Spce-Time Block Coding Bsed MIMO Arry Receiver Json W.P. Ng, T. Zhng nd A. Mniks Communictions nd Signl Processing Reserch Group Deprtment of Electricl nd Electronic Engineering Imperil College London London SW7 2BT United Kingdom AstrctcIn this pper, lind ner-fr resistnt MIMO rry receiver incorported with either Spce-Time Trnsmit Diversity (STTD) or Spce-Time Spreding (STS) schemes is proposed for time-vrying multipth DS-CDMA systems. Mny reported reserch works on MIMO, including the conventionl STTD nd STS schemes, often ssume tht the chnnel is flt fding nd is known. However, the MIMO rry receiver proposed in this study is sed on suspcetype joint spce-time estimtion lgorithm, which does not need ny power control or chnnel informtion. Furthermore, it is roust to chnnel estimtion errors in the event of ny unidentified or erroneous chnnel prmeter. The effectiveness of the proposed pproch is supported y representtive exmples nd computer simultion studies. NOMENCLATURE E Sclr E Column Vector [ Mtrix exp ÐEÑ Element y element exponentil of vector E E, Elementl power ÐÞÑ X Trnspose ÐÞÑ Complex conjugte Œ Kronecker product p Hdmrd (Schur) product ˆR Identity mtrix of R Rdimension E, Element y element power! R Zero vector of N elements dig ÐEÑ Digonlistion of vector E I. INTRODUCTION Spce-Time Trnsmit Diversity (STTD) scheme proposed y Texs Instruments [1] nd Spce-Time Spreding (STS) scheme proposed y Lucent Technologies [2], were the open loop diversity techniques sumitted nd dopted in the G moile stndrdistion odies. Both the schemes were essentilly sed on the Spce-Time Block Coding (STBC) trnsmission strtegy first suggested y Almouti in []. In these schemes, the signls re trnsmitted in lnced wy vi multiple ntenns which provides mximl pth diversity t the receiver. However most reported MIMO works on STTD nd STS trnsmission schemes frequently ssume knowledge of the chnnel in flt fding environment. In this pper, novel synchronous MIMO rry receiver, cple of exploiting either the trnsmission methodology of STTD or STS scheme, is proposed in time-vrying frequency-selective environment. Unlike mny other MIMO works which often dopt the ssumption of multiple independent ntenn elements, referred herein s multiple ntenn system, the proposed receiver is uilt on ntenn rry technology where numer of ntenn elements form n rry system of given geometry. The powerful effect of ntenn rry system, for instnce the 'smrt ntenns' technology lies in emforming in prticulr desired direction. By hrnessing the sptio-temporl properties of the chnnel provided y the ntenn rry, n extr lyer of co- chnnel interference cncelltion nd new wys for hndling unwnted chnnel effects cn e developed. This hs een demonstrted in the superresolution polristionsensitive rry in [4,5], with n overll comprehensive study investigted in [6]. Through the incorportion of the ntenn rry technology, lind ner-fr resistnt MIMO rry receiver is proposed with the incorportion of the STS nd STTD trnsmission schemes. It is roust ginst ny unidentifile or erroneous chnnel prmeter resulted in the estimtion process. Furthermore, it does not exhust, s in conventionl multi-code MIMO designs, the limited numer of spreding codes ville in the system. STTD ENCODER Figure 1: STTD Trnsmit Scheme
