T-Parameters Based Modeling for Stacked Intelligent Metasurfaces: Tractable and Physically Consistent Model

This work develops a physically consistent model for stacked intelligent metasurfaces (SIM) using multiport network theory and transfer scattering parameters (T-parameters). Unlike the scattering parameters (S-parameters) model, which is highly complex and non-tractable due to its nested nature and excessive number of matrix inversions, the developed T-parameters model is less complex and more tractable due to its explicit and compact nature. This work further derives the constraints of T-parameters for a lossless reciprocal reconfigurable intelligent surfaces (RISs). A gradient descent algorithm (GDA) is proposed to maximize the sum rate in SIM-aided multiuser scenarios, and the results show that accounting for mutual coupling and feedback between consecutive layers can improve the sum rate. In addition, increasing the number of SIM layers with a fixed total number of elements degrades the sum rate when our exact and simplified channel models are used, unlike the simplified channel model with the Rayleigh-Sommerfeld diffraction coefficients which improves the sum rate.