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We consider unsourced random access (uRA) in a cell-free (CF) user-centricwireless network, where a large number of potential users compete for a randomaccess slot, while only a finite subset is active. The random access userstransmit codewords of length $L$ symbols from a shared codebook, which arereceived by $B$ geographically distributed radio units (RUs) equipped with $M$antennas each. Our goal is to devise and analyze a \emph{centralized} decoderto detect the transmitted messages (without prior knowledge of the activeusers) and estimate the corresponding channel state information. A specificchallenge lies in the fact that, due to the geographically distributed natureof the CF network, there is no fixed correspondence between codewords andlarge-scale fading coefficients (LSFCs). This makes current activity detectionapproaches which make use of this fixed LSFC-codeword association not directlyapplicable. To overcome this problem, we propose a scheme where the accesscodebook is partitioned in location-based subcodes, such that users in aparticular location make use of the corresponding subcode. The joint messagedetection and channel estimation is obtained via a novel {\em ApproximatedMessage Passing} (AMP) algorithm for a linear superposition of matrix-valuedsources corrupted by noise. The statistical asymmetry in the fading profile andmessage activity leads to \emph{different statistics} for the matrix sources,which distinguishes the AMP formulation from previous cases. In the regimewhere the codebook size scales linearly with $L$, while $B$ and $M$ are fixed,we present a rigorous high-dimensional (but finite-sample) analysis of theproposed AMP algorithm. Exploiting this, we then present a precise (andrigorous) large-system analysis of the message missed-detection and false-alarmrates, as well as the channel estimation mean-square error.

Joint Message Detection and Channel Estimation for Unsourced Random Access in Cell-Free User-Centric Wireless Networks