A New Antenna Selection Algorithm in Cognitive MIMO Systems

Transcription

1 Cyber Journals: Mulidisciplinary Journals in Science and echnology, Journal of Seleced Areas in elecommunicaions (JSA), ovember Ediion, 11 A ew Anenna Selecion Algorihm in Cogniive MIMO Sysems Zhang an, Xu Yemao and Gao Xiao Absrac Uilizaion of muliple anenna ransmission echnique is a poenial soluion o co-channel inerference problems in coexising environmens However, addiional sysem cos and complexiies associaed wih muliple anennas limi heir applicaion in C Sysems In his paper we inroduce anenna selecion in cogniive MIMO sysems and propose low complexiy anenna selecion algorihms Wherein, using only a subse of available anennas o ransmi or receive signal grealy reduce hardware cos and complexiies of he C ransceivers; while keeping much of he benefis of muliple anennas Index erms Muliple-Inpu Muliple-Oupu (MIMO), Cogniive adio(c) I IODUCIO Looming specrum scarciy and is low uilizaion moivaed he developmen of innovaive specrum sharing echnologies o improve specrum uilizaion efficiency Cogniive radio (C) is considered as a promising echnology ha enable secondary nework o dynamically uilize he licensed specrum, under he condiion ha no harmful inerference is caused o he primary operaions [1] However; in such coexising scenarios where cogniive radios communicae wih each oher by opporunisically uilizing he specrum, a secondary (C) user usually has o radeoff beween wo conflicing goals; imizing is own hroughpu, and o minimize he inerference i produces a each primary user [] Muliple anenna echniques, promising diversiy and capaciy gains may also be an efficien soluion o comba inerference in such co-exising environmens [3] Muliple anenna can be used o allocae ransmi dimensions in space and hence provide he secondary ransmier in C nework more degree of freedom in space in addiion o ime and frequency, so as o balance beween is conflicing goals[] Moreover, in OFDM-based C sysem by ransmiing differen daa on differen anennas, he resource loss due o carrier deacivaion in LUs band and bi rae Manuscrip received ov 9, 11 his work was suppored by aional Defense Pre-esearch Foundaion of Chinese Shipbuilding indusry Zhang an is wih Wuhan Mariime Communicaion esearch Insiue China He is now a engineer in digial communicaion a Wuhan Mariime Communicaion esearch Insiue, China ( nan_zhang313@sinacom) Xu Yemao is wih Wuhan Mariime Communicaion esearch Insiue China He is now a engineer in digial communicaion a Wuhan Mariime Communicaion esearch Insiue, China( frank_xu@homailcom) Gao Xiao is wih Wuhan Mariime Communicaion esearch Insiue China He is now a engineer in digial communicaion a Wuhan Mariime Communicaion esearch Insiue, China ( gaoxiao1113@sinacom) loss due o windowing can be compensaed [] In [], i was demonsraed ha capaciy of MIMO sysems increases linearly wih min(,), where and denoe he numbers of ransmi and receive anennas respecively However, he main drawback of muliple anenna echniques is he cos of radio frequency (F) chains, including low noise power amplifiers, gain conrol unis, digial o analog converers and several filers, which are he major cos of a sysem Increasing he number of anennas will lead o significan increase in sysem size, cos and complexiy, since each anennas requires a F link In order o reduce he sysem/hardware cos as well as o preserve he advanages of MIMO sysems, a promising echnique referred o as anenna selecion is presened in [] Wih his mehod; he F chains can be opimally conneced o he bes subse of he ransmier (or receiver) anennas I has been demonsraed ha he sysem performance using anenna selecion echniques is beer han he full-complexiy sysems wih he same number of anennas bu wihou selecion [] However, he only mechanism for opimum selecion of anenna is exhausive search of all possible combinaions for one ha gives he bes S (for diversiy) or capaciy (for spaial muliplexing) he complexiy of opimally selecing he bes ransmi/receive anenna grows exponenially, which is compuaionally inefficien Moreover, C are likely o face dynamic environmens where anenna selecion changes wih changing channel condiions hence, a compuaionally efficien anenna selecion algorihm is required In his paper, we address anenna selecion in cogniive MIMO sysem o reduce is cos while keeping much of he benefis of he muliple anennas We formulae he anenna selecion problem in cogniive MIMO sysem as a combinaorial opimizaion problem In Such co-exising environmen, our main goal is o imize he capaciy of cogniive MIMO sysem under inerference consrains o primary users However, adding spaial dimension o he C resource allocaion problem increases he size and complexiies of an already immense parameer space, for which opimal soluion is compuaionally inefficien We apply evoluionary echniques for anenna selecion problem and heir effeciveness is verified hrough simulaions under differen scenarios Simulaion resuls verify ha boh evoluionary echniques Geneic algorihm () and Binary Paricle swarm Opimizaion ()-based anenna selecion algorihms provide a low complexiy soluion o he 1

