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We consider the non-coherent single-input multiple-output (SIMO) multipleaccess channel with general signaling under spatially correlated Rayleigh blockfading. We propose a novel soft-output multi-user detector that computes anapproximate marginal posterior of each transmitted signal using only theknowledge about the channel distribution. Our detector is based on expectationpropagation (EP) approximate inference and has polynomial complexity in thenumber of users, the number of receive antennas, and channel coherence time. Wealso propose two simplifications of this detector with reduced complexity. WithGrassmannian signaling, the proposed detectors outperform a state-of-the-artnon-coherent detector with projection-based interference mitigation. Withpilot-assisted signaling, the EP detector outperforms, in terms of symbol errorrate, some conventional coherent pilot-based detectors, including a spheredecoder and a joint channel estimation-data detection scheme. Our EP-baseddetectors produce accurate approximates of the true posterior leading to highachievable sum-rates. The gains of these detectors are further observed interms of the bit error rate when using their soft outputs for a turbo channeldecoder.

Multi-User Detection Based on Expectation Propagation for the Non-Coherent SIMO Multiple Access Channel