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

Abstract: 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, the developed T-parameters model is simpler and more tractable. Moreover, the T-parameters constraints for lossless reciprocal reconfigurable intelligent surfaces (RISs) are derived. Additionally, a gradient descent algorithm (GDA) is introduced to maximize sum-rate in SIM-aided multiuser scenarios, demonstrating that mutual coupling and feedback between consecutive layers enhance performance. However, increasing SIM layers with a fixed total number of elements typically degrades sum-rate, unless the simplified channel model employing Rayleigh-Sommerfeld diffraction coefficients is utilized.