2 problem, which grealy reduce hardware cos and complexiies of cogniive MIMO sysem, while keeping much of he benefis of he muliple anennas Proposed algorihms achieve near opimal sysem capaciy over wide range of S, while abiding by he inerference consrains o he primary users II MIMO I COGIIVE SYSEMS he main problem of he cogniive radios operaing in coexising environmen is he co-channel inerference Muliple-anenna ransmission echnique (MIMO) is a poenial soluion o his problem I uses space diversiy and can offer muliplexing gain, diversiy gain and co-channel inerference suppression o he wireless sysem because of he independen channel fading beween differen pairs of anennas Considering downlink ransmission in a coexising environmen; where he wo sysems know all he ransmied signals, he diry paper coding (DPC) is seen as he opimal approach for he sum capaciy performance [7, ] However, major concerns in C sysem are no jus he sum capaciy, and he paricular challenge of he C is ha boh he ransmiers and receivers are disribued and may be unable o coordinae wih each oher he imum raio ransmission (M) mehod presened in [9] imizes he received signal-o-noise raio (S), bu i does no consider he inerference o he oher radio sysem and herefore degrades is performance he zero-forcing (ZF) mehod; which comes from muliple inpu and muliple oupu muli-user deecion (MIMO-MUD) echniques [1], perfecly miigaes he inerference o oher radio sysems However, i may degrade he power of desired signals and lose some of he diversiy gain of he channel he mehod proposed in [11] for secre communicaions in MISO case imizes he secrecy capaciy, which is equal o he difference beween message channel capaciy and inerference channel capaciy In his mehod he inerference power migh be small in some cases, bu i also migh be srong when doing his leads o a grea performance increase for he desired user However, his is no allowed for he C environmen since usually he performance of he primary sysem should be guaraneed and he inerference power should be conrolled below a cerain value X Processing F Chain 1 F Chain ou of Swich Propagaion Channel r ou of Swich F Chain 1 F Chain X Processing Fig 1 Block diagram of a MIMO sysem wih ransmi and receive anenna selecion Some previous work using muliple-anenna echniques in C environmens has been performed in scenarios where only he ransmier side employs muliple anennas hese linear approaches, including imal raio ransmission (M); zero-forcing (ZF); opimal inerference free (IF), and opimal inerference-consrained (IC), are based on beamforming echnologies; and can avoid or conrol he CCI, herefore improving he sysem performance [3] However, he main drawback of muliple anenna echniques is he cos of radio frequency (F) chains, including low noise power amplifiers, gain conrol unis, digial o analogue converers; and several filers, which are he major cos of a ransmier Increasing he number of anennas will lead o a significan increase in he cos since each anenna requires a F link A Anenna selecion In MIMO sysems, adding complee adio Frequency (F) chains may resul in increased complexiy, size and cos hese negaive effecs can be drasically reduced by using anenna selecion his is because anenna elemens and digial signal processing are considerably cheaper han inroducing complee F chains In addiion, many of he benefis of MIMO schemes can sill be obained [1, 13] Besides, perfec CSI is no required a he ransmier as he anenna selecion command can be compued a he receiver and repored o he ransmier by means of a low-rae feedback channel In Fig 1, we show a ypical MIMO wireless sysem wih anenna selecion capabiliies a boh ransmi and he receive sides he sysem is equipped wih ransmi and receive anennas, whereas a lower number of F chains has been considered ( < and r < a