Multi-Source Approximate Message Passing With Random Semi-Unitary Dictionaries

Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of multiple statistically asymmetric signal sources, we introduce a multi-source AMP framework in which the dictionary matrices associated with each signal source are drawn from a random semi-unitary ensemble (rather than the standard Gaussian matrix ensemble.) While a similar model has been explored by Vehkaperä, Kabashima, and Chatterjee (2016) using the replica method, here we present an AMP algorithm and provide a high-dimensional yet finite-sample analysis of its dynamics. As a proof of concept, we show the effectiveness of the proposed approach on the problem of message detection in an unsourced random access scenario in wireless communication.