Markov Chain Monte Carlo Detectors for Channels With Intersymbol Interference

In this paper, we propose novel low-complexity soft-in soft-out (SISO) equalizers using the Markov chain Monte Carlo (MCMC) technique. We develop a bitwise MCMC equalizer (b-MCMC) that adopts a Gibbs sampler to update one bit at a time, as well as a group-wise MCMC (g-MCMC) equalizer where multiple symbols are updated simultaneously. The g-MCMC equalizer is shown to outperform both the b-MCMC and the linear minimum mean square error (MMSE) equalizer significantly for channels with severe amplitude distortion. Direct application of MCMC to channel equalization requires sequential processing which leads to long processing delay. We develop a parallel processing algorithm that reduces the processing delay by orders of magnitude. Numerical results show that both the sequential and parallel processing MCMC equalizers perform similarly well and achieve a performance that is only slightly worse than the optimum maximum a posteriori (MAP) equalizer. The MAP equalizer, on the other hand, has a complexity that grows exponentially with the size of the memory of the channel, while the complexity of the proposed MCMC equalizers grows linearly.

[1]  Xiaodong Wang,et al.  Monte Carlo methods for signal processing: a review in the statistical signal processing context , 2005, IEEE Signal Processing Magazine.

[2]  Rong-Rong Chen,et al.  Approaching MIMO capacity using bitwise Markov Chain Monte Carlo detection , 2010, IEEE Transactions on Communications.

[3]  Tor Aulin,et al.  Breadth-first maximum likelihood sequence detection: basics , 1999, IEEE Trans. Commun..

[4]  Joachim Hagenauer,et al.  8-PSK turbo equalization with the list-sequential (LISS) algorithm , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[5]  Joachim Hagenauer,et al.  Turbo Equalization for Channels with High Memory Using a List-Sequential (LISS) Equalizer , 2003 .

[6]  Moe Z. Win,et al.  Monte carlo equalization for nonlinear dispersive satellite channels , 2008, IEEE Journal on Selected Areas in Communications.

[7]  Jun S. Liu,et al.  Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes , 1994 .

[8]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[9]  Zhenning Shi,et al.  Markov chain Monte Carlo techniques in iterative detectors: a novel approach based on Monte Carlo integration , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[10]  Stephen B. Wicker,et al.  Turbo Coding , 1998 .

[11]  Dan Raphaeli,et al.  Combined turbo equalization and turbo decoding , 1998, IEEE Communications Letters.

[12]  Rong-Rong Chen,et al.  Low Complexity Markov Chain Monte Carlo Detector for Channels with Intersymbol Interference , 2009, 2009 IEEE International Conference on Communications.

[13]  Haidong Zhu,et al.  Markov chain Monte Carlo algorithms for CDMA and MIMO communication systems , 2006, IEEE Transactions on Signal Processing.

[14]  Behrouz Farhang-Boroujeny,et al.  Implementation of a Markov Chain Monte Carlo Based Multiuser/MIMO Detector , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Zhenning Shi,et al.  Turbo equalization using particle filtering with grouping , 2007, 2007 International Symposium on Communications and Information Technologies.

[16]  Andrew C. Singer,et al.  Turbo equalization: principles and new results , 2002, IEEE Trans. Commun..

[17]  John Cocke,et al.  Optimal decoding of linear codes for minimizing symbol error rate (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[18]  Alain Glavieux,et al.  Iterative correction of intersymbol interference: Turbo-equalization , 1995, Eur. Trans. Telecommun..

[19]  Kyeong Jin Kim,et al.  Joint channel estimation and data detection algorithms for MIMO-OFDM systems , 2002, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002..

[20]  G. Roberts,et al.  Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler , 1997 .

[21]  Haidong Zhu,et al.  On performance of sphere decoding and Markov chain Monte Carlo detection methods , 2005, IEEE Signal Processing Letters.

[22]  Yeheskel Bar-Ness,et al.  Reduced-complexity sequence estimation using state partitioning , 1996, IEEE Trans. Commun..

[23]  P. M. Grant,et al.  Digital communications. 3rd ed , 2009 .

[24]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[25]  Riccardo Raheli,et al.  Per-Survivor Processing: a general approach to MLSE in uncertain environments , 1995, IEEE Trans. Commun..

[26]  Takeshi Hashimoto.  A list-type reduced-constraint generalization of the Viterbi algorithm , 1987, IEEE Trans. Inf. Theory.

[27]  John B. Anderson,et al.  Concatenated Decoding with a Reduced-Search BCJR Algorithm , 1998, IEEE J. Sel. Areas Commun..

[28]  M. E. Austin,et al.  Decision-feedback equalization for digital communication over dispersive channels. , 1967 .

[29]  Alain Glavieux,et al.  Turbo equalization over a frequency selective channel , 1997 .

[30]  Andrew C. Singer,et al.  Minimum mean squared error equalization using a priori information , 2002, IEEE Trans. Signal Process..

[31]  Alain Glavieux,et al.  Iterative correction of intersymbol interference : turbo-equalization : Iterative and Turbo decoding , 1995 .

[32]  Xiaodong Wang,et al.  Monte Carlo methods for signal processing , 2005 .

[33]  Inkyu Lee,et al.  The effect of a precoder on serially concatenated coding systems with an ISI channel , 2001, IEEE Trans. Commun..

[34]  F. K. Becker,et al.  Automatic equalization for digital communication , 1965 .