he ransmier and receiver, respecively) In accordance wih he selecion crierion, he bes sub-se of ransmi and, receive anennas are seleced his reduces he number of required F chains, hus leads o significan savings In order o convey he anenna selecion command o he ransmier, a feedback channel is needed bu his can be done wih a low-rae feedback as only r bis are required Originally, anenna selecion algorihms were born wih he purpose of improving link reliabiliy by exploiing spaial diversiy More precisely, a reduced complexiy sysem wih anenna selecion can achieve he same diversiy order as he sysem wih all anennas in use However, as MIMO schemes gained populariy, anenna selecion algorihms began o be adoped in spaial muliplexing schemes aimed a increasing he sysem capaciy A brief review of he sae of he ar is presened below, where differen mehodologies are classified according o he conex: spaial diversiy or spaial muliplexing B Anenna Selecion for Spaial Diversiy In a wireless environmen, by separaing he receive anennas far enough he correlaion beween he channel fades is low hen, by selecing he bes receive anenna in erms of channel gains, a diversiy order equal o he number of receive anennas is obained Winers considered a similar procedure in a Muliple-Inpu Single-Oupu (MISO) sysem o exploi diversiy a he ransmi side wih he help of a feedback channel [] In ha work, he anenna selecion algorihm was very simple: when he received S was below a specific hreshold a command is sen o he ransmier o indicae ha he r

3 ransmi anenna mus be swiched For he SIMO case, more sophisicaed receive anenna selecion algorihms based on Hybrid Selecion/imal-raio combining echniques were derived in [1] he basic idea of hose algorihms was o selec he bes (in erms of S)L ou of receive anennas and combine he received signals By means of a imal raio combining (MC) procedure By doing so, apar from exploiing he diversiy gain, array gain can also be exraced he exension o MIMO sysems were presened by Molisch e al [1, 1] in a scenario where anenna selecion was only performed a he ransmier in combinaion wih a imal raio ransmission (M) sraegy I was shown ha by selecing he bes sub-se of ransmi anennas; he degradaion in sysem performance is sligh in comparison wih he saving in erms of hardware cos he obained resuls can be easily generalized o hose cases performing anenna selecion a he receive side of he MIMO link due o he reciprociy of he S imizaion problem An ineresing resul was obained in [1] for hose sysems performing MC a he receiver side and an anenna selecion mechanism (wih a single acive anenna) a he ransmier I was shown ha he achieved-diversiy order is equal o B, wih B sanding for he posiion aken by he channel gain of he seleced anenna when arranging he channel gains of he differen ransmiers in an increasing order C Anenna Selecion for Spaial Muliplexing In spaially correlaed MIMO fading channels, capaciy gains can be lower han expeced since spaial muliplexing gains mainly come from resolving parallel pahs in rich scaering MIMO environmens Wih his problem in mind, Gore e al proposed one of he firs papers where anenna selecion was adoped in a MIMO conex In ha paper, he auhors showed ha sysem capaciy canno be improved by using a number of ransmi anennas greaer han he rank of he channel marix By considering ha, an algorihm (exhausive search) was proposed where only anennas saisfying he full rank condiion were seleced As a resul, sysem capaciy gains were obained wih respec o he full anenna sysem, since ransmi power was efficienly disribued Upper bounds of he achievable capaciy wih anenna selecion were derived in [1] In paricular, i was shown ha capaciy resuls close o hose of he full anenna sysem can be achieved by selecing he bes r ou of receive anennas In [1], a sub-opimal approach was proposed for boh ransmi and receive anenna selecion By saring wih he full channel marix, hose rows (columns) corresponding o he receivers (ransmiers) minimizing he capaciy loss are ieraively dropped As shown in [1,1], almos he same capaciy as wih an opimal selecion scheme can be achieved wih an incremenal version of he menioned selecion algorihm; ie, by using a boom-up selecion procedure In [1] i was also proven ha he diversiy order achieved wih receive anenna selecion is he same as ha wih he full anenna scheme; where he diversiy order was defined as he slope of he ouage rae Alhough a sub-opimal approach wih decoupled ransmi