Probabilistic Receiver Architecture Combining BP, MF, and EP for Multi-Signal Detection

Abstract

Receiver algorithms which combine belief propagation (BP) with the mean field (MF) approximation are well-suited for inference of both continuous and discrete random variables. In wireless scenarios involving detection of multiple signals, the standard construction of the combined BP-MF framework includes the equalization or multi-user detection functions within the MF subgraph. In this paper, we show that the MF approximation is not particularly effective for multi-signal detection. We develop a new factor graph construction for application of the BP-MF framework to problems involving the detection of multiple signals. We then develop a low-complexity variant to the proposed construction in which Gaussian BP is applied to the equalization factors. In this case, the factor graph of the joint probability distribution is divided into three subgraphs: (i) a MF subgraph comprised of the observation factors and channel estimation, (ii) a Gaussian BP subgraph which is applied to multi-signal detection, and (iii) a discrete BP subgraph which is applied to demodulation and decoding. Expectation propagation is used to approximate discrete distributions with a Gaussian distribution and links the discrete BP and Gaussian BP subgraphs. The result is a probabilistic receiver architecture with strong theoretical justification which can be applied to multi-signal detection.

LDPC codes: tracking non-stationary channel noise using sequential variational Bayesian estimates

“…However, to model SNRs in AWGN channels, a conditional Gaussian random variable is required, which produces marginals of mixture type distributions that are not in the exponential family. As such, studies in [10,11,12,13,14,15,16] have proposed hybrid methods for jointly modelling the SNRs and the transmitted bit messages. These methods are all based on factor graphs with some graph extension that uses an inference scheme different from LBP for estimating the SNRs.…”