Multi-Beam Design for Extremely Large-Scale RIS Aided Near-Field Wireless Communications

The development of reconfigurable intelligent surface (RIS) will evolve towards the extremely large-scale RIS (XL-RIS) to overcome the “multiplicative fading effect”. With the increase in array aperture, this evolution leads to the near-field propagation becoming dominant. To achieve the performance gain of XL-RIS, it is effective to explore the near-field beam design with a codebook via beam training. Unfortunately, due to the constant modulus constraint of XL-RIS, most of the existing works in the near-field scenario focus on single-beam design. Hence, these works will face a serious loss for the quality of service in the multiple user equipments case. In this paper, we propose a block coordinate descent (BCD) based scheme with majorization-minimization (MM) algorithm for the multi-beam design. The proposed scheme handles the constant modulus constraint from two aspects. Firstly, the multi-beam design is an intractable non-convex quadratic programming problem due to this constraint. We utilize the MM algorithm to decompose this problem as a series of tractable sub-problems to be iteratively solved. Secondly, the solution space for the multi-beam design is limited due to this constraint, we introduce the phases for beam gains as an extra optimizable variable to enrich the degree of freedom for optimization. Simulation results show that the proposed multi-beam design can achieve a superior quality of service 50% higher than the existing schemes.