STS ENCODER >8"@ 2 >8"@ 2 >8"@ 2 >8"@ 2 Figure 2: STS Trnsmit Scheme II. MIMO ARRAY SYSTEM Fig. 1 nd Fig. 2 show the lock digrm of the STTD nd STS trnsmit scheme. Note tht Ò8Ó nd Ò8 "Ó represent respectively the odd nd even input dt symols, nd X -= is the dt symol period. In n Q users synchronous MIMO rry system, the th user's dt strem is first split into its odd nd even sustrems, followed y eing encoded using the ssocited trnsmit diversity encoder. The output dt strems from ech of its trnsmitting ntenn elements re given s Ò8Ó Ò8 "Ó Ò8Ó Ò8 "Ó " " ÚÝ Û Ý Ü # # œ Ò8Ó Ò8 "Ó Ò8 "Ó Ò8Ó for STTD (1) or " Ò8Ó Ò8 "Ó Ò8Ó Ò È 8 "Ó for STS (2) # Ò8 "Ó Ò8Ó Ò8 "Ó Ò8Ó where 4Ò8Ó nd 4Ò8 "Ó denotes the odd nd even th th differentil output dt symols of the user's 4 ntenn respectively. Note tht ech row of the encoder's mtrix in Eqn. (1) or (2) indictes the consecutive trnsmitted symols for ech ntenn, nd ech column represents the trnsmitted symols cross the ntenns t ech time slot. The encoded output symols re then spred y the th user's code sequence! of length - prior to trnsmission. Note tht the trnsmit diversity encoder ssocited with the STS scheme s shown in Eqn. (2) cn e rewritten s where Ò8Ó Ò8 "Ó Ò8 "Ó Ò8Ó Š Ò8Ó œ Ò8Ó Ò8 "Ó # Š Ò8 "Ó œ Ò8Ó Ò8 "Ó # È È The STS encoder siclly mps the complex dt symols Ò8Ó nd Ò8 "Ó into the form given in Eqn. (4), nd psses them through the STTD encoder. Thus, prt from () (4) the dditionl mpping complexity, the performnce of the STS system is expected to e similr to tht of the STTD system [7]. Suppose the trnsmitted signl from the 4 th ntenn th element of the user rrives t the receiver vi O4 multipths. For receiver employing n ntenn rry of R sensors, its corresponding sptil rry mnifold vector of th th th the 5 pth due to the 4 trnsmitting element of the user cn e expressed s X W 45 œ expð 4ÞÒ<ß<ß< Ó Þk Ñ (5) B C D In Eqn. (5), Ò<ß<ß< B C DÓ V R $ is defined s the Crtesin coordintes of the ntenn rry geometry nd k 45 is the wvenumer vector pointing towrds the direction ) 45. Hence, the chnnel impulse response cn e modeled s * > œ W " exp(4#1 > Ñ$ Ð> 7 45 Ñ (6) 45 45 45 45 where 7 45, " 45 nd 45 denote the pth dely, complex fding coefficient nd Doppler shift frequency respectively. Tking the mximum dely spred to e within symol period, the received signl vector is over smpled t rte of "ÎX = nd pssed through nk of R tppeddely lines (TDL), ech of length Pœ#; - (with ; eing the chip over smpling fctor). Upon conctenting the contents of the TDLs, the RP-dimensionl discretised signl vector is thus formed nd red for every symol periods. Its corresponding Sptio-Temporl Arry (STAR) mnifold vector is therefore given 8 y ± 45 645 45 œw 45 Œ œ 4 (7) where 645 œ 745 ÎX= is the discretised dely, is P P time downshift opertor given s follows œ Ô!! â!! "! â!! X!! #; - "! " â!! œ Ö Ù ˆ#;! - " ã ã ä ã ã #; - " Õ!! â "! Ø nd œ 4 corresponds to the smpled version of the th user's code signture, i.e. (8) - :; œ œ "! :Þ - (9) 4 " :œ! with the vector - eing the over smpled chip-level pulse shping function -Ð>Ñ pdded with zeros t the end, 4 X X - -Ð!Ñß -ÐX Ñß âß -ÐÐ; "ÑX Ñß! (1) œ < = = ÐP ;Ñ Hving specified the STAR mnifold vector, its discretised Doppler effect cn e esily included y extending Eqn. (7) to otin the Doppler-STAR mnifold vector due to the
5 th pth from the 4 th trnsmitting element of the th user, given s 645 8 œw ˆ œ Y 45 45 Œ p 45 8 (11) with the time-vrying Doppler component Y 45 8 modeled s follow Ô " exp 1 45 = 4# X Y45 8 œ exp 1 45 = 1 Ö 4#Þ# X exp 428 Ù ã Õexp 4#Þ P c " 1 X Ø 45X 45 = -= (12) Thus the net discretised signl vector, incorporting Inter- Symol Interference (ISI) nd Multiple-Access Interference (MAI), cn e written explicitly 8 s Ô c d 4c d 8 Q # 4 8c" B8 œ "" 4 8 4 4 8 n 8 œ" 4œ" Õ 8" Ø (1) where n is the smpled complex white Gussin noise vector, 4 œ ˆ$ Œ " contins the multipths' fding 4 coefficients with " œò" ß" ßáß" O Ó X 4, nd 4 4" 4# 4 X ; 4 8 œ< ˆ - ŒÐ Ñ 4 8 ß 4 8 ß (14) ˆ ; - Œ 4 8, #; R O with 8 œ Ò Ò8Óß Ò8Óß á ß Ò8ÓÓ V - 4 4 4" 4# 4O III. BLIND ESTIMATION AND RECEPTION A lind ner-fr resistnt MIMO rry receiver with only the knowledge of the desired W th user's code signture will e presented in this section. By exploiting the spcetime-frequency