Single Antenna Interference Cancellation Algorithm Based on Lattice Reduction

Transcription

1 Journal o Communicaions Vol 1, No 2, Feruary 215 Single Anenna Inererence Cancellaion Algorihm Based on aice Reducion ueng Zhao, ujian Cao, and Xuchu ai Key aoraory o Wireless-Opical Communicaions, Chinese Academy o Sciences, School o Inormaion Science and echnology, Universiy o Science and echnology o China, P R China {zy7, caoyjian}@mailusceducn; daixc@usceducn Asrac Single anenna co-channel inererence (CCI) cancellaion is a challenge in moile communicaion sysems, especially or downlink sysems A novel single anenna CCI cancellaion algorihm ased on laice reducion (R) and decision eedack equalizaion scheme is proposed in his paper he idea ehind he proposed algorihm is o orm a mulichannel muli-user deecion model hrough over-sampling and hen adops a decision eedack deecion mehod ased on R Complexiy analysis resuls show ha he complexiy o he proposed algorihm is quadraic wih he memory lengh o he channels and is nearly independen o he modulaion order Furhermore, simulaion resuls are also presened o indicae he i error rae perormance o he proposed algorihm and is rousness wih respec o channel esimaion errors Index erms Co-channel inererence, single anenna, inererence cancellaion, laice reducion I INROUCION Co-channel inererence (CCI) is a common phenomenon in cellular radio communicaion neworks as a resul o requen reuse I is one o he acors limiing sysem capaciy o reduce perormance degradaion, he co-channel inererence cancellaion is necessary, and has araced he aenion o many researchers or more han 2 years In paricular, inererence cancellaion is a challenging ask in he receiver equipped wih one anenna, such as he downlink ime division muliple access sysem he corresponding soluions are known as single anenna inererence cancellaion (SAIC) he SAIC echniques can generally e classiied as eiher linear iler-ased (FB) or muli-user deecion (MU) mehods [1] he asic principle ehind FB mehods is o design a linear iler o cancel CCI A linear or nonlinear iner-symol inererence (ISI) equalizer is hen applied [2]-[4] However, hese approaches can only cancel an inererence signal Moreover, he consellaion o modulaed signals should e one-dimensional (eg, inary phase-shi keying (BPSK) and Gaussian minimum shi keying (GMSK)) In conras o FB mehods, MU mehods deec all co-channel signals simulaneously he opimal muli-user deecor in erms o maximum likelihood is he joinly maximum likelihood sequence esimaion (JMSE) mehod [5] Manuscrip received ecemer 11, 214; revised Feruary 25, 215 Corresponding auhor daixc@usceducn doi:11272/jcm However, his mehod is diicul o implemen ecause o is high complexiy o reduce he complexiy, reduced sae rellis-ased join deecion algorihms have een proposed [6], [7] Unorunaely, he compuaional complexiy is sill growing exponenially wih he modulaion order o co-channel signals hus, his mehod is unsuiale or high-order modulaion signals H Arslan [8] proposed a low-complexiy, successive SAIC mehod ased on he power dierence o co-channel signals However, he perormance o his mehod declines sharply when he powers o co-channel signals are comparale Miller [9] presened a co-channel daa esimaion mehod using a se o pariioned Vieri deecors, whereas he perormance loss is unaccepale given only one anenna o improve he perormance, Wei Jiang [1] proposed several ieraive SAIC algorihms y comining he radiional SAIC mehods wih uro equalizaion wih he help o channel coding he challenge in SAIC echniques lies in designing a low-complexiy and high-perormance SAIC algorihm ha is suiale or co-channel signals wih comparale powers and high-order modulaion In he las decades, near-opimal deecors wih lower complexiy have een proposed in muliple-inpu and muliple-oupu (MIMO) sysems ecision eedack equalizaion (FE) and Successive Inererence Cancellaion (SIC) has een widely used in muliuser deecion in MIMO and CMA sysems [11]-[15] Recenly, laice reducion (R) aided deecion has proven o e an aracive soluion or near opimal MIMO deecion wih low complexiy [16] In his paper, a new SAIC algorihm ased on laice reducion and FE is hus proposed Unlike exising works on SAIC, he