Active Reconfigurable Intelligent Surfaces: Circuit Modeling and Reflection Amplification Optimization

Reconfigurable Intelligent Surfaces (RISs) constitute a promising emerging technology that enables wireless systems to control the propagation environment to enhance diverse communication objectives. To mitigate double-fading attenuation in RIS-aided links, the paradigm of active metamaterials capable of amplifying their incident wave has emerged. In this paper, capitalizing on the inherent negativeresistance region of tunnel diodes, we propose their integration into each RIS unit element to enable RISs with reflection amplification entirely in the analog domain. We derive novel realistic phase-amplitude relationships and power constraints specific to this model, addressing gaps in the existing literature where amplitude limits are often chosen arbitrarily. This characterization of our active RIS unit elements is incorporated into two novel optimization frameworks targeting the spectral efficiency maximization of RIS-assisted Multiple-Input-Multiple-Output (MIMO) systems, which are solved via a one-step approach and an iterative Alternating Optimization (AO) method. The former approach is used to initialize the AO framework, enhancing both its performance and convergence. Our numerical investigations emphasize the importance of accurately modeling phase-amplitude dependencies, and provide key insights into the impact of RIS-induced noise as well as the trade-off between available power and the number of active elements.