Low Complexity V-BLAST MIMO-OFDM Detector by Successive Iterations Reduction

Transcription

1 Low Complexty V-BLAS MIMO-OFDM Detector by Successve Iteratons Reducton Karam Amed, Serf Abuelenn, Heba Solman, Kary Al-Barbary Port-Sad Unversty, Faculty of Engneerng, 456, Egypt Suez Canal Unversty, Faculty of Engneerng, 45, Egypt Abstract V-BLAS detecton metod suffers large computatonal complexty due to ts successve detecton of symbols. In ts paper, we propose a modfed V-BLAS algortm to decrease te computatonal complexty by reducng te number of detecton teratons requred n MIMO communcaton systems. We begn by sowng te exstence of a maxmum number of teratons, beyond wc, no sgnfcant mprovement s obtaned. We establs a crteron for te number of maxmum effectve teratons. We propose a modfed algortm tat uses te measured SNR to dynamcally set te number of teratons to aceve an acceptable bt-error rate. en, we replace te feedback algortm wt an approxmate lnear functon to reduce te complexty. Smulatons sow tat sgnfcant reducton n computatonal complexty s aceved compared to te ordnary V-BLAS, wle mantanng a good BER performance. Index erms MIMO, OFDM, sgnal detecton, V-BLAS I. INRODUCION Multple Input Multple Output (MIMO) systems can sgnfcantly ncrease te spectral effcency n wreless communcatons. e correspondng tecnology s known as spatal multplexng, n wc, bot transmt and receve sdes use antenna arrays to transmt dfferent data concurrently [, ]. e broadband communcaton cannels are frequency-selectve; utlzng Ortogonal Frequency Dvson Multplexng (OFDM) overcomes te frequency selectve nature of broadband cannels, by convertng tem to multple flat fadng sub-cannels [3, 4]. Vertcal-Bell Laboratores Layered Space-me (V-BLAS) arctecture s effectvely used for detecton n MIMO systems. It s based on successve nterference cancellaton and needs to calculate te pseudo-nverse of te cannel matrx and ts deflated matrces [5, 6]. Integratng OFDM and MIMO systems rapdly ncreases te complexty. s s because detecton s requred for eac subcarrer of te OFDM system. V-BLAS requres optmal orderng of te cannel matrx to maxmze te mnmum post-detecton sgnal-tonose rato (SNR) of all data streams [7, 8], wc means te strongest sgnal as to be detected frst to reduce ts effect on te remanng sgnals [9]. After detectng a suffcent number of te strongest symbols, tere s no need to contnue n teratons of detecton, and te remanng part of sgnals can be detected drectly usng a lnear detector; e.g. Zero Forcng (ZF) or Mnmum Mean Square Error (MMSE) detectors [5]. Oter metods ave been ntroduced n order to reduce te complexty of V-BLAS algortm e.g., [0-]. In ts paper, we ntroduce a V-BLAS algortm wt reduced complexty. We reac a crteron for te maxmum number of effectve teratons (Nmax) n a quadrate MIMO system, (system wt equal number of transmttng antennas N t and recevng antennas N r ). en, we buld a complete teratve V-BLAS detector wt varable number of successve teratons (N). We frst utlze a feedback based algortm usng te measured SNR value. In eac teraton, te algortm cecks te requred BER value s reaced. If so, te remanng symbols are detected lnearly. Oterwse, extra teratons are performed untl acevng te target BER, or reacng Nmax. o reduce complexty furter, we use a lnear functon to approxmate te performance of te dynamc teratve algortm. e two algortms are compared wt te ordnary V-BLAS detector usng two crtera; BER performance and complexty. Complexty s assessed based on te average executon tme of te algortms. e rest of ts paper s organzed as follows; secton II brefly descrbes MIMO-OFDM systems, followed by te model of ordnary V-BLAS detecton algortm n secton III. Secton IV descrbes te proposed modfcatons. Fnally, te paper s concluded n secton V. II. MIMO OFDM MODEL s secton presents te model for te N r xn t MIMO system at N t =N r =N a. We consder non-lne-of-sgt (NLOS) Rayleg flat fadng cannel.. e entres of te cannel matrx (H) are ndependent and dentcally dstrbuted (..d) complex Gaussan random varables. e sgnal s corrupted by..d zero mean addtve wte Gaussan nose [3, 4]. Block dagram of MIMO-OFDM system for one subcarrer k, were k = 0,, K- s sown n Fg. [5]. Fgure. Block dagram of te baseband subcarrer (k) of MIMO-OFDM system. e receved sgnal s gven by: Y = H X + N( k) () Were

