Fluid Reconfigurable Intelligent Surface With Element-Level Pattern Reconfigurability: Beamforming and Pattern Co-Design

This paper proposes a novel pattern-reconfigurable fluid reconfigurable intelligent surface (FRIS) framework, where each fluid element can dynamically adjust its radiation pattern based on instantaneous channel conditions. To evaluate its potential, we first conduct a comparative analysis of the received signal power in point-to-point communication systems assisted by three types of surfaces: 1) the proposed pattern-reconfigurable FRIS, 2) a position-reconfigurable FRIS, and 3) a conventional RIS. Theoretical results demonstrate that the pattern-reconfigurable FRIS provides a significant advantage in modulating transmission signals compared to the other two configurations. To further study its capabilities, we extend the framework to a multiuser communication scenario. In this context, the spherical harmonics orthogonal decomposition (SHOD) method is employed to accurately model the radiation patterns of individual fluid elements, making the pattern design process more tractable. An optimization problem is then formulated with the objective of maximizing the weighted sum rate among users by jointly designing the active beamforming vectors and the spherical harmonics coefficients, subject to both transmit power and pattern energy constraints. To tackle the resulting non-convex optimization problem, we propose an iterative algorithm that alternates between a minimum mean-square error (MMSE) approach for active beamforming and a Riemannian conjugate gradient (RCG) method for updating the spherical harmonics coefficients. Simulation results show that the proposed pattern-reconfigurable FRIS significantly outperforms traditional RIS architectures based on the 3GPP 38.901 and isotropic radiation models, achieving average performance gains of 161.5% and 176.2%, respectively. Additionally, it reduces the required number of antennas and RIS elements by over 300%, offering substantial improvements in hardware efficiency.