Here we consider a problem of multiple measurement vector (MMV) compressed sensing with multiple signal sources. The observation model is motivated by the application 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) algorithm devised for the model. As the system dimensions in the order, say $\mathcal O(L)$, 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 $\mathcal O(L^{-\frac 1 2})$. Furthermore, we have shown the asymptotic consistency of the 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 motivating the algorithm.

翻译：本文研究了具有多个信号源的多测量向量（MMV）压缩感知问题。观测模型受无线无蜂窝MIMO（多输入多输出）网络中**无源随机接入**应用的启发。我们针对该模型设计的AMP（近似消息传递）算法，提出了一种新颖且严谨的高维分析。当系统维度按$\mathcal O(L)$的数量级趋于无穷时，我们证明描述AMP动态过程的经验动态序参量以$\mathcal O(L^{-\frac 1 2})$的收敛速率收敛至确定性极限（由状态演化方程描述）。此外，我们证明了AMP分析与静态问题的复制对称计算在渐近意义上具有一致性。同时，我们还提供了关于无蜂窝系统中无源随机接入（或初始接入）的一些有趣视角，这正是该算法所面向的应用场景。