Performance Analysis of High-Rae Full-Diversiy Space Time Frequency/Space Frequency Codes for Muliuser MIMO-OFDM R. SHELIM, M.A. MATIN AND A.U.ALAM Deparmen of Elecrical Engineering and Compuer Science Norh Souh Universiy, Dhaka, Bangladesh Deparmen of Elecrical and Elecronic Engineering Insiu Teknologi Brunei, Negara Brunei Darussalam Email:main.mn@gmail.com Absrac: - MIMO-OFDM has been recognized as one of he mos promising echniques o suppor high daa rae and high performance wireless sysems. In paricular, coding over he space, ime, and frequency domains provided by MIMO-OFDM enables a much more reliable and robus ransmission over he harsh wireless environmen. In his paper, he auhors provide an overview of spacefrequency (SF) coding and space-ime-frequency (STF) coding for MIMO-OFDM sysems and compare he performance of differen coding schemes. Performance resuls show ha STF coding can achieve beer coding and diversiy gain in an end-o-end MIMO-OFDM sysem over broadband wireless channels. Key-Words: -muliple-inpu muliple- oupu sysems, mulipah fading channels, muliple access channel (MAC), muliuser space ime frequency (STF) coding, muliuser space-frequency (SF) coding. Inroducion Fuure broadband wireless sysems require high daa rae and high performance over fading channel ha is ime selecive and frequency-selecive fading which are quie challenging. To address hese challenges, one promising soluion is o combine wo powerful echnologies, namely, muliple-inpu muliple-oupu (MIMO) anennas and orhogonal frequency division muliplexing (OFDM) modulaion []. I encodes a daa sream across differen ransmi anennas and ime slos, so ha muliple redundan copies of he daa sream can be ransmied hrough independen fading channels. As a resul, more reliable deecion can be obained a he receiver. Therefore, his opic has drawn a lo of ineress among he researchers o dae, consequenly, a large number of space-ime (ST) or space-frequency (SF) coding have been designed for MIMO-OFDM sysem []-[0] o exploi he spaial diversiy gain. However, mos of he codes are designed for single user sysem uilizing single-user space-ime codes for each of he users and separaing he users in signal space or canceling muliuser inerference. However, hese approaches lead o reduce ransmission rae or subopimum performance significanly, if he number of users is high. Considering he above issue, Gärner and Bölcskei designed a muli-user space-ime/frequency code [] based on Gallager s idea in [], which is derived from he dominan error mechanisms in wo-user Addiive Whie Gaussian noise (AWGN) muliple access channel (MAC) bu deailed code design seems o be missing. Zang and Leaief [3] inroduced a sysemaic design of full diversiy muli-user space-frequency code. Bu, he symbol or code rae of heir proposed design is hough some remarks have been given for high rae full diversiy code design. Recenly, a sysemaic high symbol rae full-diversiy STF/SF codes for muli-user MIMO-OFDM sysem have been designed [-6]. To increase he symbol rae of heir proposed code design, he space-frequency and space-ime-frequency layering concep wih algebraic componen code is uilized. For boh ST and STF design, each componen code is assigned o a hread in he space-frequency (for SF E-ISSN: -86 5 Volume 3, 0