conriuion o our work has wo aspecs One is o conver a single channel-received signal model o a virual muliple channel signal model, which is undamenal in he proposed SAIC algorihm he oher is o design a signal deecion mehod ased on he R algorihm and he FE scheme Essenially, he proposed SAIC algorihm is a nonlinear scheme, and can eecively cancel inererence signals In addiion, our analysis and simulaions show ha he complexiy o he proposed algorihm or he lock ading channel is quadraic wih he channel lengh and is independen o modulaion order he remainder o his paper is organized as ollows he co-channel signal model is descried in he nex 215 Engineering and echnology Pulishing 93

2 Journal o Communicaions Vol 1, No 2, Feruary 215 secion, speciically he consrucion o he equivalen virual muli-channel discree signal model he principles o R and o he proposed SAIC mehod are presened in secion III he numerical resuls and analysis are provided in secion IV Conclusions are drawn in he inal secion A simple mehod or deecing s1 (n ), ased on he signal model (3), is o use he Wiener iler or is low complexiy and opimaliy in he sense o he minimum mean square error (MMSE) Assuming ha he iler lengh is, hus he linear iler oupu can e expressed as P 1 1 II MOEING OF CO-CHANNE SIGNAS WIH A SINGE ANENNA RECEIVER z (n ) MSE v( ) k s1(n K are he desired signal 2 signal and can e expressed as sk (l )hk ( ls ), k 1,2,,K (2) l modulaion symol sequence o he kh co-channel signal he ype MQAM, M sk (l ) o is resriced, ha is, sk (l ) hk ( ) is he equivalen channel impulse response, which consiss o a pulse shaping iler, a physical ransmission channel, and a receiving iler Wihou loss o generaliy, he eecive memory lengh o he received signal y( ) is over-sampled P imes per symol, ha is, P 2 he discree ime model can e represened as y( ) K s(n) vi (n ), i P (3) y(ns o y( ) and hk,i (l ) (hk,i (l ))P equivalen channel vi (n), y(n) [y1(n),, yp (n)],, sk (n)], v(n) [v1 (n),, vp (n )], and ), an oserving window o he, yi (n } is required according o equaion (4) By denoing (n ), S(n ), and is / P ) denoes V (n ) as he discree channel noise he noise power and hk,i (l ) (n ) are presumaly known a he receiver he purpose o his sudy is o develop an eecive mehod o derive he S(n ) V (n ) desired signal s1 (n ) rom yi (n ) 215 Engineering and echnology Pulishing K received signal {yi (n), is / P ) is he discree v(ns [s1(n), o deec s1 (n is / P ) is he discree orm hk (ls (7) suscrip denoes ranspose k 1 l where yi (n) v(n) l) l where H(l ) l )hk,i (l ) H(l )s(n y(n) n ip /s sk (n A Virual Muliple Channel Signal Model he signal model expressed y (3) can e ransormed ino he ollowing vecor orm hk ( ) is assumed o e symol periods yi (n) (6) o improve he deecion perormance, we invesigae he R-aided SAIC mehod in his secion R-aided linear deecion and nonlinear deecion is widely sudied in MIMO communicaions in recen years However, hese mehods canno e applied direcly o he signal model expressed y (3) hus, we need o conver his model rom a scalar o a vecor orm o 4, 8,16 he modulaion symol alphae is denoed y q (z(n)) ) III INERFERENCE CANCEAION BASE ON MUIUSER EECION where s is he symol period and sk (l ) is he ransmied modulaion (5) I is well known ha linear iler mehod is simple, u is perormance is aeced y he power o inererence Unorunaely, he linear iler mehod lowers he deecion perormance signiicanly when he powers o he co-channel signals are comparale Hence, he direc use o he linear iler algorihm is unavorale, and new mehods should e developed his noise is Co-channel signal x k ( ) is a digial modulaion x k ( ) 2 where q {} denoes quanizaion wih respec o and he inererer signals, respecively, and v( ) is he whie Gaussian noise wih variance independen o he co-channel signals ) } E { z (n) e oained via he Wiener Khinchin algorihm he esimaion resuls are hen given y ( k 1 where x 1 ( ) and xk ( ),2 s1(n (4) is he iler delay he iler coeiciens ai,k can where K x k ( ) k) he MSE o z (n ) is Given a scenario wih muliple co-channel signals, K 1 co-channel inererers along wih a desired user s signal are capured y a receiver equipped wih an anenna he received aseand co-channel signals can e expressed as y( ) ai,k yi (n i k 94 y (n ) s (n ) v (n ) y (n s (n v (n y (n s (n v (n

