Robust Beamfocusing Design for Near-Field Secure Communications

In this paper, we present a secure beamforming method tailored for near-field multi-user communication scenarios. In particular, the exact location of the eavesdropper is unknown but presumed to be within a potential region, as the base station cannot determine its accurate location. The objective is to maximize the worst case secure capacity across the entire potential region subject to the transmit power constraint. To address this challenge, we propose an alternating optimization (AO) algorithm. Specifically, we decouple the original multi-user joint optimization problem into multiple single-user feasibility problems, and then alternately design each user's beamfocusing vector. For each subproblem, we develop a single-point control method inspired by the adaptive array theory, enabling precise control of secure communication capacity at any spatial location to a specified desired value. By sampling a set of points within the potential eavesdropping region and sequentially applying the proposed method to each point, we ensure that the entire region reaches the required secure capacity after a number of iterations, thus obtaining a feasible solution for each subproblem. By employing a binary search method, we can iteratively refine the secure capacity threshold and obtain a group of beamfocusing vectors that maximizes the secure communication capacity. Numerical results indicate that the proposed algorithm can effectively fulfill the requirements for near-field multi-user secure communication even when the eavesdropper and the users are located at the same angle with respect to the transmit antenna array. Moreover, the proposed algorithm offers advantages in computational efficiency and flexibility. When the location of the eavesdropper changes, the current beamformer can be readily adapted to meet new secure communication requirements without requiring a complete redesign.