and receive selecion was adoped in [], similar conclusions in erms of he diversiy-muliplexing rade-off curare [9] were drawn ha is, he same rade-off curve, as wih all anennas in use can be obained wih ransmi and receive anenna selecion D Anenna Selecion in Cogniive MIMO Sysems he anenna selecion mechanisms oulined above are for he sysems wihou addiional inerference consrains as posed by cogniive radios As discussed earlier, cogniive radios operaing in coexising scenarios have o opimize heir performance under heir own power as well inerference consrains of he primary users herefore, problems implemening anenna selecion in cogniive MIMO sysems need o accoun for hese C specific consrains Moreover, he proliferaion of muliple anennas in cogniive radio sysems increases he size and complexiies of an already immense parameer space, for which compuaionally efficien anenna selecion mechanisms are required Signal Processing and coding Primary Sysem ransmier F Chain 1 F Chain ou of Swich Channel Primary Sysem eceiver Secondary Sysem eceiver Fig Block diagram of a cogniive MIMO sysem wih ransmis and receives anenna selecion Given hese opporuniies and challenges hus far, only a small se of published lieraure invesigaes anenna selecion in cogniive sysems o reduce complexiy of cogniive broadcas sysems having a large number of secondary users (and only one PU), a subse of users and single receive anenna selecion was presened in [1] However, he aemp o reduce he sysem complexiy is compromised by serving a subse of seleced users wih one receive anenna and a he cos of significan reducion in sum-rae capaciy Hence, rue benefis of MIMO like ransmi diversiy are no uilized Moreover in pracical co-exising environmen cogniive sysems have o operae in an environmen proliferaed wih a mass of legiimae primary users where, cogniive radios have o limi heir ransmissions o avoid any harmful inerference a he primary users In coexising environmens more chances of inerference are from he ransmi side Wherein, uilizing muliple anennas on he ransmi side and performing anenna selecion for a subse of useful anennas which creae lile or no inerference o he primary users, can improve overall performance of cogniive sysems Bu, o he bes of our knowledge no published work has so far been cied addressing ransmi anenna selecion in cogniive MIMO sysems In his paper we address ransmi anenna selecion in cogniive MIIVIO sysem o reduce he sysem cos We formulae he ransmi anenna selecion in cogniive MIMO sysem, while considering is own power and inerference consrains of he primary users And propose low complexiy ransmi anenna selecion algorihms for cogniive MIMO 3

4 sysem ha provide near opimal performance over a wide range of signal o noise raio III SYSEM MODEL We consider cogniive mufi-inpu mufi-oupu (MIMO) sysems wih ransmi anennas and received anennas as shown in Fig here are M primary users each equipped wih single anenna Because of cos concern, we consider a sysem ha has only F chains a he ransmier, where I is assumed ha he receiver and ransmier has he channel side informaion (CSI) We denoe he channel sae beween cogniive MIMO sysems by he complex H C marix and he channel sae beween he cogniive ransmi anennas and M primary users by he complex marix M G C r On he basis of his known CSI, he ransmier selecs a mos ransmi anennas from he ransmi anennas for he ransmission so ha inerference o he primary users is under some hreshold A Problem formulaion As discussed earlier, he capaciy of MIMO sysem under assumpions of whie Gaussian noise assumpions, is given as: P H C = log de( I + HH ) (1) r where, P is he oal ransmier power, is r r ideniy marix and H H I r, denoes he conjugae ranspose of channel marix H We assume ha ransmier allocaes power uniformly among he seleced ransmi anennas and channel inpus o hese anennas are uncorrelaed We formulae he ransmi anenna selecion in cogniive MIMO sysem as combinaorial opimizaion problem Our main goal of anenna selecion in cogniive MIMO sysem is o imize he capaciy of secondary sysem under inerference consrains o primary users Mahemaically: P log de I + HΩH r Subjec o he consrains C1: race( Ω) P C : Ω( i, i) G( m, i) Im for all m = 1,, M i= 1 where, Ω is a diagonal indicaor marix, whose diagonal enries are eiher 1 or depending on wheher an anenna is seleced or no Example Le = and = he one possible value of Ω can be: H () 1 1 B ransmi anenna selecion in cogniive MIMO he mos sraigh forward