Decoupling Networks and Super-Quadratic Gains for RIS Systems with Mutual Coupling

We propose decoupling networks for the reconfigurable intelligent surface (RIS) array as a solution to benefit from the mutual coupling between the reflecting elements. In particular, we show that when incorporating these networks, the system model reduces to the same structure as if no mutual coupling is present. Hence, all algorithms and theoretical discussions neglecting mutual coupling can be directly applied when mutual coupling is present by utilizing our proposed decoupling networks. For example, by including decoupling networks, the channel gain maximization in RIS-aided single-input single-output (SISO) systems does not require an iterative algorithm but is given in closed form as opposed to using no decoupling network. In addition, this closed-form solution allows to analytically analyze scenarios under mutual coupling resulting in novel connections to the conventional transmit array gain. In particular, we show that super-quadratic (up to quartic) channel gains w.r.t. the number of RIS elements are possible and, therefore, the system with mutual coupling performs significantly better than the conventional uncoupled system in which only squared gains are possible. We consider diagonal as well as beyond diagonal (BD)-RISs and give various analytical and numerical results, including the inevitable losses at the RIS array. In addition, simulation results validate the superior performance of decoupling networks w.r.t. the channel gain compared to other state-of-the-art methods.