Optimization of RIS-Aided MIMO -- A Mutually Coupled Loaded Wire Dipole Model

In this letter, we consider a reconfigurable intelligent surface (RIS) assisted multiple-input multiple-output (MIMO) system in the presence of scattering objects. The MIMO transmitter and receiver, the RIS, and the scattering objects are modeled as mutually coupled thin wires connected to load impedances. We introduce a novel numerical algorithm for optimizing the tunable loads connected to the RIS. Compared with currently available algorithms, the proposed approach does not rely on the Neumann series approximation, but it optimizes the tunable load impedances alternately and one by one. At each iteration step, a closed-form expression for each impedance is provided by applying the Gram-Schmidt orthogonalization method. The algorithm is provably convergent and has a polynomial complexity with the number of RIS elements. Also, it is shown to outperform, in terms of achievable rate, two benchmark algorithms, which are based on a similar electromagnetic model, while requiring fewer iterations and a reduced execution time to reach convergence.