Grant-free random access is a promising protocol to support massive access in beyond fifth-generation (B5G) cellular Internet-of-Things (IoT) with sporadic traffic. Specifically, in each coherence interval, the base station (BS) performs joint activity detection and channel estimation (JADCE) before data transmission. Due to the deployment of a large-scale antennas array and the existence of a huge number of IoT devices, JADCE usually has high computational complexity and needs long pilot sequences. To solve these challenges, this paper proposes a dimension reduction method, which projects the original device state matrix to a low-dimensional space by exploiting its sparse and low-rank structure. Then, we develop an optimized design framework with a coupled full column rank constraint for JADCE to reduce the size of the search space. However, the resulting problem is non-convex and highly intractable, for which the conventional convex relaxation approaches are inapplicable. To this end, we propose a logarithmic smoothing method for the non-smoothed objective function and transform the interested matrix to a positive semidefinite matrix, followed by giving a Riemannian trust-region algorithm to solve the problem in complex field. Simulation results show that the proposed algorithm is efficient to a large-scale JADCE problem and requires shorter pilot sequences than the state-of-art algorithms which only exploit the sparsity of device state matrix.

中文翻译：

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一种基于降维的大规模访问联合活动检测和信道估计算法

免授权随机访问是一种很有前途的协议，可支持具有零星流量的超第五代 (B5G) 蜂窝物联网 (IoT) 中的大规模访问。具体地，在每个相干区间，基站（BS）在数据传输之前执行联合活动检测和信道估计（JADCE）。由于大规模天线阵列的部署和大量物联网设备的存在，JADCE通常计算复杂度高，需要长导频序列。为了解决这些挑战，本文提出了一种降维方法，该方法利用原始设备状态矩阵的稀疏和低秩结构将其投影到低维空间。然后，我们为 JADCE 开发了一个带有耦合全列秩约束的优化设计框架，以减少搜索空间的大小。然而，由此产生的问题是非凸的且非常棘手，传统的凸松弛方法不适用于这些问题。为此，我们提出了对非平滑目标函数的对数平滑方法，将感兴趣的矩阵转化为半正定矩阵，然后给出黎曼信任域算法来解决复杂领域的问题。仿真结果表明，与仅利用设备状态矩阵稀疏性的最新算法相比，该算法对大规模 JADCE 问题是有效的，并且需要更短的导频序列。我们提出了对非平滑目标函数的对数平滑方法，将感兴趣的矩阵转换为半正定矩阵，然后给出黎曼信任域算法来解决复杂领域的问题。仿真结果表明，与仅利用设备状态矩阵稀疏性的最新算法相比，该算法对大规模 JADCE 问题是有效的，并且需要更短的导频序列。我们提出了对非平滑目标函数的对数平滑方法，将感兴趣的矩阵转换为半正定矩阵，然后给出黎曼信任域算法来解决复杂领域的问题。仿真结果表明，与仅利用设备状态矩阵稀疏性的最新算法相比，该算法对大规模 JADCE 问题是有效的，并且需要更短的导频序列。