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

TL;DR

The paper tackles unsourced random access in cell-free, user-centric networks and proposes a location-based partitioned codebook to cope with location-dependent large-scale fading. It develops a novel multisource AMP framework for joint message detection and channel estimation, supported by finite-sample concentration and replica-symmetric analyses that link to state evolution predictions. The approach yields near-closed-form expressions for miss-detection and false-alarm rates and channel estimation error, and it enables analytical characterization of DL beamformed ACK performance under MRT precoding. The results demonstrate that the centralized AMP-based detector can closely approach genie-aided performance in favorable regimes and offer practical insights for low-latency, scalable random access in CF networks.

Abstract

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 $L$ symbols from a shared codebook, which are received by $B$ geographically distributed radio units (RUs) equipped with $M$ antennas each. Our goal is to devise and analyze a \emph{centralized} 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 {\em Approximated Message Passing} (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 \emph{different statistics} for the matrix sources, which distinguishes the AMP formulation from previous cases. In the regime where the codebook size scales linearly with $L$, while $B$ and $M$ 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.

Figures (9)

• Figure 1: A schematic of the RACH slot, followed by a DL packet (referred to as ACK in this paper) and subsequent UL/DL TDD slots for allocated traffic.
• Figure 2: A simple $B = 2$, $U = 2$ toy model example of the proposed location-based approach.
• Figure 3: The empirical MSE of AMP for $10$ instances of AMP dynamics and its theoretical deterministic prediction for the toy model example (Fig. \ref{['fig1']}) with $N_u= 2048$, $L = 1024$, $\wp = 1/2$, and UL ${\sf SNR} = 10$ dB .
• Figure 4: The performance comparison of the AMP and sAMP algorithms for the toy model example (Fig. \ref{['fig1']}) with $N_u= 2048$, $L = 1024$, and ${\sf SNR}=10$ dB.
• Figure 5: Hexagonal network topology with equilateral triangle tiles. The crosses denote the user locations and the circles denote the RUs.

Theorems & Definitions (44)

• Definition 1: State Evolution
• Theorem 1
• proof
• Corollary 1
• proof
• Remark 1
• Example 1
• Claim 1
• Definition 2: Message detection
• Theorem 2