codes) and space-ime-frequency (for STF codes) marix ha provide full access o he channel frequency, ime and spaial diversiy in he absence of oher hreads. Diophanine approximaion heory is hen used where he Diophanine numbers are, and is chosen such ha he hreads are ransparen o each oher. Furhermore, anoher Diophanine approximaion is used where he Diophanine numbers are as follows so ha users are ransparen o each oher. Depending on he pair wise-error probabiliy of muliuser MIMO sysem, he full diversiy performance of he muli-user STF codes is associaed wih he full-rank propery of any codeword difference marix and any se of users. In his paper, we aemp o provide an overview of SF coding, and STF coding for MIMO OFDM wireless sysems, in paricular focusing on recen work on high rae and full diversiy muli-user SF/STF code design. For beer undersanding of SF/STF code design, SF and STF codes have been discussed in wo separae secions. Simulaion secion compares he performance of he proposed STF codes wih SF codes. The organizaion of his paper is as follows. The MIMO- OFDM sysem is briefly inroduced in secion. In secion 3, he design of full diversiy and high code rae muliuser SF code wih an example is presened. In secion, a design of STF code is provided wih an example o verify he code design. The presened code can also achieve full diversiy and high code rae. Secion 5 compares he performance of he STF codes wih muliuser SF code and oher ypical SF codes. Finally, a conclusion is given in secion 6. MIMO-OFDM Sysem MIMO-OFDM is he combinaion of MIMO and OFDM where MIMO can enhance he capaciy and diversiy and OFDM can miigae he inerference effecs due o, mulipah fading. Suppose ha he MIMO-OFDM sysem shown in Fig. has Z users, where each user is equipped wih A ransmi anennas, a base saion (BS) wih A r receive anennas and N-one OFDM. The MIMO channels experience frequency selecive fading induced by L independen pahs beween each pair of ransmi and receive anennas and can be expressed as, L i, j i, j a a 0 h a, where, is he delay of h a a pah, i, j a denoes he h channel coefficien of he a pah from he ransmi anenna j o he receive anenna i, where, i=, A r ; j,, A ; and a = 0,,,,L-. The source in MIMO-OFDM sysem generaes a block of N s informaion symbols from he discree alphabe, which is a quadraure ampliude modulaion (QAM) consellaion normalized ino he uni power. Using a Ns mapping, he informaion symbol vecor S is encoded ino N A code marix ( z ) N A C which is hen sen hrough ransmiing anennas. The symbol rae or code rae per channel use of he code marix C is given by, Ns. N Le, each user has N-one OFDM. For user z, he codeword C can be wrien as, where, he OFDM symbol C () A, is assumed o be ( z ) n ransmied from he n h ransmi anenna. The OFDM symbols are sen simulaneously from all ransmi anennas afer IFFT and cyclic prefix (CP) inserion. Afer passing hrough he MIMO Channels, he received signals will be firs sen o he reverse OFDM block o remove CP and FFT demodulaion and hen sen i o he decoder. E-ISSN: -86 5 Volume 3, 0
User: A Frequency Selecive Fading Channel Base Saion User: z A A r Fig.: Muliuser MIMO OFDM Sysem 3 Muliuser Space-Frequency Code Design The design of full diversiy ArA L and high code rae (i.e. rae- A ) muliuser SF code design has been discussed in his secion. Our SF code has been consruced based on hreaded layering concep []. Exploiing he dualiy, space-frequency coding in frequency-selecive channel is consruced from spaceime coding in ime-selecive channel. The proposed design of full diversiy A r A L and high rae A, SF codes have been shown in Fig.. An example of he presened muli-user SF codes has also been given. Here, i is considered ha he sysem has N-OFDM ones. A block of NA informaion symbols S [ S S S ] from he discree alphabe ( z ) z z ( z ) T BK, where ( z ) NA S, and S is a QAM consellaion are normalized ino he uni power and are parsed ino N B, subblocks, Each sub block K S WZ AW LW, b,,, B is composed of he b signal w vecors S w w, w, w=,,3, and W W A. The signal vecor comprises of QAM symbols. Z L Each sub-block, S b=,, 3 B is W Z AW L W b respecively, encoded ino an SF code marix K A marix. Le K WZWLW, C b of size logl log A log where,, Z W W, W, The L Z SF code marix can be expressed as,, c b,, W L L Z W, W, W Z, () Nex, for muli-user MIMO-OFDM MAC, he encoded codeword Cb is, E-ISSN: -86 53 Volume 3, 0
