A Beamshaping Framework for Physically Consistent Reconfigurable Intelligent Surfaces

Understanding beamshaping in reconfigurable intelligent surfaces (RIS) is crucial for practical deployment, especially with the recent emphasis on self-configuring RISs. However, accurate beamshaping must account for factors such as mutual coupling and structural scattering. This paper proposes a beamshaping framework for physically consistent RISs using a modified signal model that bridges communication theory and multiport network theory. By focusing on desired beam and null locations, we enable pre-calculation of RIS channel gain matrices, reducing computational complexity. The optimization problems are then solved using constrained simulated annealing (CSA). Numerical simulations validate the framework by demonstrating wide beam and null formation and the necessity of discrete optimization for accurate beamshaping with less than 7 bits of discrete control. Results also reveal that ignoring mutual coupling in structural scattering leads to a notable decline in null quality.