structurl property on the signl dt vector, the covrince mtrix BB of the discretised signl vector in Eqn. (1) will preserve nd provide sis for the desired signl suspce. This lgorithm cn e pplied for ny pths originted from the sme source rriving from the sme direction (co-directionl) or rriving t the sme time (co-dely); nd even in scenrio wherey the pths originted from the different sources of the desired user rriving in the sme spce nd time domins (colocted in spce nd time). However, for pths of the sme source hving the sme Doppler shift frequencies, singulrity in BB will occur. This specil cse cnnot e resolved for generl rry geometry ut for uniform liner rry where sptil smoothing cn e overlid on top of BB to form the smoothed covrince mtrix smooth. Hving otined the covrince mtrix, MUSIC-type chnnel estimtion cn e performed y minimising the following cost function 4 L ) ) ) Ðß6Ñ œ W L 4 ß6 n n W 4 ß6 L W4) ß6 W4) ß6 W (15) 6 where W4 ) ß6 œ ) Œ œw4 is the STAR mnifold vector with œ W4 eing the code signture due to the desired W th user s seen in Eqn. (9), nd n is the mtrix with columns the noise eigenvectors corresponding to the second order sttistics of Eqn. (1). Now y denoting \ sw4 œ s W s s 4" ß W4# ß áß W4O, the W4 STAR mnifold vector of the desired user cn e reconstructed sed on the estimted spce-time chnnel prmeters s \ sw œ< \ sw \ s " ß W#. In order to suppress the contriutions from the MAI nd ISI interferences, the received discretised signl vector B8 in Eqn. (1) is pssed through spce-time multipth filter nk to yield C8 œ L ÞB8 (16) L " with ¼ œ j \ s ¼ \ s WŠ \ s W j \ s 8> 8> \ sw (17) ¼ L " L where jš œ ˆ ŠÐŠ ŠÑ Š is the complementry projection opertor of the mtrix Š; nd W \ s \ s \ s \ s 8> œ ˆ X ; - ŒÐ -97ß ˆ ; Ñ - ŒÐ Ñ -97ß -97 in which \ s \ s \ s \ s -97 œ < " ß # ß áß Q is the estimted composite chnnel prmeters nd \s W is the composite -97 mtrix \ s with the exclusion of the mtrix \ s -97 W. The output of the filter nk, comprising of 2 œ! 4œ" OW rnches needs to e prtitioned to 4 differentite those rnches elonging to ech of the trnsmitting elements of the desired user. This cn e done y pssing the filter nk output in Eqn. (16), following the decision device, to the Brnch Identifiction Process, wherey cross-correltion is performed with prespecified threshold vlue nd ggroup together when itexceeds the threshold. Hving segregted the rnches s C c8d, with ech contining the outputs elonging to the W4 th th th 4 ntenn element of the desired W user, the 8 symol decision sttistic for ech of the trnsmitting ntenn elements cn then e relised s follows: s Ò8Ó œ A L W4 W4ÞC c 8 d (18) W4 where A W4 is the comining weight vector otined using the principl eigenvector of the utocorreltion mtrix ssocited with the output rnches from the desired user's 4 th ntenn element. Note tht it is not necessry to ssign ech nd every of the rnches to either trnsmitting elements of the desired user. If the chnnel prmeters of ny prticulr rnch is erroneous (incorrect chnnel estimtion) or unidentified (incomplete chnnel estimtion), the Brnch Identifiction Process will leve
TABLE I: USERS' PARAMETERS User " with code vector! " User # with code vector! # User $ with code vector! $ (Ant, Pth) s) "45 s6 "45 s (Ant, Pth) s) s6 s (Ant, Pth) s) s6 s #45 #45 $45 $45 "45 #45 $45 Ð4ß 5Ñ œ Ð"ß "Ñ )! #&X '&LD Ð4ß 5Ñ œ Ð"ß "Ñ %! #$X '&LD Ð4ß 5Ñ œ Ð"ß "Ñ )! #%X &!LD Ð4ß 5Ñ œ Ð"ß #Ñ (! "!X '!LD Ð4ß 5Ñ œ Ð"ß #Ñ )& "$X $!LD Ð4ß 5Ñ œ Ð"ß #Ñ "!! "%X (&LD Ð4ß 5Ñ œ Ð"ß $Ñ "$! #&X *!LD Ð4ß 5Ñ œ Ð"ß $Ñ )& "&X (&LD Ð4ß 5Ñ œ Ð"ß $Ñ ""& "(X $!LD Ð4ß 5Ñ œ Ð"ß %Ñ %& #!X '&LD Ð4ß 5Ñ œ Ð"ß %Ñ ""! &X %&LD Ð4ß 5Ñ œ Ð"ß %Ñ *! ")X!LD Ð4ß 5Ñ œ Ð#ß "Ñ && "&X!LD Ð4ß 5Ñ œ Ð#ß "Ñ (& )X %!LD Ð4ß 5Ñ œ Ð#ß "Ñ '! "* X (&LD Ð4ß 5Ñ œ Ð#ß #Ñ ""! &X %&LD Ð4ß 5Ñ œ Ð#ß #Ñ *! ")X $&LD Ð4ß 5Ñ œ Ð#ß #Ñ (& "!X %!LD Ð4ß 5Ñ œ Ð#ß $Ñ ""! ")X &!LD Ð4ß 5Ñ œ Ð#ß $Ñ "!