mehod o obain he opimal ransmi anenna subse is exhausive search However, he complexiy of opimally selecing ransmi anenna increase exponenially wih he number of ransmi anennas Exhausive Search Algorihm (ESA) evaluaes all possible i= 1 i combinaions of ransmi anennas o selec he anenna combinaion ha gives he bes performance (such as channel capaciy, bi error probabiliy, ec) Enumeraing over all possible combinaions and finding he one ha can give bes performance is compuaionally inefficien herefore, low complexiy algorihms are required o solve anenna selecion in cogniive MIMO sysem Evoluionary echniques, have successfully been applied for low complexiy soluion o he C parameer adapaion and o he oher combinaorial opimizaion problems of communicaion sysems In his paper, we apply geneic algorihm () and binary paricle swarm opimizaion () for ransmi anenna selecion in cogniive MIMO sysem he finess funcion used by and -based anenna selecion algorihms o converge o opimal soluion is objecive funcion () under he consrains C1and C IV SIMULAIO ESULS AD AALYSIS Simulaions are performed o validae he effeciveness of proposed anenna selecion algorihms as well as o compare heir performance wih opimal exhausive search algorihm (ESA) In our simulaions we receive anennas under he assumpions disribuions Generae channel gains beween ransmi and ha hey have independen complex Gaussian disribuions For performance analysis we presen simulaion resuls of eigh differen scenarios having differen number of oal/seleced ransmi anennas, as well as differen number of primary users and inerference hresholds: For all of hese scenarios, he populaion size of he individuals/paricles for / is and he imum number of generaion/ieraion is se o uses a crossover rae and muaion probabiliy of 9 and 1 respecively Whereas, he parameers for are, c1 c, V 7 o -7 = = + Figures 3 o 1, show sysem capaciy as a funcion of signal o noise raio (S) he effeciveness of he proposed anenna selecion algorihms is verified in various co- exising scenarios and over a wide range of S

5 In figures 3 and, wih same number of primary users and seleced anennas for secondary ransmissions, an increase in olerable inerference limi ( I ) by he primary users in Fig, yields increased C sysem capaciy a higher S Because of he fac ha, C is able o ransmi a higher power while sill obeying inerference consrains of he primary users Whereas, an increase in number of primary users in Fig, increases chances of inerference and hence decreases C sysem capaciy compared wih Fig 3, having he same inerference hresholds Because, wih increased number of primary users, inerference consrains for secondary (C) operaion increase oo herefore, C has o limi is ransmi power o avoid unaccepable level of inerference o he primary users Capaciy 1 (bis/s/hz) S (db) Fig7 Sysem capaciy versus S wih =, =, M = and I Fig3 Sysem capaciy versus S wih = 1, =, M = and I S (db) Fig Sysem capaciy versus S wih =, =, M = and I S (db) Fig Sysem capaciy versus S wih = 1, =, M = and I S (db) Fig Sysem capaciy versus S wih = 1, =, M = and I S (db) Fig Sysem capaciy versus S wih =, =, M = 1 and I In figures o, number of seleced ransmi anennas and primary users inerference hreshold are same whereas, number of primary users are varied he same is he case in figures 9 and 1 In all hese scenarios, an increase in number of primary users resuls in reducion of C sysem capaciy a higer S S (db) Fig9 Sysem capaciy versus S wih = 1, =, M = 1 and I S (db) Fig1 Sysem capaciy versus S wih = 1, =, M = and I Simulaions resuls verify ha, proposed algorihms achieve sysem capaciy near o ha of opimal exhausive search algorihm (ESA) hey effecively selec and uilize subse of ransmi anennas, which grealy reduces sysem cos and complexiies hey imize capaciy of he cogniive MIMO sysem under inerference consrains o primary users, wih much lesser compuaional complexiy as compare o opimal ESA