2 Y = [ y k y,, y k ( ), K N ( )] () r And te cannel matrx for subcarrer k s: K Nt L H = Nt (3) M M O M Nr Nr L NrNt were, H s a Rayleg flat fadng cannel mpulse response. e transmtted (nput) sgnal s: X = [ x k x,..., x k ( ), N ( )] (4) t, te added nose s: N = [ n k n,..., n k ( ), N ( )] (5) r and te estmated sgnal s: X = [ x, x,..., x k N ( )] (6) t III. NON-LINEAR V-BLAS DEECOR V-BLAS nonlnear detecton algortm [5] provdes a good BER performance compared to ZF and MMSE. It s regarded as an Ordered Successve Interference Cancellaton (OSIC) detecton sceme, were te output sgnals are detected successvely combned wt spatal nullng process [6]. In an (N r xn t ) MIMO system, we need N t detecton steps, correspondng to te number of transmt antennas. e man problem wt V-BLAS s te error propagaton. o crcumvent error propagaton, detecton s aceved n a descendng order startng from te strongest sub-stream. e nullng process plays te man role n detecton. In eac detecton teraton, te detector treats te oter sub-streams as nterference sgnals. After detectng te strongest substream, ts contrbuton s subtracted from te receved sgnal. e remanng part contans te weak sgnals tat can be recovered n te next teraton wtout te nterference effect of te strongest one. s procedure s repeated untl detectng all sub-streams. Bot ZF, MMSE can be used to provde te spatal nullng process and to separate te ndvdual streams. Fnally, a quantzaton process s appled to approxmate eac estmated sgnal to te nearest value n te constellaton []. e general algortm for V-BLAS detecton s as follows [7, 8]. Orderng: by coosng te row w k of w(k) wt te mnmum Eucldean norm. w k = ( G ) k (7) Nullng: were we use te null vector w k to null out te undesred sgnals and obtan te requred one. Z k = w k Y (8) Slcng: approxmate te detected sgnal to ts nearest value n sgnal constellaton. X ˆ b = O( Z k ) (9) Cancellaton: Subtract te detected sgnal from te receved sgnal vector and zerong ts correspondng column n cannel matrx H. k Y Y H Xˆ + = ( ) k (0) H K H + = H ( ) () Fnally te detected symbols are exported. Export: X ˆ = [ Xˆ, Xˆ,..., Xˆ M ] () were G = Pnv(H) for ZF-V-BLAS, and reorderng s done wt te smallest row norm of G. If we use MMSE H lnear detector, we ave G= DH [9], were D = [ H H H+ I ] Nt (3) SNR And we do te reorderng at te smallest dagonal entry of D [0]. (G) j,(h) b ndcate te jt row of G and te b column of H, respectvely. A. Estmatng Nmax IV. MEHODOLOGY V-BLAS detects stronger symbols frst. Detectng te remanng weak sgnals successvely does not provde a sgnfcant performance mprovement. o sow ts, we vary te number of teratons from zero (lnear detector) to (N t -) teratons (ordnary V-BLAS). e remanng sgnals n eac tme are detected usng a lnear metod. We perform ts routne on dfferent MIMO antenna confguratons at dfferent codng scemes. Fgs. ( troug 4) sow te results for 4x4, 8x8 and 6x6 MIMO systems usng QPSK and 6QAM modulaton scemes. Bot ZF and MMSE lnear detectors are used as te core of our V-BLAS detector.

3 c) c) d) Fgure. e BER performance for 4x4 MIMO system usng te varable teratons V-BLAS detector ZF/QPSK, MMSE/QPSK, c) ZF/6QAM, and d) MMSE/6QAM d) Fgure 3. e BER performance for 8x8 MIMO system usng te varable teratons V-BLAS detector ZF/QPSK, MMSE/QPSK, c) ZF/6QAM, and d) MMSE/6QAM 3

4 from N=0 to N=Nmax, as sown n Fg. 6. able I lsts te requred N values for te defned acceptable performance under dfferent SNR condtons. For smplcty, we approxmate te relaton between SNR and N as a lnear formula, as sown n Fg. 6. c) d) Fgure 4. e BER performance for 6x6 MIMO system usng te varable teratons V-BLAS detector ZF/QPSK, MMSE/QPSK, c) ZF/6QAM, and d) MMSE/6QAM We can clearly see tat for N > Nt/, no sgnfcant mprovement n performance s obtaned for all studed confguratons. MMSE s preferred as a lnear detector for ts superor performance over ZF [, ]. B. V-BLAS wt varable teratons (N) For furter complexty reducton, we dynamcally set te number of teratons based on te measured (estmated) SNR value. Dfferent metods may be utlzed for SNR estmaton, e.g. te plot preamble sceme (data-aded) and sem-blnd SNR Estmaton (none-data-aded). e blnd sceme can be appled smply on MIMO-OFDM systems, were te sceme can be used drectly before or after te MIMO equalzer [3]. Our algortm s appled on a 6QAM-8X8 MIMO system. e ntal modfcaton s sown n Fg. 5. Startng from te frst teraton, te algortm cecks f te estmated SNR leads to te accepted BER. If so, te remanng symbols are detected lnearly. Oterwse, te teratons contnue untl reacng te BER requrement or reacng Nmax. e drawback of ts metod s tat t actually ncreases te complexty for low values of SNR. s s manly because te nullng, slcng and cancellaton steps are repeated N+ tmes. e second algortm, wt flowcart sown n Fg. 5, uses a formula, to drectly determne te number of teratons, N, from te SNR value. Assumng a maxmum requred BER of E- n an 8x8 6-QAM MIMO system, wt SNR rangng between 6 db and 34dB [4]. Frst, we smulate te V-BLAS startng Fgure 5. e flow cart of te proposed metod for 8x8 MIMO systems based on te feedback and te formula metods e feedback metod and e formula metod 4

