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). 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 to estimate the linear superposition of matrix-valued "sources" corrupted by Gaussian noise. The matrices to be estimated exhibit zero rows for inactive messages and Gaussian-distributed rows corresponding to the active messages. The asymmetry in the LSFCs and message activity probabilities 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 analysis of the proposed AMP algorithm. Then, exploiting the fundamental decoupling principle of AMP, we provide a comprehensive analysis of Neyman-Pearson message detection, along with the subsequent channel estimation.

翻译：我们考虑一种无小区用户中心无线网络中的无源随机接入场景，其中大量潜在用户竞争随机接入时隙，但仅有有限子集处于活跃状态。随机接入用户从共享码本中传输长度为$L$个符号的码字，这些码字由配备$M$根天线的$B$个地理分布式射频单元接收。我们的目标是设计并分析一种\emph{集中式}解码器，以检测传输消息（无需预知活跃用户）并估计相应的信道状态信息。一个特殊挑战在于：由于无小区网络的地理分布特性，码字与大尺度衰落系数之间不存在固定对应关系。为解决此问题，我们提出一种方案，将接入码本划分为"基于位置"的子码，使特定位置的用户使用对应的子码。联合消息检测与信道估计通过一种新型{\em 近似消息传递}算法实现，用以估计受高斯噪声污染的矩阵值"源"的线性叠加。待估计矩阵包含对应于非活跃消息的零行，以及对应于活跃消息的高斯分布行。大尺度衰落系数与消息活跃概率的不对称性导致矩阵源具有\emph{不同统计特性}，这使近似消息传递公式区别于先前案例。在码本规模与$L$线性缩放、而$B$和$M$固定的条件下，我们对所提近似消息传递算法进行了严格的高维分析。进而，利用近似消息传递的基本解耦原理，我们提供了奈曼-皮尔逊消息检测及其后续信道估计的全面分析。