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

We consider unsourced random access (uRA) in a cell-free (CF) user-centric wireless network, where a large number of potential users compete for a random access slot, while only a finite subset is active. The random access users transmit codewords of length <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> symbols from a shared codebook, which are received by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> geographically distributed radio units (RUs), each equipped with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antennas. Our goal is to devise and analyze a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">centralized</i> decoder to detect the transmitted messages (without prior knowledge of the active users) and estimate the corresponding channel state information. A specific challenge lies in the fact that, due to the geographically distributed nature of the CF network, there is no fixed correspondence between codewords and large-scale fading coefficients (LSFCs). This makes current activity detection approaches which make use of this fixed LSFC-codeword association not directly applicable. To overcome this problem, we propose a scheme where the access codebook is partitioned in location-based subcodes, such that users in a particular location make use of the corresponding subcode. The joint message detection and channel estimation is obtained via a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Approximated Message Passing</i> (AMP) algorithm for a linear superposition of matrix-valued sources corrupted by noise. The statistical asymmetry in the fading profile and message activity leads to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">different statistics</i> for the matrix sources, which distinguishes the AMP formulation from previous cases. In the regime where the codebook size scales linearly with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i>, while <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> are fixed, we present a rigorous high-dimensional (but finite-sample) analysis of the proposed AMP algorithm. Exploiting this, we then present a precise (and rigorous) large-system analysis of the message missed-detection and false-alarm rates, as well as the channel estimation mean-square error. The resulting system allows the seamless formation of user-centric clusters and very low latency beamformed uplink-downlink communication without explicit user-RU association, pilot allocation, and power control. This makes the proposed scheme highly appealing for low-latency random access communications in CF networks.