A Lorentzian Dispersion Model for Stacked Intelligent Metasurfaces
Stacked intelligent metasurfaces (SIM) provide a low-power means for MIMO transmission and reception using large multi-layer apertures that are digitally controlled. In this letter, we develop a SIM model that is consistent with metasurface theory. We use the Lorentzian function to emulate the amplitude-phase trade-off in meta-atoms. Therefore, realistic hardware impairments are introduced that change the system performance. Then, the general sheet transition conditions (GSTC) map the amplitude-phase trade-off to reflective and transmissive scattering parameters. Since the latter is only applicable to a single layer, we use network theory to extend it to multiple layers yielding an end-to-end SIM system model. Given the new feature, we derive a new Euclidean gradient of the system for optimization. Numerical results show that the ideal model overestimates sum rate by up to 7.5 bps/Hz at deeper configurations and that aperture size should be prioritized over cascade depth in physical SIM design.