XL-RIS Placement Strategies for Beam Focusing in Coexisting Near-Field and Far-Field mmWave Communications

Integrating extremely large antenna arrays (ELAAs) with extremely large reconfigurable intelligent surfaces (XLRISs) in millimeter wave (mmWave) communications places devices in the near-field (NF) region, significantly boosting spectral efficiency (SE). This paper investigates beam focusing for SE maximization by determining the optimal placement of XL-RIS in a multi-input single-output (MISO) system. Specifically, to maximize SE, the transmit beamforming vector at the base station (BS) and the phase-shifting vector at the XL-RIS are jointly optimized. To explore the optimal placement of XL-RIS, we consider three scenarios where the positions of the BS and user are fixed, but the XL-RIS is placed in either the NF or farfield (FF) of both. Since the SE maximization problem is nonconvex with highly coupled variables, we propose an alternating optimization algorithm that decouples the problem into two subproblems: transmit beamforming optimization and phase shift optimization. Both sub-problems are reformulated as convex problems using the semi-definite programming (SDP) technique and are then solved with standard convex optimization tools. Simulation results show that placing the XL-RIS in the NF region of the BS achieves higher SE compared to other configurations.