Mutual Coupling and Unit Cell Aware Optimization for Reconfigurable Intelligent Surfaces

We introduce algorithms for optimizing a single-input single-output reconfigurable intelligent surface (RIS) assisted system. The RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances and its reconfigurability is realized through tunable lumped impedances. In the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which accounts for the interplay between the amplitude and phase of the lumped loads of the RIS. In the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling significantly affects the end-to-end received power. If the RIS is optimized by taking the mutual coupling into account, the received power can be increased.