3 Journal o Communicaions Vol 1, No 2, Feruary 215 where S = 1S is an ineger symol vecor Hence, we hen ormula (3) can e rewrien in he ollowing vecor orm, HS(n) V (n) (n) where H is a P K ( ha is, H () H ( H (8) ) lock-oepliz marix, H () H () H ( K ( ) can deec S ased on hrough he ZF or MMSE algorihm insead o deecing S ased on For linear ZF deecion, he received signal is muliplied y he pseudo-inverse o marix o oain he esimaion o S, ha is, H () S = H = S+H V H () H ( Given he non-orhogonal channel marix, ZF deecion suers rom enhanced noise MMSE deecion minimizes he overall error conaining noise and oher inererers and can perorm eer han ZF deecion Raided MMSE deecion (R-MMSE) is achieved y applying R o he exended channel marix H and he exended received vecor [19], ha is, H () We regard equaion (8) as he virual muliple channel model or virual MIMO model ecause his signal model is similar in orm o ha o muliple physical receiving channels, such as MIMO Given he virual muliple channel signal model, he SAIC prolem may e reaed as a delay-ormed muli-channel MU prolem In conras o he Wiener iler mehod, we consider he deecion o vecor S(n ), which conains he desired signal s1 (n H H ) I K (, I K ( ) ) he resul o he R-MMSE deecion is S = q{h } B R-aided Symol eecion he undamenal principle o R-aided MIMO deecion is explained as ollows For a given ime n, equaion (8) can e regarded as a P K ( ) MIMO model, which can e expressed riely as S V [h1, h2, where he marix Sˆ (9), hk ( ) ] and each K ( ) S(n) (s (n) s (n 215 Engineering and echnology Pulishing ) has a peculiar k ), k 1,2,, 1 A naural prolem rough y aove oservaion is how o uilize he peculiar srucure o S(n ) o improve deecion perormance Noicing ha s(n,, s(n are he K ( ) Z given Z Marices H and H span he same laice i and only i is unimodular [17], ie, he elemens o marix 1 I he laice asis is are all inegers and de( ) eer condiioned, he laice-ased linear deecors (eg, zero-orcing (ZF) and MMSE deecors) are increasingly reliale hus, he main issue is how o ind he marix so as o make H well condiioned Forunaely, he complex ensra ensra ovász (C) algorihm [18] oers an excellen soluion Aer oaining y perorming he C algorihm, ormula (9) can e rewrien as V ) can hus srucure; ha is, S(n ) is composed o s(n ) and is ( +-1 delay versions, s(n S ), s1 (n C Applicaion o FE o he Symol eecion Process According o Susecion B, R-aided linear deecion can e applied direcly in SAIC ased on he virual MIMO model However, we noice ha in his virual muliple channel model, he inpu symol vecor Any elemen o he laice can e represened as V= (14) e oained direcly rom S m 1 1S q {S } Given ha S conains s1 (n K ( ) hm z m : z m (13) K ( ) where S, q {} denoes an ineger rounding operaion he inal deecion resul or he ransmission symols is hen oained y column o can e considered as a asis or he K ( ) dimensional laice he ransmied M-ary quadraure ampliude modulaion (MQAM) symol can e regarded as a complex ineger, and he symol vecor K ( ) his se is he S elongs o he se K ( ) dimensional complex ineger space Hence, laice generaes all possile noiseless received signals (12) ime delay versions mechanism can e perormance and o S(n ) ino wo pars, o s(n ), a decision eedack adoped o improve deecion reduce complexiy We divide namely, he orward-moving par S (n ) and eedack par S (n ) as ollows S (n) (1 95 S (n) s (n),, s (n s (n,, s (n )

4 Journal o Communicaions Vol 1, No 2, Feruary 215 A ime index n, S ( ) is deeced y he previous n daa vecor ( n,, ( n ) hus, he deecion resuls can e used o cancel he ISI o s( n,, s ( n in ( n) Based on he reduced ISI daa vecor, a reliale s( n ) can e oained hrough R-ased deecion mehods such as R-MMSE According o he aoremenioned descripion, expression (9) can e expressed as ( n) ( n) S ( n) H S ( n) V ( n) (15) where and are he eedack and eed-orward channel marices, respecively ha is, (:,1 : K ( ) H (:, K( 1 : K( )) S ( ) is he eedack symol vecor oained rom he n previous symol deecion process From expression (15), i can e known ha ( n) equals ( n) S ( n), which means ha he par ISI is eliminaed hereore, deecing