Inference in Linear Observations with Multiple Signal Sources: Analysis of Approximate Message Passing and Applications to Unsourced Random Access in Cell-Free Systems
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Here we consider a problem of multiple measurement vector (MMV) compressed sensing with multiple signal sources. The observation model is motivated by the application of unsourced random access in wireless cell-free MIMO (multiple-input-multiple-output) networks. We present a novel (and rigorous) high-dimensional analysis of the AMP (approximate message passing) algorithm devised for the model. As the system dimensions in the order, say 𝒪(L), tend to infinity, we show that the empirical dynamical order parameters – describing the dynamics of the AMP – converge to deterministic limits (described by a state-evolution equation) with the convergence rate 𝒪(L^-1/2). Furthermore, we have shown the asymptotic consistency of the AMP analysis with the replica-symmetric calculation of the static problem. In addition, we provide some interesting aspects on the unsourced random access (or initial access) for cell-free systems, which is the application motivating the algorithm.
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