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

Burak Çakmak; Giuseppe Caire

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arXiv · 2410.13021

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

Burak Çakmak·Giuseppe Caire

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Abstract

Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of \emph{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 \emph{random semi-unitary ensemble} (rather than the standard Gaussian matrix ensemble.) While a similar model has been explored by Vehkaper{\"a}, Kabashima, and Chatterjee (2016) using the replica method, here we present an AMP algorithm and provide a high-dimensional yet \emph{finite-sample} analysis. As a proof of concept, we show the effectiveness of the proposed approach on the problem of \emph{message detection and channel estimation} in an unsourced random access scenario in wireless communication.

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Burak Çakmak, Giuseppe Caire. 2024-10-16. Multi-Source Approximate Message Passing with Random Semi-Unitary Dictionaries. https://arxiv.org/abs/2410.13021

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