A message passing approach to iterative Bayesian SNR estimation

We study the design of iterative receiver structures for a simple communication system, operating over an AWGN channel with unknown gain and unknown noise power. Based on a generic message passing framework, which contains Belief Propagation (BP), Variational Message Passing (VMP), and Expectation Maximization (EM) as special cases, we first rederive a non-Bayesian EM-based SNR estimator which has been proposed before in the literature. We then switch to a Bayesian model and derive a refined algorithm, which uses VMP instead of EM for estimating the channel gain and noise precision. We demonstrate via simulations that the proposed VMP-based SNR estimator outperforms the EM-based estimator in terms of a lower frame error rate, at hardly any increase of computational complexity. While we focus on coherent SNR estimation in this work, we briefly discuss a possible extension to the non-coherent case.

I. Introduction

After the discovery of Turbo codes and their powerful iterative decoders, the systematic design of iterative receiver structures which include other components beyond the decoder has attracted a lot of research interest. One of the most prominent techniques is Belief Propagation (BP), the theoretical foundation of Turbo and LDPC decoders [1], which is typically presented as a message passing scheme over a graphical model of the underlying probability network [2]. However, receiver tasks like synchronization and channel estimation mainly involve continuous parameters, for which BP is not well suited due to analytically intractable integrals. While this problem can be circumvented by discretizing the continuous random variables [3], this approach is quite ad hoc and, more importantly, results in a rather high complexity for sufficiently fine quantizations.