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Antoine O. Berthet (1) , Raphael Visoz (2) , Sami Chtourou (2)

Efficient MMSE-based Turbo-Decoding of Space-Time BICM over MIMO Block Fading ISI Channel with Imperfect CSIR. Antoine O. Berthet (1) , Raphael Visoz (2) , Sami Chtourou (2) (1) École Supérieure d'Électricité (SUPELEC) Wireless Communications Department

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Antoine O. Berthet (1) , Raphael Visoz (2) , Sami Chtourou (2)

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  1. Efficient MMSE-based Turbo-Decoding ofSpace-Time BICM over MIMO Block Fading ISI Channel with Imperfect CSIR Antoine O. Berthet (1), Raphael Visoz (2), Sami Chtourou (2) (1) École Supérieure d'Électricité (SUPELEC) Wireless Communications Department www.supelec.fr/ecole/radio/berthet.html (2) France Telecom R&D, DMR/IIM www.francetelecom.com/...

  2. Presentation outline • Context and motivations • Communication model • Information-theoretic limits • Joint equalization and decoding of STBICM (perfect CSIR case) • Simplified MMSE-based turbo-processing • Numerical results and discussion • Turbo principle extended to joint channel estimation, equalization and decoding (imperfect CSIR case) • Simplified MMSE-based turbo-processing • Numerical results and discussion (cont.) • Open issues

  3. Context and motivations • Research context. Since the last few years, space-time coding has been the scene of considerable attention and progress • Design of efficient space-time codes • Known result: BICM offer remarkable diversity gain on ergodic SISO fading channel  space extension • STBICM with iterative decoding (ID) on ergodic MIMO fading (flat) channel approaches the capacity • Hochwald, Ten Brink, “Achieving Near-Capacity on a Multiple Antenna Channel,” IEEE COM-51, May 2003. • In non-ergodic scenarii (without or with ISI)  excellent performance compared to other existing space-time coding schemes • Berthet, Visoz and Boutros, “Space-Time BICM versus Space-Time Trellis Code for MIMO Block Fading Multipath AWGN Channel,” IEEE ITW’03, Mar 2003.

  4. Context and motivations (cont.) • Problemstatement.when neither space, time nor frequency dimensions are orthogonalized at the transmitter, strong ISI and Multiple Antenna Interference (MAI) come as a result and have to be compensated for at the receiver • Interleaver between the channel code and the modulator, source of design flexibility, precludes any brute force optimum joint decoding  sub-optimum 2-step procedure • Most demanding task: MIMO detection • Since several iterations will be required to converge towards optimum results, it is even more crucial to find very low-complexity algorithms to realize symbol digit detection and decoding

  5. Context and motivations (cont.) • Contribution. Our concern is to solve the problem of ISI and MAI cancellation with polynomial (at most cubic) complexity in all system parameters, while performing as close as possible from the theoretical available benchmarks, namely the Matched-Filter Bound (MFB) and the channel outage • Our equalizing strategy is basically inspired from the seminal papers by • Glavieux and al., “Turbo-equalization over a Frequency-Selective Channel," Int. Symp. Turbo Codes, Brest, France, 1997 • Wang and Poor, “Iterative (Turbo) Soft-Interference Cancellation and Decoding for Coded CDMA,” IEEE COM-47, July 1999. • Chan, Wornell, "A Class of Block-Iterative Equalizers for InterSymbol Interference Channels: Fixed Channel Results,“ IEEE COM-49, Nov. 2001. • Space-Time generalization not so obvious  interesting degree of freedom in the receiver design

  6. Communication model • General assumptions • Point-to-point transmission • Unknown CSI at the transmitter • Perfect or imperfect CSI knowledge at the receiver • R  T MIMO channel • Frequency-selective (memory M) • B-block fading channel • Typical wireless mobile radio environment

  7. Space-Time BICM RT MIMO fading ISI channel Modulator Binary code Binary Interleaver Modulator • Channel code: any binary linear code with high dmin • Interleaver: bitwise interleaver before modulation • Constellation: PSK or QAM per antenna Qt bits/symbol • Labeling: from Q interleaved bits to T constellation symbols • Stefanov, Duman, “Turbo-Coded Modulations for Systems with Transmit and Receive Antenna Diversity over Block Fading Channels…” IEEE JSAC, May 2001