6 V COCLUSIO In his paper, we oulined sae of ar on MIMO echniques along wih an overview of anenna selecion mechanism We presened ransmi anenna selecion algorihms based on evoluionary echniques o reduce he cos and complexiies of cogniive MIMO sysems Anenna selecion was formulaed as a combinaorial opimizaion problem wih he main goal o imize he capaciy of cogniive MIMO sysem under inerference consrains o legiimae primary users he effeciveness of proposed algorihms is verified hrough simulaions in differen scenarios and compared wih ha of opimal exhausive search algorihm (ESA) Simulaion resuls show ha proposed algorihms achieve sysem capaciy near o ha of high complexiy opimal ESA, over a wide range of S, while adhering inerference consrains o he primary users he simple model, low implemenaion complexiy and near opimal performance of evoluionary algorihms-based anenna selecion, all make i a suiable soluion o reduce hardware cos and complexiies of cogniive MIMO sysems, while keeping much of he benefis of he muliple anennas EFEECES [1] Zhang and Ying-Chuang Liang, "Exploiing Muli-Anennas for Opporunisic Sharing in Cogniive adio eworks," IEEE Journal of Seleced opics in Signal Processing, vol, o 1, pp -1, February [] J Zhou and J hompson, "Linear precoding for he downlink of muliple inpu single oupu coexising sysem," IE Journal on Communicaions, special issue: Cogniive Specrum Access, vol, no, pp7-7, July [3] A Weiss and F K Jondral, "Specrum pooling: an innovaive sraegy for he enhancemen of specrum efficiency," IEEE Communicaions Magazine, vol, no 3, pp S-S1, March [] I E elaar, "Capaciy of mufi-anenna Gaussian channels," Eur rans elecomm vol 1, no, pp -9, ov1999 [] A F Molisch, M Z Win, Y S Choi and J H Winers, "Capaciyof MIMO sysems wih anenna selecion," IEEE rans Wireless Commun:, vol, pp , July [] Y1 W, Cioffi JM: `Sum capaciy of Gaussian vecor broadcas channels' rans Inf heory,,, (9), pp [7] Csire G, Shamai S, "On he achievable hroughpu of a mufi anenna Gaussian broadcas channel", IEEE rans Inf heory, 3, 9, (7); pp [] LO KY, "Maximum raio ransmission"(1), pp 1-11 rans Commun, 1999, 7, [9] Spencer Q H, Swindlehurs AL, Haard M,"Zero-forcing mehods for downlink spaial muliplexing in muliuser MIMO channels", IEEE rans Signal Process,,, (), pp 1-71 [1] Li Z, rappe W, Yaes, "Secre communicaion via mulianenna ransmission", Informaion Sciences and Sysems, 7, CISS'7, 1s Annual Conf,1-1 March 7, pp 9-91 [11] AF Molisch, and MZ Win, "MIMO sysems wih anenna selecion" Microwave Magazine, vol, no 1, pp -, Mar [1] S Sanayei, and A osrainia, Communicaions Magazine, vol "Anenna selecion in MIMO sysems", no: 1, pp -73, Oc : [13] AF Molisch, MZ Win, and JH Winers, "educed-complexiy ransmi/receive diversiy sysems", in Proc VC Spring, ov 1 [1] AF Molisch, MZ Win, and JH Winers, "educed-complexiy ransmi/receive diversiy sysems", IEEE rans on Signal Processing-Special Issue on MIMO Wireless Communicaions, vol 1, no 11, pp 79-73, ov 3 [1] A Gorokhov, DA Gore, and AJ Paulraj, "eceive anenna selecion for mimo spaial muliplexing: heory and algorihms", IEEE rans on Signal Processing-Special Issue on MIMO Wireless Communicaions, vol 1, no 11, pp 79-7, ov 3 [1] K Hamdi, W Zhang and K B Laief, User scheduling in Cogniive MIMO "Low-Complexiy Anenna Selecion and Broadcas sysems", proc of IEEE ICC [17] Zhang an, Gao Xiao, Deerminaion Of Minimal Marices Of Simple Cycles In LDPC Codes Inernaional Journal of Wireless & Mobile eworks (IJWM) Vol 3, o 3, pp 13-17,June 11 [1] Zhang an, Gao Xiao, Joinly Ieraive Decoding of Low-Densiy Pariy Check codes (LDPC) coded Coninues Phase Modulaion (CPM) Mulidisciplinary Journals in Science and echnology JSA, Vol, o 3, pp -31, March 11 [19] Gao Xiao, Zhang an, Cycle Analysis in Expanded QC LDPC Codes Mulidisciplinary Journals in Science and echnology (JSA) Vol, o : pp 13-1, May 11 [] Gao Xiao, Zhang an, Deerminaion of he shores balanced cycles in QC-LDPC codes Marix Mulidisciplinary Journals in Science and echnology (JSA) Vol, o : pp1-, April 11 [1] resch, M Guillaud, and E iegler, On he achievabiliy of inerference alignmen in he K-user consan MIMO inerference channel, in Proc IEEE Workshop on Saisical Signal Processing (SSP), Cardiff, Wales, UK Sep 9 [] J Dumon, W Hachem, S Lasaulce, P Loubaon, and J ajim, On he capaciy achieving covariance marix of ician MIMO channels: An asympoic approach, o appear in IEEE rans on Inform heory: evised on 9 [3] W Sanipach and M L Honig, Capaciy of a Muliple-Anenna Fading Channel wih a Quanized Precoding Marix, IEEE rans Inform hoery, vol, o3, pp 11-13, Mar 9 Zhang an He received he BE degree in elecronical informaion engineering, from Henan Universiy of echnology, China, in and he MS degree in elecrical engineering form China Ship esearch and Developmen Academy, in 9 He currenly is a engineer in digial communicaion a Wuhan Mariime Communicaion esearch Insiue, his ineress include wireless communicaion sysem, error conrol coding echniques and applied informaion heory