Where, Φ, z is he which is given by Φ C C z z b b Φ, z A h z column of he Q K Z K Z Z K Q Q K, (5) K WZ marix Φ, (6) encoded sub blocks. Thus, he presened rae - codes C C N M for he h z user is of he form:- T T T C C C B T A SF Noe ha as TASF code confirms ha N is he ineger muliple of K, no zero-padding marix is required in our proposed code srucure. Thus he rae- A can be always guaraneed. Deailed code design is given in [].. (7) Where is given by K where number wih degree of a leas K is an algebraic W L over where is he field exension of which conains all he enries of he signal alphabe, j and j l Ts e,( l 0,,,L ). Here, he SF code for one sub block is illusraed as in Fig. and he same phenomena is applied for oher Fig..SF coding srucure in MIMO-OFDM sysem [] Example of SF codes: For, A 3, L, Z, For z=, C () () () () () 3 () () 3 () () 3 () () () () () () (3) () () 3 3 3 () 3 () 3 () 3 () 3 () () 3 5 () 5 () 5 3 () (7) 6 () 6 () 6 () 3 7 3 () 7 () 7 () 3 (3) (3) (3) (7) (7) (7) (8) (8) (8) (8) (9) (9) (9) (9) () () () 8 () 8 3 8 () 3 9 () 9 () 9 3 () 0 () 0 () 0 () 3 (5) 3 () () () 3 () 3 () () 3 3 () 3 () 3 3 () () () () 3 5 3 () 5 () 5 () 3 () (5) (5) (5) (6) (6) (6) (6) (0) (0) (0) (0) () () () () () () () () E-ISSN: -86 5 Volume 3, 0
For z=, C () () () () 5 () 5 3 () 5 () 3 () () 3 () () () () () () (3) () () 3 3 () () () 3 3 () 3 3 () 3 () 3 () () 3 () 5 () 5 () 5 () 3 6 3 () 6 () 6 () 3 (3) (3) (3) (7) (7) (7) (7) (8) (8) (8) (8) (9) (9) (9) (9) () () () 7 () 7 3 7 () 3 8 () 8 () 8 3 () 9 () 9 () 9 () 3 (5) 0 3 () 0 () 0 () 3 () 3 () () 3 () () 3 () 3 () 3 () 3 () 3 3 () () () 3 () (5) (5) (5) (6) (6) (6) (6) (0) (0) (0) (0) () () () () () () () () T T Where, w W () S S W, W,,3,. W Muliuser Space-Time-Frequency Code Design In his secion, we have presened a design of STF code ha is capable o achieve full diversiy and high code rae (i.e. rae- ) over MIMO frequency selecive block fading channel. The design of he presened muliuser STF is illusraed in Fig. 3. I is assumed ha he source generaes a block of informaion symbols for user z, where z=,,,z and, which are QAM from he discree alphabe and he sysem has N-OFDM ones. Then each sub-block, b=,, B is encoded ino an STF code marix of size marix.le, where,,.i is obvious ha is always a power of wo. The, marix is srucured as The block of informaion symbols is as which are normalized ino he uni power and are evenly spli ino sub blocks, For muliuser MIMO-OFDM MAC, he encoded codeword is given by, E-ISSN: -86 55 Volume 3, 0
where, is he column of he marix. Bu for ease, STF coding for one subblock is illusraed in Fig.3. Thus, he presened STF codes for he user is of he form, Where, K where is an algebraic number wih degree of a leas K over, where is he field exension of which conains he signal alphabe, and all he enries of The presened STF coding applies he same coding phenomena o all encoded sub blocks,, Noe ha as no zero-padding marix is required in he presened code srucure, he rae- can always be guaraneed.also noe ha he difference of he STF codes beween wo users is made by he selecion of differen columns of