  We consider the non-coherent single-input multiple-output (SIMO) multiple
access channel with general signaling under spatially correlated Rayleigh block
fading. We propose a novel soft-output multi-user detector that computes an
approximate marginal posterior of each transmitted signal using only the
knowledge about the channel distribution. Our detector is based on expectation
propagation (EP) approximate inference and has polynomial complexity in the
number of users, the number of receive antennas, and channel coherence time. We
also propose two simplifications of this detector with reduced complexity. With
Grassmannian signaling, the proposed detectors outperform a state-of-the-art
non-coherent detector with projection-based interference mitigation. With
pilot-assisted signaling, the EP detector outperforms, in terms of symbol error
rate, some conventional coherent pilot-based detectors, including a sphere
decoder and a joint channel estimation-data detection scheme. Our EP-based
detectors produce accurate approximates of the true posterior leading to high
achievable sum-rates. The gains of these detectors are further observed in
terms of the bit error rate when using their soft outputs for a turbo channel
decoder.
