ABSTRACT
Many statistical signal processing problems found in digital communications involve making inferences 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 these problems. These methods fall into two categories: the Markov chain Monte Carlo (MCMC) methods for batch signal processing and the sequential Monte Carlo (SMC) methods for adaptive signal processing. We provide an overview of the theories and applications of both the MCMC and SMC methods. The salient features of these techniques include the following: (1) they are optimal in the sense of achieving minimum symbol error rate; (2) they do not require the knowledge of the channel states, and they do not explicitly estimate the channel by employing training signals or decision feedback; and (3) being soft input soft output in nature, they are well suited for iterative (turbo) processing in coded systems.
