Belief Propagation Decoding of Tensor-Based Modulation for Unsourced Random Access

We target the problem of random access over a noncoherent flat-fading single-input multiple-output (SIMO) channel with short packets. Specifically, we consider an unsourced joint coding and modulation approach based on the idea of tensor-based modulation (TBM) introduced by Decurninge et al., where the component codebooks are restricted to phase-shift keying (PSK) symbols. At the receiver, we leverage the fact that PSK symbols are on the unit circle to relax the problem to the continuous domain; we propose a low-complexity message passing belief propagation (BP) multi-user decoding algorithm, to jointly estimate the information bearing symbols and the channel coefficients. The proposed method allows efficient inter-user interference cancellation without prior knowledge of the identity of the active user nor of their channels. We establish its convergence behaviour and derive its complexity and further demonstrate the effectiveness of the algorithm for multiple antenna receiver system in comparison with meta-converse lower bound.