A Comparison of Traditional Meth.ods and Sequential Bayesian Meth.ods for Blind Deconvolution Problems

This work concerns sequential techniques for the canonical blind deconvolution problem in communications signal processing, relating to the estimation of the transmitted (discrete-valued) data sequence from the observed signal at the receiver input, in the presence of unknown linear channel filtering, without recourse to extended training sequences for start-up. This problem has a significant history within communications signal processing due to its fundamental importance in the design of high-speed modems; common methods include the well-known Viterbi, List Viterbi Algorithms and BCJR algorithms enhanced with suitable blind channel estimators. Of late, the problem has attracted the attention of computational Bayesians such as Liu and Chen Liu and Chen (1995) who introduced Sequential Importance Sampling (SIS). Subsequently, several extensions have been proposed (e.g. Rejuvenation, Rejection Control, Fixed-Lag Smoothing, Metropolis-Hastings Importance Resampling, etc.) as improvements to SIS. Simulations comparing SIS and Rejuvenation to the more traditional methods were inconclusive as to whether Sequential Importance Sampling is always preferable to the traditional methods. Although Sequential Importance Sampling can be helpful in certain circumstances, it shows signs of instability, and therefore, may not be useful in practice. In conclusion, one should be cautious in using Sequential Importance Sampling or Rejuvenation for blind deconvolution problems.