Covariance-Based Device Activity Detection for Near-Field Communications

This paper investigates the device activity detection problem in a massive multiple-input multiple-output system for near-field communications. In this setup, active devices transmit their preassigned signature sequences to the base station, which identifies the active devices based on the received signal. The nearfield communication channels are modeled as correlated Rician fading, and the device activity detection problem is formulated as a maximum likelihood estimation (MLE) problem. This paper proposes two efficient algorithms for solving the MLE problem. The first is the exact coordinate descent (CD) algorithm, which exactly solves the one-dimensional optimization subproblem through matrix eigenvalue decomposition and polynomial root-finding techniques. The second is the inexact CD algorithm, which approximates the objective function appropriately and solves the one-dimensional optimization subproblem inexactly, resulting in lower computational complexity and improved numerical robustness. Simulation results demonstrate the computational efficiency of the proposed algorithms.