This paper studies the device activity detection problem in a massive multiple-input multiple-output (MIMO) system for near-field communications (NFC). In this system, active devices transmit their signature sequences to the base station (BS), which detects the active devices based on the received signal. In this paper, we model the near-field channels as correlated Rician fading channels and formulate the device activity detection problem as a maximum likelihood estimation (MLE) problem. Compared to the traditional uncorrelated channel model, the correlation of channels complicates both algorithm design and theoretical analysis of the MLE problem. On the algorithmic side, we propose two computationally efficient algorithms for solving the MLE problem: an exact coordinate descent (CD) algorithm and an inexact CD algorithm. The exact CD algorithm solves the one-dimensional optimization subproblem exactly using matrix eigenvalue decomposition and polynomial root-finding. By approximating the objective function appropriately, the inexact CD algorithm solves the one-dimensional optimization subproblem inexactly with lower complexity and more robust numerical performance. Additionally, we analyze the detection performance of the MLE problem under correlated channels by comparing it with the case of uncorrelated channels. The analysis shows that when the overall number of devices $N$ is large or the signature sequence length $L$ is small, the detection performance of MLE under correlated channels tends to be better than that under uncorrelated channels. Conversely, when $N$ is small or $L$ is large, MLE performs better under uncorrelated channels than under correlated ones. Simulation results demonstrate the computational efficiency of the proposed algorithms and verify the correctness of the analysis.

翻译：本文研究了近场通信（NFC）场景下大规模多输入多输出（MIMO）系统中的设备活跃性检测问题。在该系统中，活跃设备向基站（BS）发送其签名序列，基站根据接收信号检测活跃设备。本文将近场信道建模为相关莱斯衰落信道，并将设备活跃性检测问题表述为一个最大似然估计（MLE）问题。与传统的非相关信道模型相比，信道的相关性使得MLE问题的算法设计和理论分析都更为复杂。在算法方面，我们提出了两种计算高效的算法来求解该MLE问题：一种精确坐标下降（CD）算法和一种非精确CD算法。精确CD算法通过矩阵特征值分解和多项式求根精确求解一维优化子问题。通过适当近似目标函数，非精确CD算法以较低的复杂度和更稳健的数值性能非精确地求解一维优化子问题。此外，我们通过与非相关信道情况的对比，分析了相关信道下MLE问题的检测性能。分析表明，当设备总数 $N$ 较大或签名序列长度 $L$ 较小时，相关信道下MLE的检测性能往往优于非相关信道下的性能。反之，当 $N$ 较小或 $L$ 较大时，MLE在非相关信道下的性能优于相关信道下的性能。仿真结果证明了所提算法的计算效率，并验证了分析的正确性。