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Abstract

Many statistical signal processing problems found in wireless communications involves making inference about the transmitted information data based on the received signals in the presence of various unknown channel distortions. The optimal solutions to these problems are often too computationally complex to implement by conventional signal processing methods. The recently emerged Bayesian Monte Carlo signal processing methods, the relatively simple yet extremely powerful numerical techniques for Bayesian computation, offer a novel paradigm for tackling wireless signal processing problems. These methods fall into two categories, namely, Markov chain Monte Carlo (MCMC) methods for batch signal processing and sequential Monte Carlo (SMC) methods for adaptive signal processing. We provide an overview of the theories underlying both the MCMC and the SMC. Two signal processing examples in wireless communications, the blind turbo multiuser detection in CDMA systems and the adaptive detection in fading channels, are provided to illustrate the applications of MCMC and SMC respectively.

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References

  1. J.G. Proakis, Digital Communications, 3rd edn., New York: McGraw-Hill, 1995.

    Google Scholar 

  2. S. Verdú, Multiuser Detection, Cambridge, UK: Cambridge University Press, 1998.

    MATH  Google Scholar 

  3. R. Haeb and H. Meyr, “A Systematic Approach to Carrier Recovery and Detection of Digitally Phase Modulated Signals on Fading Channels,” IEEE Trans. Commun., vol. 37,no. 7, 1989, pp. 748-754.

    Article  Google Scholar 

  4. J.S. Liu, Monte Carlo Methods in Scientific Computing, New York: Springer-Verlag, 2001.

    Google Scholar 

  5. N. Metropolis, A.W. Rosenbluth, A.H. Teller, and E. Teller, “Equations of State Calculations by Fast Computing Machines,” J. Chemical Physics, vol. 21, 1953, pp. 1087-1091.

    Article  Google Scholar 

  6. W.K. Hastings, “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, vol. 57, 1970, pp. 97-109.

    Article  MATH  Google Scholar 

  7. S. Geman and D. Geman, “Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6,no. 11, 1984, pp. 721-741.

    Article  Google Scholar 

  8. M.A. Tanner and W.H. Wong, “The Calculation of Posterior Distribution by Data Augmentation (with Discussion),” J. Amer. Statist. Assoc., vol. 82, 1987, pp. 528-550.

    Article  MathSciNet  Google Scholar 

  9. A.E. Gelfand and A.F.W. Smith, “Sampling-Based Approaches to Calculating Marginal Densities,” J. Amer. Stat. Assoc., vol. 85, 1990, pp. 398-409.

    Article  MathSciNet  MATH  Google Scholar 

  10. J.S. Liu, “The Collapsed Gibbs Sampler with Applications to a Gene Regulation Problem,” J. Amer. Statist. Assoc, vol. 89, 1994, pp. 958-966.

    Article  MathSciNet  MATH  Google Scholar 

  11. C.J. Geyer, “Markov Chain Monte Carlo Maximum Likelihood,” in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, E.M. Keramigas (Ed.), Fairfax: Interface Foundation, 1991, pp. 156-163.

    Google Scholar 

  12. J.S. Liu, F. Ling, and W.H. Wong, “The Use of Multiple-Try Method and Local Optimization in Metropolis sampling,” J. Amer. Statist. Assoc, vol. 95, 2000, pp. 121-134.

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Liang and W.H. Wong, “Evolutionary Monte Carlo: Applications to c p Model Sampling and Change Point Problem,” Statistica Sinica, vol. 10, 2000, pp. 317-342.

    MATH  Google Scholar 

  14. X. Wang and R. Chen, “Adaptive Bayesian Multiuser Detection for Synchronous CDMA in Gaussian and Impulsive Noise,” IEEE Trans. Sign. Proc, vol. 48,no. 7, 2000, pp. 2013-2028.

    Article  Google Scholar 

  15. J. Hagenauer, “The Turbo Principle: Tutorial Introduction and State of the Art,” in Proc. International Symposium on Turbo Codes and Related Topics, Brest, France, Sept. 1997, pp. 1-11.

  16. L.R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate,” IEEE Trans. Inform. Theory, vol. IT-20,no. 3, 1974, pp. 284-287.

    Article  MathSciNet  Google Scholar 

  17. G.E. Box and G.C. Tiao, Bayesian Inference in Statistical Analysis, Reading, MA: Addison-Wesley, 1973.

    MATH  Google Scholar 

  18. A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin, Bayesian Data Analysis, Chapman & Hall, 1995.

  19. E.L. Lehmann and G. Casella, Theory of Point Estimation, 2nd edn., New York: Springer-Verlag, 1998.

    MATH  Google Scholar 

  20. J.O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd edn., New York: Springer-Verlag, 1985.

    Book  MATH  Google Scholar 

  21. T.J. Rothenberg, “The Bayesian Approach and Alternatives in Econometrics,” in Studies in Bayesian Econometrics and Statistics, vol. 1, S. Fienberg and A. Zellners (Eds.), Amsterdam: North-Holland, 1977, pp. 55-75.