  8. Channel model • B-block fading channel model.Space-Time code word X  X1,…,XB spans over a finite number of independent channel realizations H1,…,HB • Fading blocks are thought as separated both in time and/or frequency and may be correlated or not. • Model well suited to represent a slowly time-varying MIMO multipath channel where blocks may either result from frequency-hopping in TDMA systems or be identified with subcarriers in OFDM systems. • If MAI is perfectly removed (GAD assumption), the MIMO block fading channel decomposes into a virtual SISO BT-block fading channel  actually assumed for designing STBICM interleaving

  9. Channel model (cont.) • Convolutional model • Discrete-time base-band equivalent vector channel output • Additive noise vectors i.i.d circularly symmetric complex Gaussian with covariance matrix ²I • Channel taps are RT complex random matrix with zero-mean and mean power satisfying the normalization constraint

  10. Channel model (cont.) • Length-LF sliding-window model as a valid approximation of the blockwise matrix model where we introduce the stacked vectors and the Sylvester channel matrix

  11. Joint equalization and decoding • Overall MAP decoding  minimum BLER • Brute force resolution intractable due to the random interleaver which breaks the outer code structure • Belief propagation (BP) iterative joint decoder applied on the underlying factor graph approximates the marginal pmfs • Decision made after a fixed number of iterations

  12. Exact BP-ID • BP iterative joint decoder. Locally optimal results (i.e., decisions coincide with MAP) provided that the word length is large enough and the number of iterations sufficient. • The BP iterative joint decoder relies on the definition of some computation building blocks that exchange messages in the form of pmfs on variables of interest • For STBICM, the two computation building blocks, namely MIMO detector and outer decoder trivially inherited from the serial scheme structure • Bitwise interleaving  variable nodes are symbol digits and coded bits • Exchanged messages have the form of binary pmfs (or equivalently logarithmic probability ratios)

  13. Factor graph Information bit nodes Code constraint node Coded bit nodes Interleaver connections Symbol digit nodes Labeling constraint nodes Channel constraint nodes

  14. Exact BP-ID (cont.) • Exchanged messages. Define log priors on symbol digits as • Messages from MIMO detector relative to symbol digits • Messages from decoder relative to coded bits

  15. Part 1: Efficient MMSE-based joint equalization and decoding with perfect CSIR

  16. Classical MMSE-based ID • Motivation. Simplify the exact BP iterative decoder  various algorithms, all inspired from the seminal paper by Wang et al. • Classical approach. Consider antennas as distinct users • Problem formally equivalent to the one of MUD in the presence of ISI • Inner MIMO detector block replaced by a much simpler soft-in soft-out module, which transforms the optimal APP estimation of vector xk into a sub-optimum MMSE estimation of each vector component xt,k individually, followed by a soft-in soft-out APP demapper • El Gamal, Hammons, "A New Approach to Layered Space-Time Coding and Signal Processing," IEEE IT-47, Sept. 2001.

  17. Novel MMSE-based ID (cont.) • Drawbacks for such approaches • One single-dimensional Wiener filter for each transmit antenna (computationally costly for large MIMO systems) • Both ISI and MAI cancellation tasks rely on the sub-optimum MMSE criterion • New strategy. Based on a 2-stage process (some kind of group detection in two dimensions) • Multidimensional filtering stage to remove the ISI corrupting the T-dimensional vectors xk(only one single Wiener filter) • Symbol digit MIMO detection stage to deal with the residual MAI

  18. Novel MMSE-based ID (cont.) ISI cancellation MAI resolution XTR Multidim. Wiener filter F MIMO detector (log-domain) Interleaver Channel Decoder (log-domain)    Deinterleaver XTR Interference Regenerator MMSE symb. estimator XTR • Linear front end for ISI cancellation (in T-dimensional sense). Possible criteria are conditional or unconditional MMSE (or even max SNR) • Regenerated interference:using log extrinsic ratios coming from channel decoder • MIMO detection (MAI resolution): bitwise APP computation on symbol digits. Possible criteria are MAP, MMSE and max SNR

  19. Novel MMSE-based ID (cont.) • MMSE vector symbol estimate • Tentative soft decision vector used to regenerate the ISI (in multidimensional sense) corrupting symbol xk where E is the T(LFM)T matrix defined as

