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Here we consider a problem of multiple measurement vector (MMV) compressedsensing with multiple signal sources. The observation model is motivated by theapplication of {\em 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) algorithmdevised for the model. As the system dimensions in the order, say $\mathcalO(L)$, 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 $\mathcalO(L^{-\frac 1 2})$. Furthermore, we have shown the asymptotic consistency ofthe 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 motivatingthe algorithm.

Inference in Linear Observations with Multiple Signal Sources: Analysis  of Approximate Message Passing and Applications to Unsourced Random Access in  Cell-Free Systems