S ( n) ased on ( n) is more reliale han he using ( n) R-FE Algorihm or SAIC According o Susecion B and C, S ( n) can e derived rom ( n) y using he mehod discussed in Susecion A ha is, i is he reduced asis, 1 hen S ( n) S ( n) o improve deecion perormance urher, we apply a successive inererence cancellaion algorihm [2] o deec S ( n) By conducing QR-decomposiion on marix, QR, we hen oain S ( n) Q ( n) RS ( n) Q V( n) (16) ue o he up-riangular srucure o he R, elemens o S ( n) can e deeced successively hrough inererence cancellaion Once S ( n) is deermined, he desired esimaion resul s ( n ) can e oained rom S ˆ ( n) y Sˆ ( n ) q { S ˆ ( n )} (17) Because S ˆ ( n ) conains s( n ),, s ( n ), he R-ased mehod deecs s( n ),, s ( n ) simulaneously he direc soluion is o selec s( n ) as he esimaion o s ( n ) and discard s( n,, s ( n ) Clearly, his mehod is suopimal Given he peculiar srucure o S ˆ ( n), s( n ) can e deeced imes y using ( n ),, ( n However, some esimaion resuls, eg, s ( n ), are ( n ) unreliale ecause hese resuls conain insuicien inormaion regarding s ( n ) Given ha ( n n ),, ( n conain enough inormaion regarding s ( n ), he corresponding esimaion resuls can e used o improve he esimaion resul o s ( n ) In his case, n denoes he numer o eecive deecion resuls, and n can e seleced according o, n he opimal soluion can e deermined y comining he esimaion resuls according o heir deecion proailiy However, i is diicul o calculae he deecion proailiy Hence, we provide a lowcomplexiy, suopimal esimaion o s ( n ) n 1 s ( n ) q { s ( n ) } (18) ( n k) n 1 k where s ( n ) represens he esimaion o ( n k ) s ( n ) hrough using ( n k) Based on he analysis and discussion aove, he R- FE SAIC algorihm is descried in ale I ABE I: HE R-FE SAIC AGORIHM Inpu: y ( n), n N,,, i Oupu: s ( n) Iniialize: s ( n), n 1 C( ) n //laice reducion o he exend eed-orward channel marix 2 or n : N 3 S ( n ) s ( n,, s ( n, ( n) ( n) S ( n), ( n) // ge he exended eed-orward vecor 4 S ( n) q{ SIC( ( n)} // SIC deecion on he laice ield 5 S ( n) q { S ( n)} 6 //ransorm he deecion resul o he original ield n ( n) K 1, ( 1 s( n ) q { s ( n ) } ( n k) n 1 7 end or 8 reurn he esimaed soluion s ( n) k 215 Engineering and echnology Pulishing 96

5 Journal o Communicaions Vol 1, No 2, Feruary 215 Remark 1: he principle o SIC is similar o ha o FE Hence, he proposed algorihm is mainly composed o wo nesed FEs, which is he reason he proposed algorihm is named as he R-FE algorihm he inner SIC deecion is ased on he ransormed laice asis and can improve he esimaion perormance o S ( n) Given S ( n) S ( n), hus he perormance o S ( n) is also enhanced In addiion, an improved esimaion o S ( n) implies ha ewer error propagaion appears in he ouer FE process Remark 2: he real and imaginary pars o he modulaion symols or MQAM are oained rom he se { ( M,, 1,1,, M 1}, which is no a consecuive ineger se hereore, we should ranser he symol consellaion o a consecuive ineger se a he eginning o he algorihm he implemenaion o he ransormaion is deailed in Re [21] Remark 3: he over-sampling parameer P is an imporan parameer in he proposed algorihm he oversampling acor P 2 is necessary o ully uilize he excess andwidh From he perspecive o he Nyquis heorem, P should e larger han 2 However, P should e equal or larger han he numer o co-channel signals o consruc an over-deermined virual MIMO sysem hereore, P max{2, K } is suiale or pracical applicaions E Channel Esimaion Channel sae inormaion (CSI) and noise power is presumaly known in he proposed algorihm However, CSI should e esimaed in pracical sysems Channel esimaion is more diicul in muliple-user scenario han in a single user scenario ecause more channel coeiciens mus e esimaed Given a slow ading channel, channels can e esimaed via a join leassquare channel esimaor when he raining symols o all he co-channel users are known o he receiver Assume ha N is he numer o raining symols o each user, S [ s, s,, s ] is he raining :1 1:2 N : N 1 symol marix ha consiss o he raining symols o all users, = [ y( ), y(,, y ( N )] is he received daa marix, and H [ H(), H(,, H( )] is he channel marix o e esimaed According o equaion (7), we can oain he