& #%X '!LD Ð4ß 5Ñ œ Ð#ß - - $Ñ *! (X &&LD - Ð4ß 5Ñ œ Ð#ß %Ñ "#& "&X '&LD Ð4ß 5Ñ œ Ð#ß %Ñ "$& "&X )!LD Ð4ß 5Ñ œ Ð#ß %Ñ "#! #%X - (!LD - - tht rnch unssigned, thus inducing roustness to the receiver. Hving otined the differentilly decoded symols sw4ò8ó nd sw4ò8 "Ó from oth ntenn elements of the desired user, t he verge vlue of these pir set is given s swò8ó œ ÐsW" Ò8Ó sw# Ò8ÓÑÎ# swò8 "ÓœÐsW" Ò8 "Ó sw# Ò8 "ÓÑÎ# (19) For MIMO systems employing the STTD scheme, the estimted odd nd even symols ( swò8ó nd swò8 "Ó) of the desired user cn then e found directly s œ swò8ó swò8ó swò8 "Ó œ swò8 "Ó (2) On the other hnd, for MIMO systems using the STS scheme, the estimted odd nd even symols need to e further dempped s follows swò8ó œ Š swò8ó swò8 "Ó È # swò8 "Ó œ Š swò8 "Ó swò8ó È # IV. NUMERICAL ANALYSIS (21) Consider uniform Rœ5 element liner rry (of hlf-wvelength spcing) with Qœ co-chnnel DQPSK users employing either the STTD or STS schemes cross 4œ2 trnsmitting ntenn elements. Ech of the users is ssigned n unique PN code sequence of length - œ 1. Let's tke user 1 s the desired user, with n input Signlto-Noise Rtio (SNR) of 2 db, nd the other 2 interferers ech constituting n interference rtio of 2 db (i.e. nerfr prolem). The chip rte is set t 1.2288 Mchips/s with crrier frequency of 2 GHz. The Doppler spred is set t 1 Hz which corresponds to mximum speed of 54 km/h. Ech user is ssumed to hve 8 multipths with its prmeters s listed in Tle I. The rry collects 2 dt symols for processing with ;œ1. The spce-time estimtion of ll the 8 multipths due to the desired user is s illustrted in Fig.. It cn e seen tht ll the 8 multipths ssocited with the two trnsmitting elements of the desired user cn e identified/estimted successfully using the proposed lgorithm. The multipth elonging to ech of the two trnsmitting elements of the desired user re then singled out y pplying the Brnch Identifiction Process to the filter nk output. Its cross-correltion with the first output rnch is s illustrted in Tle II. The performnce of the proposed receiver employing the STTD nd STS schemes re then compred with n ST decorrelting detector nd 2D RAKE receiver s depicted in Fig. 4. It is therefore cler tht the proposed receiver is more tolernt with the multipth Doppler spred, whilst the ltter two deteriorte drsticlly t the onset of the spred. It cn lso e inferred from the figure tht the performnce of the proposed receiver employing the STS scheme is the sme s tht employing the STTD scheme. Now lets exmine the performnce of the proposed receiver versus the level of multiple ccess interference (MAI) with the following ssumptions: (1) ech ntenn element is ssocited with % multipths; (2) ech interferer is 2! db higher thn the desired user; () Doppler spred is set t "!! Hz; (4) TOA nd DOA prmeters of ech multipth re uniformly distriuted over Ò!X -, $"X-Ñ nd Ò!, ")! Ñ respectively. It is pprent from Fig. 5 tht the proposed STS nd STTD receivers re much more tolernt to the MAIs, while the ST decorrelting detector nd 2D RAKE receiver degenerte with the incresing numer of users. Finlly, it is worthwhile to note tht the employment of the STS or STTD scheme, unlike the Orthogonl Trnsmit Diversity (OTD) scheme, will still e le to operte even with the reception from only one trnsmitting ntenn element. It cn e seen from Fig. 6 tht the it error rte (BER) of the OTD receiver is nerly twice s high s tht of the STTD nd STS receiver. This is due to the nture of the OTD encoding scheme, in which the odd nd even symols re trnsmitted seprtely through the different ntenn elements, thus cusing hlf of the trnsmitted symols to e lost in the reception process.
