In this paper, we study the problem of user activity detection and large-scale fading coefficient estimation in a random access wireless uplink with a massive MIMO base station with a large number $M$ of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the $M$ -dimensional channel vector of each user remains constant over a coherence block containing $L$ signal dimensions in time-frequency. In the considered setting, the number of potential users $K_{\text {tot}}$ is much larger than $L$ but at each time slot only $K_{a} \ll K_{\text {tot}}$ of them are active. Previous results, based on compressed sensing, require that $K_{a}\le L $ , which is a bottleneck in massive deployment scenarios. In this work, we show that such limitation can be overcome when the number of base station antennas $M$ is sufficiently large. More specifically, we prove that with a coherence block of dimension $L$ and a number of antennas $M$ such that $K_{a}/M = o(1)$ , one can identify $K_{a} = O\left({L^{2}/\log ^{2}\left({\frac {K_{\text {tot}}}{K_{a}}}\right)}\right)$ active users, which is much larger than the previously known bounds. We also provide two algorithms. One is based on Non-Negative Least-Squares, for which the above scaling result can be rigorously proved. The other consists of a low-complexity iterative componentwise minimization of the likelihood function of the underlying problem. While for this algorithm a rigorous proof cannot be given, we analyze a constrained version of the Maximum Likelihood (ML) problem (a combinatorial optimization with exponential complexity) and find the same fundamental scaling law for the number of identifiable users. Therefore, we conjecture that the low-complexity (approximated) ML algorithm also achieves the same scaling law and we demonstrate its performance by simulation. We also compare the discussed methods with the (Bayesian) MMV-AMP algorithm, recently proposed for the same setting, and show superior performance and better numerical stability. Finally, we use the discussed approximated ML algorithm as the inner decoder in a concatenated coding scheme for unsourced random access , a grant-free uncoordinated multiple access scheme where all users make use of the same codebook, and the receiver must produce the list of transmitted messages, irrespectively of the identity of the transmitters. We show that reliable communication is possible at any $E_{b}/N_{0}$ provided that a sufficiently large number of base station antennas is used, and that a sum spectral efficiency in the order of $\mathcal {O}(L\log (L))$ is achievable.

中文翻译：

---

非贝叶斯活动检测，大规模衰落系数估计和大规模MIMO接收器的无源随机访问

在本文中，我们研究了用户问题 活动检测 大规模MIMO基站的随机接入无线上行链路中的大规模衰落系数估计 $ M $ 天线和大量无线单天线设备（用户）。我们考虑一个块衰落信道模型，其中 $ M $ 每个用户的三维通道矢量在a上保持恒定 相干块 包含 $ L $ 时间频率中的信号尺寸。在考虑的设置中，潜在用户数 $ K _ {\ text {tot}} $ 比 $ L $ 但仅在每个时隙 $ K_ {a} \ ll K _ {\ text {tot}} $ 他们是活跃的。基于压缩感测的先前结果要求 $ K_ {a} \ le L $ ，这是大规模部署方案中的瓶颈。在这项工作中，我们表明当基站天线的数量可以克服这种局限性 $ M $ 足够大。更具体地说，我们证明了维的连贯性块 $ L $ 和一些天线 $ M $ 这样 $ K_ {a} / M = o（1）$ ，一个可以识别 $ K_ {a} = O \ left（{L ^ {2} / \ log ^ {2} \ left（{\ frac {K _ {\ text {tot}}} {K_ {a}}} \ right）} \ right）$ 活跃用户，比以前已知的范围大得多。我们还提供了两种算法。一种基于非负最小二乘法，可以严格证明上述缩放结果。另一个包括底层问题的似然函数的低复杂度迭代分量最小化。虽然对于该算法无法给出严格的证明，但我们分析了最大似然（ML）问题（具有指数复杂度的组合优化）的约束版本，并为可识别用户的数量找到了相同的基本缩放定律。因此，我们推测低复杂度（近似）的ML算法也可以实现相同的缩放定律，并通过仿真证明了其性能。我们还将所讨论的方法与（贝叶斯（Bayesian））MMV-AMP算法进行比较，最近提出了相同的设置，并显示出优越的性能和更好的数值稳定性。最后，在级联编码方案中，我们将讨论的近似ML算法用作内部解码器，用于无源随机访问 ，一种无授予的非协调多址访问方案，其中所有用户都使用相同的密码本，并且接收方必须生成所发送消息的列表，而与发送方的身份无关。我们证明，任何情况下都可以进行可靠的通信 $ E_ {b} / N_ {0} $ 前提是使用了足够多的基站天线，并且总频谱效率约为 $ \ mathcal {O}（L \ log（L））$ 是可以实现的。