ollowing equaion he leas squares esimaion o H S V (19) H is H S ( S S ) H H 1 (2) Given he esimaed channel, noise power can e easily deermined via he power o he received signal minus he signal power o all users In some cases, he receiver can only acquire knowledge on he raining sequence o he desired signal u none regarding he inererences his scenario can e regarded as a semi-lind CSI esimaion prolem, as discussed in Re [22] F Complexiy Analysis he main compuaional complexiy o he proposed algorihm lies in he preprocessing procedure and he deecion procedure he rough analysis o he complexiy is as ollows he preprocessing procedure includes he C algorihm and QR decomposiion Noice ha QR decomposiion can e done in C algorihm Given ha he size o is P K (, he average complexiy o he C algorihm is hereore 3 3 O( KP ( log2 P )[18] he deecion procedure conains hree pars: SIC deecion (ie SIC( ( n) ), marix muliplicaion (ie S ( n) ) and eedack process (ie S ( ) n ) For simpliciy, we ignore he cos o rounding hus, he complexiy o he deecion procedure or each symol is approximaely O( KP( )) For a slow or lock ading channel, he channel can e regarded as ime-invarian over a inie daa lock hus he preprocessing procedure need only e execued once in a daa lock However, he deecion procedure has o e execued or every symol in a daa lock hereore, he average complexiy or deecing each symol is O KP P N O KP, 3 3 (( ( log2 )/ ) ( ( )) d where N is he numer o symols in a daa lock d Noice ha he size o oserving window is mainly decided y channel lengh, and is usually slighly larger han hereore, he complexiy o he R-FE algorihm is quadraic wih he memory lengh o he channel and is nearly independen o he modulaion order M By conras, he complexiy o he JMSE mehod is OM 2 ( ), which is exponenially increased wih channel lengh Hence, he complexiy o he proposed algorihm is much lower han ha o he JMSE mehod, especially in high-order modulaion he numerical comparison o he complexiy or he some given parameers is presened in he nex secion IV NUMERICA RESUS he perormance o he proposed R-FE algorihm was evaluaed via numerical simulaion using QPSK and 16QAM modulaed signals (QPSK signal can e seen as a phase shied 4QAM signal) Simulaions were perormed in Mala A desired signal and an inererence signal are considered A slow-ading requency-selecive channel similar o ha in Re [8] is employed 6, n 2, and 5 is se or he simulaion he desired user and 215 Engineering and echnology Pulishing 97

6 Journal o Communicaions Vol 1, No 2, Feruary 215 he inererence are similar in erms o pulse shape, symol alphae and ransmission power he desired signal-o-noise (SNR) power raio is deined as SNR E / N, where s s E denoes he average received energy per symol o he desired signal and N is he specrum densiy o noise BER JMSE proposed mehod R-MMSE 1-4 MMSE SNR Fig 1 BER perormance vs SNR or co-channel QPSK signals wih perec CSI Fig 1 plos i error rae (BER) perormance as a uncion o SNR or wo QPSK co-channel signals his perormance is compared wih ha o he JMSE [5] and MMSE deecors he MMSE deecor is a linear deecion mehod ha applies he MMSE deecion algorihm direcly o ormula (5) he direc MMSE mehod can e regarded as a linear iler mehod ha miigaes CCI and ISI he JMSE deecor can achieve opimal perormance using a join Vieri algorihm Given he low SINR in his insance (SINR < db), he BER o MMSE is high However, an improved channel marix is oained y uilizing he R algorihm hereore, he R-MMSE ouperorms MMSE Noneheless, he proposed R-FE algorihm perorms eer han R-MMSE According o Fig 1, he SNR loss when he R-FE algorihm is used is approximaely 15 3 db a a BER o 1, unlike ha when JMSE is employed Given he signiican reducion in compuaional complexiy, he proposed mehod is highly suiale or realisic applicaion Fig 2 depics BER perormance as a uncion o SNR or wo 16QAM co-channel signals R and decision eedack can consideraly improve he perormance o he MMSE deecor However, a high SNR is sill required or he 16QAM co-channel signals Because o a huge ime consuming or he JMSE deecor in 16QAM case, JMSE perormance has no een oained hrough simulaion According o parameers se in simulaions and complexiy analysis in secion