V. CONCLUSION In this pper, we hve devised lind ner-fr resistnt MIMO rry receiver incorported with either the STTD or STS trnsmit schemes. By using these trnsmit schemes, dditionl diversity cn e gined without hving to exhust the numer of spreding codes ville. The proposed receiver does not require the need of ny power control or the knowledge of the chnnel. Simultion results hve shown tht the proposed STS nd STTD receiver chieves much etter performnce thn the conventionl receivers in time-vrying frequency selective environment. REFERENCES [1] Texs Instruments, "Spce-time lock coded trnsmit ntenn diversity for WCDMA", TI proposl TDOC662/98 to ETSI SMG2 UMTS stndrds, Dec 1998. [2] A. Kogintis, R. Soni, B. Hochwld nd C. Ppdis, "Downlink improvement through spce-time spreding," Lucent Technologies proposl GPP2-C-1999817-14 to m-2 stndrd, Aug 1999. [] S. M. Almouti, "A simple trnsmit diversity technique for wireless communictions'', IEEE Journl Selected Ares in Comms., vol. 16, no. 8, pp.1451-1458, Oct 1998. [4] Json W.P. Ng nd A. Mniks, "Diversely polrised rrys in DS-CDMA: A spce-time chnnel estimtion pproch", Int. Conf. Acoust., Speech, Sig. Proc., vol., pp. 2617-262, My 22. [5] Json W.P. Ng nd A. Mniks, "Polristion-ngle-dely estimtion using crossed-dipole rry for DS-CDMA systems", Interntionl Conference on Digitl Signl Processing, Vol.1, pp.259-262, Sntorini, Greece, Jul 22. [6] A. Mniks nd Json W.P. Ng, "Crossed-dipole rrys for synchronous DS-CDMA systems", IEEE Trnsctions on Antenns nd Propgtion, Vol.52, No.1, pp.122-11, Jn 24. [7] G. Wu, H. Wng, M. Chen nd S. Cheng, "Performnce comprison of spce-time spreding nd spce-time trnsmit diversity in m2", IEEE 54th Vehiculr Technology Conference, vol. 1, Fll 21. [8] Json W.P. Ng nd A. Mniks, "MIMO rry DS-CDMA system: lind spce-time-doppler estimtion/reception", Int. Conf. Acoust., Speech, Sig. Proc., vol. 2, pp. 7-4, My 24. TABLE II: BRANCH IDENTIFICATION PROCESS OF USER œ" (Ant 4, Pth 5) Ð"ß "Ñ Ð"ß #Ñ Ð"ß $Ñ Ð"ß %Ñ Ð#ß "Ñ Ð#ß #Ñ Ð#ß $Ñ Ð#ß %Ñ Correltion "Þ!!!!Þ)*(!Þ**)!Þ**)!Þ!!#!Þ!!"!Þ!!#!Þ!!" Figure : ST spectrum of ll multipths due to desired user. Averge output SNIR (db) 4 2 1-1 2D RAKE Rx ST Decorrelting Rx -2 5 1 15 2 Doppler spred (Hz) Figure 4: SNIR performnce versus Doppler spred Averge Output SNIR (db) 4 2 1-1 2D RAKE Rx ST Decorrelting Rx -2 1 2 4 5 6 7 8 9 1 Numer of Users Figure 5: SNIR performnce versus numer of users BER.7.6.5.4..2.1 Proposed OTD Rx -2-15 -1-5 5 1 15 2 Input SNR (db) Figure 6: BER performnce with signls received from only one trnsmitting ntenn element of the desired user