baed on the whole equence of,, 1 n, t poble that the ML oluton excluded a ome brache are removed. hu, the oluton of the QR-MLD may not be a ML oluton. But the complexty of QR-MLD totally under control by choong C. On the other hand, n phere decodng, condtoned on the radu, each earchng move along the 1,, C n 1 branche to the end o the whole equence of,, 1 n condered. he radu reduced baed on the 1.7. Mult-Uer MIMO dtance between R ˆ ' and Q y. So phere decodng can alway provde the ML oluton unle there no oluton due to mall radu. he dadvantage of phere decodng that the complexty of the algorthm a random varable nce the number of pont to be vted n a phere unknown. In ome cae, phere decodng need mlar amount of computaton a that of full ML detecton, whle ometme the complexty of phere de- codng near to that of lnear detecton. All the MIMO ytem decrbed before are for ngle uer,.e., there only one tranmtter and one recever. owever, mult-uer topology even more popular n current communcaton ytem where many moble uer communcate wth one bae taton. here are two typcal mult-uer topologe: one multple acce channel (MAC) whch correpondng to uplnk com muncaton, the other broadcat channel (BC) whch correpondng to downlnk communcaton. For MAC, the ytem model can be expreed a y 1 M n where y denote the receved gnal vector at the BS, M the number of uer, gnal vector from the th MS, and the channel matrx from the th MS to the BS. On the other hand, n cae of BC, the ytem model gven by 1 y1 1 n1 y n y M M nm M (1.4) tand for the tranmtted (1.43) 3

24 where y denote the receved gnal vector at the th MS, the tranmtted gnal vector from the BS and the channel matrx from the BS to the th MS. h model vald for any number of antenna at the MS. Fndng the mult-uer channel capacty ha alway been a hot t opc [30, 31]. Early reearche focued on the achevable data rate for a vector Gauan MAC where only the BS ha multple antenna. It ha been hown that by ung an optmum decon feedback multuer equalzer and ucceve detecton at the BS, the um-rate of all uer can acheve the maxmal capacty of the channel [30]. On the other hand, the concept of water-fllng can be employed at the MS de to acheve the ytem capacty [3,33,34]. Later, thee work were extended to the cae where multple antenna are deployed at both BS and MS. By generalzng the aforementoned decon feedback equalzer to the vector acce gnal cae [35], the achevable um capacty gven by M M R log deti Q 1 1 E (1.44) where Q the covarance matrx of,.e., Q. By degnng the et of covarance matrx and power allocaton cheme, the um capacty (1.44) can be maxmzed. If each uer ha a fxed power contrant, an teratve water-fllng method can be employed to olve the optmzaton problem [36]. he capacty can alo be optmzed under the overall power contrant for all uer [37]. Although there ha been much effort to evaluate the capacty regon of the vector MAC, le known on the degn of actual codng/gnal proceng ytem that take full beneft of the rch capacty of the channel. A et of tranmt and receve vector can be computed by ung a drect SVD (D-SVD) method to explot the patal reource to enhance the ytem performance [38]. Wth the dualty between uplnk and downlnk, the D-SVD method can alo be appled n downlnk cenaro by nterchangng the correpondng tranmt and receve vector of each uer. Comparng to vector MAC (uplnk), the capacty regon of vector BC (downlnk) even more dffcult to obtan and tll unknown to date. Due to the fact that BC and MAC are dual to each other [39], Cota pre-codng method [40] n uplnk can be ued n downlnk a well. he pre-codng method wa later re-tuded for the more general cae where each MS ha multple antenna [36,41,4] and uch tude have opened up a new branch of nformaton theory called drty-paper codng (DPC) [43]. owever, the theory eem to be far from beng ueful for the degn of effcent wrele communcaton. Recent work on mprovng downlnk capacty focu on beamformng approache for realzng pace dvon multplexng [44,45]. Beamformng algorthm can be degned to mantan the gnal to nterference-plu-noe rato (SINR) of every uer at a preet value for acceptable gnal recepton [31,44]. he BS antenna array can alo be operated ung a mple maxmal rato tranmon for dverty renforcement at the MS [46]. Further performance mprovement obtaned by ung BS dverty array n combnaton wth jont detecton at the MS de [47]. here ext a cloed-form antenna oluton that optmze the BS antenna array n maxmzng the product of mult-uer SINR [45]. In thee approache, the co-channel uer are not truly uncoupled. he redual co-channel nterference (CCI) wll degrade uer performance, and, mot mportantly, detroy the ndependency for managng mult-uer gnal, nce the power of co-channel uer mut be carefully adjuted jontly. When dealng wth mult-uer communcaton, t alway advantageou to handle uer n an orthogonal manner, a n conventonal ytem uch a tme, frequency or code dvon multplexng (/F/CDM) ytem. Orthogonal pace dvon multplexng (OSDM) n BC can be acheved by ung mult-uer MIMO antenna. he patal orthogonalzaton realzed by projectng every uer gnal onto the nullpace of the channel from the BS to the antenna of all the unntended moble recever. A et of tranmt and/or receve weght vector are ued to eparate dfferent group of tream among dfferent uer and (f poble) dfferent tream of each uer. By dong o, the mult-uer ytem can be mplfed to everal ndependent ngle-uer ytem each wth correpondng ntant channel gan (mlar to Fgure 1.11), o that the FEC can be ued for each uer ndependently. Although the eparaton of patal doman proceng and tme doman proceng may degrade the overall ytem performance, th concept can mplfy the ytem degn a lot. A mple example of OSDM to make the BC block dagonal o that co-channel uer are not nterfered wth each other [48,49,50]. In order to obtan the rch dverty of the channel and reduce the number of antenna at the BS, the OSDM optmzaton and recever dverty combnng hould be condered jontly. Aumng that every MS ue a MRC recever and the number of BS antenna equal to the number of total co-channel gnal co-extng n 4

25 Fgure 1.1. One typcal tructure for mult-uer MIMO the ytem, an teratve method can be employed to jontly optmze the BS and MS antenna weght for downlnk OSDM to obtan dverty gan [45]. h method fnally extended to a more general cae by Pan [51,5] a demontrated n Fgure 1.1 where each uer can further upport multple ndependent tream Concluon Multple antenna technque are extenvely revewed n th chapter. For ngle-uer pont-to-pont ytem, pace-tme codng, SIMO and MISO cheme are ntroduced to provde patal dverty. Moreover, precodng and combnng a mple way to explot multplexng gan when CSI known at the tranmtter. On the other hand, f channel tate only known at the recever, effcent detecton algorthm are needed, uch a non-ordered ZF/MMSE-SIC, BLAS, ML detecton, and phere decodng. Fnally, MIMO technque are alo dcued n mult-uer cenaro. Reference [1] L. C. Godara, Applcaton of antenna array to moble communcaton part I: Performance mprovement and feablty and ytem conderaton, IEEE Proceedng, Vol. 85, No. 7, pp , [] L. C. Godara, Applcaton of antenna array to moble communcaton and part II: Beamformng and drecton-of-arrval conderaton, IEEE Proceedng, Vol. 85, No. 8, pp , [3] J. Capon, gh reoluton frequency wave number pectrum analy, Proc. IEEE, Vol. 57, pp , [4] J. P. Burg, Maxmum entropy pectral analy, n Proceedng of the 37th Annual Internatonal SEG Meetng, Oklahoma Cty, Okla., [5] R. O. Schmdt, Multple emtter locaton and gnal parameter etmaton, n Proc. RADC Spectrum Etmaton Workhop, pp , Grff AFB, N. Y., [6] R. O. Schmdt, A Sgnal Subpace Approach to Multple Emtter Locaton and Spectral Etmaton, Ph.D. he, Stanford Unverty, Stanford, CA., [7] G. Benvenu and L. Kopp, Prncple de la gonometrc pave adaptve, n Proc. 7 eme Colloque GRESI, pp. 106/1 106/10, Nce, France, [8] R.. Roy, ESPRI etmaton of gnal parameter va ratonal nvarance technque, Ph.D. he, Stanford Unverty, Stanford, CA., [9] J.. Wnter, On the capacty of rado communcaton ytem wth dverty n a Raylegh fadng envronment, IEEE J. Select. Area Commun., Vol. 5, pp , [10] J.. Wnter, J. Salz and R. D. Gtln, he mpact of antenna dverty on the capacty of wrele communcaton ytem, IEEE ran. Commun., Vol. 4, pp ,

