  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.