marix given in ( ). As can be known in advance and each ransmier can know is fixed seleced column before he daa ransmission, he cooperaion among he differen users is no necessary in he uplink process. Deailed code design is given in [5] Fig.3. STF coding srucure in MIMO-OFDM sysem [5] Code Design Example: Le, The STF coding applies he same coding sraegy o every sub-block. For convenience, we jus consider he subblock and as an example for user z= and z=, respecively. Here, and which are defined earlier. user-, E-ISSN: -86 56 Volume 3, 0
for user-, 5 Simulaion Resuls In he simulaion experimens, we consider wo users scenario where each user has wo ransmi anennas and he base saion has wo receive anennas wih equal power gain. The MIMO frequency selecive fading channels are simulaed from a wo ray channel model in which he second pah delay is assumed o be 0.5µs ha is, 0 imes he sampling inerval for each pair of ransmi-receive anennas. The lengh of he cyclic prefix is chosen as ¼ of N where N=6 OFDM ones is used for each ransmi anenna. In he simulaion, he channel E-ISSN: -86 57 Volume 3, 0
coefficiens are independen from one OFDM block o oher block bu are remain consan during one OFDM block. The following hree codes are simulaed and compared in symbol error rae (SER) performance wih baseband symbols, muliuser SF codes wih 6-QAM, proposed muliuser space-frequency wih 6-QAM and he proposed muliuser space-ime-frequency codes wih 6-QAM. From Fig., i is observed ha in he low-omiddle SNR region, presened SF code shows he similar performance as [3]. Bu, in he high SNR region, he proposed muli-user SF codes have beer performance han [3]. Therefore, a higher coding gain is achieved compared wih muli-user SF code in [3] in he high SNR region. Again i can be seen from he simulaion resul ha he proposed muliuser STF codes have larger slope curve, compared wih he wo SF codes (i.e. muliuser SF codes [3], proposed muliuser spacefrequency) and wih he baseband signal. Fig:: SER performance comparison beween he proposed muliuser SF, muliuser STF code, he muliuser SF code in [3] and he baseband symbol. muliuser SF codes wih a gap of abou db over all he examined SNR values. This indicaes ha he rae- STF code from 6-QAM has a beer coding and he diversiy gain han he rae- SF code [3] and proposed rae- SF from 6QAM. The simulaion resul also shows ha our presened high rae muliuser SF and STF codes achieve much beer performance han he baseband symbols ha jusifies our proposed schemes. Therefore, he presened muliuser SF and STF codes do no affec he code performance while he symbol rae is increased o. 7 Conclusion The auhors presen wo coding schemes for muli-user MIMO-OFDM sysem in his paper. The high-rae (rae- ) and full-diversiy A A r L (for muli-user SF codes) and A Ar Au L (for muli-user STF codes) for each user is achieved wihou bandwidh expansion. The presened schemes are bandwidh efficien and always ensure rae- A as no zero padding is needed. Moreover, he presened coding schemes do no require he cooperaion of muliple ransmiers in he uplink process. Few examples of he presened code designs are given. Simulaion resul proves ha he presened SF codes has a beer coding gain in compare o [3] in he high SNR region whereas STF codes has a beer coding and diversiy gain in compare o [3] in boh low and high SNR regions. Furhermore, he presened coding schemes do no affec he code performance while he symbol rae is increased o rae- A. References: This implies ha he proposed STF codes achieve a larger diversiy gain han boh SF codes. From he analysis, i is clear ha he proposed full-diversiy muliuser STF code can achieve a diversiy gain A A A L =6, whereas he proposed full-diversiy r u muliuser SF and he muliuser SF codes [3] codes achieves AA rl =8 only. Moreover, i is observed ha he proposed muliuser rae- STF code achieves he bes SER performance among he simulaed cases, and ouperforms he rae- SF code [3] and proposed rae- [] H. Bölcskei, MIMO-OFDM wireless sysems: Basics, perspecives and challenges, IEEE Wireless Commun. Mag., vol. 3, no. 8, pp. 3 37, Aug. 006. [] W. Zhang,.