III, ale II gives he average numer o loaing-poin operaions (lops) o hree dieren mehods or QPSK and 16QAM cochannel signals, where he numer o lops equals 2 or complex addiion and 6 or muliplicaion GSM urs srucure wih N 61 daa symols is used From he d ale II, we noice ha hough he complexiy o he proposed R-FE mehod is 6 imes o ha o he MMSE mehod, he dramaic perormance improvemen is provided y he R-FE mehod (see Fig 1 and Fig 2) On he oher hand, compared o he JMSE mehod, he complexiy o R-FE mehod is signiicanly reduced wih small perormance degradaion ABE II: HE NUMERICA COMPARISON OF AVERAGE COMPEXI FOR EECING EACH SMBO (IN FOPS) BER R-FE MMSE JMSE mehod mehod mehod M= M= perec CSI 13 raining symols 26 raining symols SNR Fig 3 BER perormance vs SNR or co-channel QPSK signals wih channel esimaion raining symols 26 raining symols BER 1-2 MSE 1-2 proposed mehod R-MMSE MMSE SNR Fig 2 BER perormance vs SNR or co-channel 16QAM signals wih perec CSI SNR Fig 4 MSE channel esimaion vs SNR or co-channel QPSK signals 215 Engineering and echnology Pulishing 98

7 Journal o Communicaions Vol 1, No 2, Feruary 215 Fig 3 displays he BER perormance o he proposed R-FE mehod wih channel esimaion, whereas Fig 4 illusraes he perormance o he channel esimaor wih dieren raining symols he BER perormance o he proposed R-FE mehod wih 13 raining symols is nearly similar o ha o he perec CSI Given 26 raining symols, he perormance loss is aou 2dB when he 2 BER is equal o1 hereore, he proposed R-FE algorihm is rous wih respec o channel errors V CONCUSIONS In his paper, we invesigaed SAIC in erms o laice reducion R can e applied o SAIC ased on he virual MIMO model, which is consruced using he oversampled received signal Given he special consrucion o he virual MIMO model, a low-complexiy SAIC algorihm, ie, he R-FE algorihm, was developed o eecively reduce he eecs o CCI and ISI he proposed algorihm is ased on R and he FE scheme; hus, he complexiy increases only quadraically wih channel lengh and is nearly independen o he modulaion order he BER perormance was compared wih ha o he radiional MMSE, JMSE SAIC mehods hrough compuer simulaion he simulaion resuls showed a loss o only 15 db occurs or he QPSK 3 signals a a BER 1, compared o JMSE mehod Furhermore, he complexiy is signiicanly reduced In addiion, he proposed algorihm is consideraly superior o he MMSE mehod or he QPSK and 16QAM modulaion signals Finally, he simulaions demonsraed he rousness o he proposed algorihm wih respec o channel esimaion error ACKNOWEGMEN his work was suppored in par y he Naional High echnology Research and evelopmen Program o China (863 Program) under gran numer 212AA1A52 We would like o hank he edior and anonymous reviewers or heir consrucive commens, which helped improve he qualiy o he presenaion o heir work REFERENCES [1] P A Hoeher, S Badri-Hoeher, W Xu, e al, Single-anenna co-channel inererence cancellaion or MA cellular radio sysems, IEEE Wireless Communicaions, vol 12, no 2, pp 3-37, 25 [2] P Chevalier and F Pipon, New insighs ino opimal widely linear array 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8 Journal o Communicaions Vol 1, No 2, Feruary 215 source separaion u-feng Zhao was orn in HuBei Province, China, in 1986 He received he BS degree rom he Universiy o Science and echnology o China (USC), Heei, in 29 in elecrical engineering He is currenly pursuing he Ph degree wih he eparmen o Elecrical and Engineering, USC His research ineress include communicaion signal processing, lind u-jian Cao was orn in Shanong Province, China, in 1988 He received he BS degree rom he Universiy o Science and echnology o China (USC), Heei, in 211 in elecrical engineering He is currenly pursuing he Ph degree wih he eparmen o Elecrical and Engineering, USC His research ineress include communicaion signal processing Xu-Chu ai was orn in AnHui Province, China, in 1963 He received he Ph degree rom he Universiy o Science and echnology o China (USC), Heei, in 1998 in elecrical engineering He is currenly a proessor wih he eparmen o Elecrical and Engineering, USC His research ineress include communicaion signal processing, inormaion heory 215 Engineering and echnology Pulishing 1