  20. Novel MMSE-based ID (cont.) • Projection theorem associated to stochastic matrix inner product x,y  E[xy]  x,y and projection space generated by • Detailed biased multidimensional Wiener filter • Covariance matrix structure (infinite space-time interleaving) with the variance evaluated using the consistent estimator

  21. Novel MMSE-based ID (cont.) • Output of the multidimensional Wiener filter. Equivalent TT MIMO fading ‘flat’ channel • Gaussian approximation on the compound residual ISI + noise term (valid for large M) • Exact APP estimation on each symbol digit replaced by (Cholesky factorization of the spatial correlation matrix )

  22. Novel MMSE-based ID (cont.) • Genie-aided decoder (GAD) assumption • Biased multidimensional Wiener filter • Tends to the matched filter(apart from the multiplication by a TT constant matrix) • Filter output tends to the canonical flat fading AWGN channel

  23. Numerical results • Design. Terminated convolutional codes with max dfree & PSK • Malkamäki, “Coded Diversity on Block Fading Channels”, IEEE IT-45, Mar. 1999. • Ariyavisitakul, “Turbo-Space-Time Processing to Improve Wireless Channel Capacity”, IEEE COM-48, Aug. 2000. • Objective 1. Test the potential of the novel equalizing strategy in its simplest mode  MMSE-IC ISI / MF-IC MAI • Rate-1/3 64-state NRC, 8-PSK (Gray) • Quasi-static channel (B  1) • Code word length N  1536 coded bits

  24. Numerical results (cont.) MIMO 1-block 22 EQ2, 2 bpcu

  25. Numerical results (cont.) MIMO 1-block 22 EQ10, 2 bpcu

  26. Numerical results (cont.) MIMO 1-block 44 EQ4, 4 bpcu

  27. Numerical results (cont.) MIMO 1-block 88 EQ4, 8 bpcu

  28. Numerical results (cont.) • Objective 2. Classical approach vs. novel approach • Rate-1/2 64-state NRC, 8-PSK (Gray) • Quasi-static channel (B  1) • Code word length N  1536 coded bits • Objective 3. (corollary). Adaptation of the chosen criterion for MAI resolution to the system load • Rate-1/3 64-state NRC, 8-PSK (Gray)  relax criterion (MMSEMF) • Rate-2/3 64-state NRC, 8-PSK (Gray)  upgrade criterion (MMSEMAP) • Quasi-static channel (B  1) • Code word length N  1536 coded bits

  29. Numerical results (cont.) MIMO 1-block 44 EQ4, 6 bpcu

  30. Numerical results (cont.) MIMO 1-block 44 EQ4, 8 bpcu

  31. Part 2: Efficient MMSE-based turbo-decoding with imperfect CSIR

  32. Novel MMSE-based ID (cont.) ISI cancellation MAI resolution XTR Multidim. Wiener filter F MIMO detector (log-domain) Interleaver Channel Decoder (log-domain)    Deinterleaver XTR Interference Regenerator MMSE symb. estimator XTR • Additional iterative loop (channel estimation): APP-based MMSE symbol estimate, MMSE channel estimate MMSE channel estimator MMSE symb. estimator APP Interleaver Channel estimation

  33. Numerical results • Objective 4. Test the convergence of the double loop • Rate-1/3 64-state NRC, 8-PSK (Gray) • 44 MIMO quasi-static (B  1) EQ4 • Code word length N  3072 coded bits • Ideal 424 matrix symbol pilot (0.39 dB insertion loss) or ideal 432 matrix symbol pilot (0.51 dB insertion loss) • MMSE-IC ISI / MAP or MMSE-IC MAI / MMSE channel estimation

  34. Numerical results (cont.) MIMO 1-block 44 EQ4, 4 bpcu, 8.57% pilot

  35. Numerical results (cont.) MIMO 1-block 44 EQ4, 4 bpcu, 12.1% pilot

  36. Open research topics • Convergence analysis of such turbo receivers • Improved turbo receivers for high loads • Design of STBICM: rate-diversity tradeoff, code universality • El Gamal, Damen, “Universal Space-Time Coding,” IEEE IT-49, May 2003 • Boutros, Gresset, “Turbo Coding and Decoding for Multiple Antenna Channels,” Sept. 2003. • Fabregas, Caire, “Coded Modulation in the Block Fading Channels,” submitted IT, 2004 • Tight bounds on the performance limits • Debate single-carrier vs. multi-carrier transmission for 4G

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