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27 [39] P. Vwanath and D. N. C. e, Sum capacty of the vector Gauan broadcat channel and uplnk-downlnk dualty, IEEE ran. Info. heory, Vol. 49, No. 8, pp , 003. [40] M.. M. Cota, Wrtng on drty paper, IEEE ran. Info. heory, pp , [41] D. e and P. Vwanath, On the capacty of the multple antenna broadcat channel, n Proc. DIMACS Sere Dcrete Math. and heoretcal Computer Scence, Amercan Mathematcal Socety, 00. [4] S. Vwanath, G. Kramer, S. Shama, S. A. Jafar and A. Goldmth, Capacty bound for Gauan vector broadcat channel, n proceedng of the DIMACS Workhop n Sgnal Proceng n Wrele Communcaton, 00. [43] G. J. Fochn and A.. Daz, Drty paper codng: Perturbng off the nfnte dmenonal lattce lmt, n Proc. DI- MACS Sere Dcrete Math. and heoretcal Computer Scence, Amercan Mathematcal Socety, 003. [44] C. Farakh and J. A. Noek, Spatal covarance baed downlnk beamformng n an SDMA moble rado ytem, IEEE ran. Commun., Vol. 46, No. 11. pp , [45] K. K. Wong, R. D. Murch, and K. B. Letaef, Perfomance enhancement of multuer MIMO wrele communcaton ytem, IEEE ran. Commun., Vol. 50, No. 1, pp , Dec. 00. [46] J. K. Caver, Multuer tranmtter dverty through adaptve downlnk beamformng, n Proc. WCNC 1999, pp , [47] S. J. Grant and J. K. Caver, A method for ncreang downlnk capacty by coded multuer tranmon wth a bae taton dverty array, n Proc. IEEE GLOCBECOM 001, Vol. 5, pp , 001. [48] R. L. U. Cho and R. D. Murch, A tranmt pre-proceng technque for multuer MIMO ytem: A decompoton approach, IEEE ran. Wrele Commun., Vol.3, No.1, pp.0 4, Jan [49] M. Rm, Multuer downlnk beamformng wth multple tranmt and receve antenna, Elect. Letter, Vol. 38, pp , 00. [50] Q.. Spencer and M. aardt, Capacty and downlnk tranmon algorthm for a multuer MIMO channel, n Proc. 36th Alomar Conf. Sgnal, Sytem, and Computer, Pacfc Grove, CA, 00. [51] Z. G. Pan, K. K. Wong, and. S. Ng, Analy of multuer MIMO downlnk network u lnear tranmtter and re- cever, EURASIP Specal Iue on Wrele Communcaton and Networkng, Vol. 004, No., Dec [5] Z. G. Pan, K. K. Wong, and. S. Ng, Generalzed multuer orthogonal pace dvon multplexng, IEEE Wrele Commun., Vol. 3, pp , Nov ran. About the Author Dr. Yqng ZOU receved the B.S. degree n communcaton and nformaton engneerng and the M.S. degree n gnal and nformaton proceng from the Southeat Unverty, Nanjng, Chna, n 1997 and 000, repectvely. In February 004, he receved the Ph.D. degree n electrcal and electronc engneerng from the Unverty of ong Kong, ong Kong. From June 004 to Oct. 008, he wa wth the Department of Electrcal and Electronc Engneerng at the Unverty of ong Kong a a Potdoctoral Fellow. Snce Nov. 008, Dr. Zhou ha been wth ong Kong Appled Scence and echnology Inttute Corp. a a prncpal engneer. She leadng a project of core IP R&D on LE Advanced. Dr. Zhou ha publhed more than 30 paper n IEEE journal and nternatonal conference. er reearch nteret nclude codng theory, pread pectrum, OFDM ytem, nterference cancellaton, hybrd ARQ, MIMO and other wrele technque for hgh peed data communcaton. Dr. Zhengang PAN receved the Bachelor and Mater degree, all n Rado Engneerng, from Southeat Unverty, Nanjng, Chna, n July 1997 and March 000, repectvely. Durng the year from Sept to Dec. 000, he wa workng n Nanjng Xuj Communcaton and Automaton Co. Ltd on the development of power lne communcaton equpment. From January 001 to Aprl 004, he ha been n Department of Electrcal and Electronc Engneerng, the Unverty of ongkong, puru Ph.D degree and uccefully obtaned the degree n December 004. After that, he joned DoCoMo Bejng Communca ng ton Lab Co. Ltd, workng on the front end reearch for the next generaton wrele communcaton tandard, ncludng 80.11n, 80.16d/e, SPA and LE. e ha nvolved n many techncal feld ncludng tme/frequency/amplng ynchron technology for ngle carrer/mult carrer(ofdm/a) baed ytem, channel etmaton, forward error correcton zaton codng, multple antenna ytem (MIMO) and pace tme proceng/codng, cro layer optmzaton and o on. In the year 006, he joned ASRI, a one of the foundaton team member of the Practcal MIMO Core project. In th project, he 7