    Google Scholar 

  22. C.P. Robert, The Bayesian Choice: A Decision-Theoretic Motivation, New York: Springer-Verlag, 1994.

    Book  MATH  Google Scholar 

  23. J.S. Liu, R. Chen, and W.H. Wong, “Rejection Control for Sequential Importance Sampling,” Journal of the American Statistical Association, vol. 93, 1998, pp. 1022-1031.

    Article  MathSciNet  MATH  Google Scholar 

  24. N.J. Gordon, D.J. Salmon Salmon, and A.F.M. Smith, “A Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation,” IEE Proceedings on Radar and Signal Processing, vol. 140, 1993, pp. 107-113.

    Article  Google Scholar 

  25. J.S. Liu and R. Chen, “Blind Deconvolution Via Sequential Imputations,” Journal of the American Statistical Association, vol. 90, 1995, pp. 567-576.

    Article  MATH  Google Scholar 

  26. J.S. Liu and R. Chen, “Sequential Monte Carlo Methods for Dynamic Systems,” Journal of the American Statistical Association, vol. 93, 1998, pp. 1032-1044.

    Article  MathSciNet  MATH  Google Scholar 

  27. R. Chen and J.S. Liu, “Mixture Kalman Filters,” Journal of Royal Statistical Society (B), vol. 62,no. 3, 2000, pp. 493-509.

    Article  MATH  Google Scholar 

  28. R. Chen, X. Wang, and J.S. Liu, “Adaptive Joint Detection and Decoding in Flat-Fading Channels Via Mixture Kalman Filtering,” IEEE Trans. Inform. Theory, vol. 46,no. 6, 2000, pp. 2079-2094.

    Article  MathSciNet  MATH  Google Scholar 

  29. S.Y. Kung, VLSI Array Processing, Englewood Cliffs, NJ: Prentice Hall, 1988.

    Google Scholar 

  30. B. Lu and X. Wang, “Bayesian Blind Turbo Receiver for Coded OFDM Systems with Frequency Offset and Frequency-Selective Fading,” IEEE J. Select. Areas Commun., vol. 19,no. 12, 2001, Special issue on Signal Synchronization in Digital Transmission Systems.

  31. V.D. Phan and X. Wang, “Bayesian Turbo Multiuser Detection for Nonlinearly Modulated CDMA,” Signal Processing, to appear.

  32. X. Wang and R. Chen, “Blind Turbo Equalization in Gaussian and Impulsive Noise,” IEEE Trans. Vehi. Tech., vol. 50,no. 4, 2001, pp. 1092-1105.

    Article  Google Scholar 

  33. Z. Yang, B. Lu, and X. Wang, “Bayesian Monte Carlo Multiuser Receiver for Space-Time Coded Multi-Carrier CDMA Systems,” IEEE J. Select. Areas Commun., vol. 19,no. 8, 2001, pp. 1625-1637, Special Issue on Multiuser Detection Techniques with Application to Wired & Wireless Communication System.

    Article  Google Scholar 

  34. Z. Yang and X. Wang, “Blind Turbo Multiuser Detection for Long-Code Multipath CDMA,” IEEE Trans. Commun., to appear.

  35. Z. Yang and X. Wang, “Turbo Equalization for GMSK Signaling Over Multipath Channels Based on the Gibbs Sampler,” IEEE J. Select. Areas Commun., vol. 19,no. 9, 2001, pp. 1753-1763, Special Issue on the Turbo Principle: From Theory to Practice.

    Article  Google Scholar 

  36. IEEE Trans. Sig. Proc., Special Issue on Monte Carlo Methods for Statistical Signal Processing, 2002.

  37. Signal Processing, Special Issue on Markov Chain Monte Carlo (MCMC) Methods for Signal Processing, vol. 81,no. 1, 2001.

    Google Scholar 

  38. A. Doucet, N. de Freitas, and N. Gordon (Eds.), Sequential Monte Carlo Methods in Practice, New York: Springer-Verlag, 2001.

    MATH  Google Scholar 

  39. W.R. Wilks, S. Richardson, and D.J. Spiegelhalter (Eds.), Monte Carlo Monte Carlo in Practice, London: Chapman & Hall, 1998.

    Google Scholar 

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Wang, X., Chen, R. & Liu, J.S. Monte Carlo Bayesian Signal Processing for Wireless Communications. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 30, 89–105 (2002). https://doi.org/10.1023/A:1014094724899

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