5 e feedback algortm % Fxed Number of Iteratons at N=Nmax 74.% e formula algortm 57% Fgure 7. Comparson of BER performance of te two proposed algortms wt eac oter and te ordnary V-BLAS Fgure 6. e plot of Bt Error Rate of 6QAM MMSE/V-BLAS at N from 0 to Nt- e plot of te relaton between te number of V-BLAS teratons and te SNR n db under te condton of (BER <= E-) ABLE I. NUMBER OF IERAION AND IS CORRESPONDING SNR VALUES FOR PROPOSED CONDIION Number of teratons SNR value n db e relaton between N and SNR can be approxmated as (te lnear curve n Fg 6. ); N 3 N= mn( t,max(, round( (9 SNR))) (4) 4 e round functon rounds te obtaned value to te nearest nteger number. Also to mantan te teratons between and N t /, we use mnmum and maxmum operators. Note tat, we can cange te value of te mnmum accepted SNR as requred to comply wt dfferent practcal stuatons. able II sows tat te formula metod as a sgnfcant reducton n complexty over te feedback metod and over te ordnary V-BLAS. Ordnary V-BLAS sgnfcantly outperformed te modfed algortm for SNR values greater tan 4 db, but wt te prce of unnecessary added complexty after reacng te requred BER performance. Wle, Fg. 7 sows tat te two proposed algortms almost ave te same performance. ABLE II. AVERAGE COMPLEXIY RAIO FOR EACH V-BLAS DEECION YPE WIH RESPEC O ORDINARY V-BLAS OF EACH DEECION ALGORIHEM Detecton Algortm Rato of Complexty e Ordnary V-BLAS 00% V. CONCLUSION In ts paper, we establsed a crteron of te maxmum effcent number of teratons n V-BLAS; we sowed tat for N > N t / (at N r =N t ) no sgnfcant mprovement s obtaned. For complexty reducton, we proposed a varable teraton V-BLAS algortm wtn te maxmum lmt of teratons. We obtaned a complexty reducton of about 43% compared to te ordnary V-BLAS algortm wtout a sgnfcant degradaton n BER n te SNR range of nterest. A practcal mplementaton s consdered n future work. REFERENCES [] D. A. Kare, Performance Analyss of V-Blast Based MIMO-OFDM System wt Varous Detecton ecnques, IOSR Journal of Engneerng, vol., no., pp , Jan. 0. [] D. M. Petal and M. Petal, Cannel estmaton for MIMO OFDM usng plot carrer, Indan Streams Researc Journal, vol. 3, no. 4, pp. 3, May 0. [Onlne]. Avalable: ttp://dx.do.org/0.6084/m9.fgsare [3] Henucul Le, Byeongs Lee, and Inkyu Lee, Iteratve detecton and decodng wt an mproved V-BLAS for MIMO-OFDM systems, IEEE Journal on Selected Areas n Communcatons, vol. 4, no. 3, pp , Mar [Onlne]. Avalable: ttp://dx.do.org/0.09/jsac [4] E. Konguvel, J. Raja, and M. Kannan, A Low Power VLSI Implementaton of X MIMO OFDM ranscever wt ICI-SC Sceme, Internatonal Journal of Computer Applcatons, vol. 77, no. 5, pp. 9 5, Sep. 03. [Onlne]. Avalable: ttp://dx.do.org/0.50/ [5]. Km and S. C. Park, Reduced complexty detecton for V-BLAS systems from teraton cancelng, n Proc. 3rd Internatonal ecncal Conference on Crcuts/Systems Computers and Communcatons, Smonosek, 008, pp [6] Z. Luo, S. Lu, M. Zao, and Y. Lu, A Novel Fast Recursve MMSE-SIC Detecton Algortm for V-BLAS Systems, IEEE ransactons on Wreless Communcatons, vol. 6, no. 6, pp. 0 05, Jun [Onlne]. Avalable: ttp://dx.do.org/0.09/wc [7] Q. Gao, X.-D. Zang, J. L, and W. S, Lnear precodng and fnte rate feedback desgn for V-BLAS arctecture, IEEE ransactons on Wreless Communcatons, vol. 7, no., pp , Dec [Onlne]. Avalable: ttp://dx.do.org/0.09/- WC [8] W. Yan, S. Sun, and Z. Le, A low complexty VBLAS OFDM detecton algortm for wreless LAN systems, IEEE 5

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