-G. ia, and P. C. Ching, High-rae full-diversiy spaceime-frequency codes for broadband MIMO block-fading channels, IEEE Trans. Commun., vol. 55, no., pp. 5 3, Jan. 007. E-ISSN: -86 58 Volume 3, 0
[3] W. Zhang,.-G. ia, and K. B. Leaief, Spaceime/frequency coding for MIMO-OFDM in nex generaion broadband wireless sysems, IEEE Wireless Commun. Mag., vol., no. 6, pp. 3 3, Jun. 007. [] V. Tarokh, N. Seshadri, and A. R. Calderbank, Space-ime codes for high daa rae wireless communicaion: Performance crierion and code consrucion, IEEE Trans. Inf. Theory, vol., no. 3, pp. 7 765, Mar. 998. [5] H. Bölcskei and A. J. Paulraj, Space-frequency coded broadband OFDM sysems, in Proc. IEEE WCNC, Chicago, IL, Sep. 3 8, 000, pp. 6. [6] H. Bölcskei, Space-frequency codes for broadband fading channels, in Proc. IEEE ISIT, Washingon, DC, Jun. 9, 00, p. 9. [7] Y. Gong and K. B. Leaief, An efficien spacefrequency coded OFDM sysem for broadband wireless communicaions, IEEE Trans.Commun., vol. 5, no., pp. 09 09, Dec. 003. Codes, IEEE Transacion On Signal VOL. 58, no. 3, March 00. Processing, [] R. Shelim, M A Main and A U Alam, A Sysemaic Design of High-Rae Full-Diversiy Space-Frequency Codes for Muliuser MIMO- OFDM Sysem, WSEAS ransacion on Communicaions, vol., no., pp. 5-63, April 03. [5] R. Shelim, A U Alam and M A Main, High-Rae Full-Diversiy Space-Time-Frequency Code for Muliuser MIMO-OFDM sysems over Frequency Selecive Muliple Access Channels Journal of Convergence Informaion Technology, vol. 6, no. 8, pp. 8-, Augus 0. [6] R S Topu, A Alam and M A Main, High-rae fulldiversiy muliuser space-frequency codes in ICCIT 00 proceedings, korea, pp.-6, Nov. 30- Dec., 00. [8] W. Su, Z. Safar, M. Olfa, and K. J. R. Liu, Obaining full-diversiy space-frequency codes from space-ime codes via mapping, IEEETrans. Signal Process., vol. 5, no., pp. 905 96, Nov. 003. [9] W. Su, Z. Safar, and K. J. R. Liu, Full-rae fulldiversiy space-frequency codes wih opimum coding advanage, IEEE Trans. Inf. Theory, vol. 5, no., pp. 9 9, Jan. 005. [0] W. Zhang,.-G. ia, and P. C. Ching, Fulldiversiy and fas ML decoding properies of general orhogonal space-ime block codes for MIMO- OFDM sysems, IEEE Trans. Wireless Commun., vol. 6, no.5, pp. 67 653, May 007. [] M. E. Gärner and H. Bölcskei, Muliuser spaceime/frequency code design, in Proc. IEEE ISIT, Seale, WA, Jul. 9, 006, pp.89 83. [] R. G. Gallager, A perspecive on muliaccess channels, IEEE Trans. Inf. Theory, vol. 3, no. 3, pp., Mar. 985. [3] W. Zhang, and K. B. Leaief, A Sysemaic Design of Full Diversiy Muliuser Space-Frequency E-ISSN: -86 59 Volume 3, 0
APPENDI STF CODE DESIGN EAMPLE IN DETAILS An example of our recenly proposed STF code [5] design has been given. We have jus shown he sub-block for convenience because he same coding sraegies can be applied o every sub-block, b=,, B. Le, So,,. Thus, is marix and given by, = and is 8 marix and given by, =. Now, for i=, l=, d=, =0; i=, l=, d=, =; i=, l=, d=, =; i=, l=, d=, =6; For z=,,,,. Now, =. Thus, E-ISSN: -86 60 Volume 3, 0
Similarly, for z=, E-ISSN: -86 6 Volume 3, 0