Physically Consistent Modeling for Multi-Layer Reconfigurable Intelligent Surface-Based Multi-User Communications

The advent of multi-layer reconfigurable intelligent surfaces (RIS) has introduced new possibilities for integrating communication, sensing, and computation within the wave domain. Existing models, however, often rely on simplified mathematical abstractions, failing to accurately represent the physical behavior of multi-layer RIS-assisted systems. To bridge this gap, we present a physically consistent model for multi-layer RIS-enabled multi-user communications. The model is based on electromagnetic (EM) theory and Chu’s antenna principles, incorporating mutual coupling (MC) effects through an impedance-parameterized multi-port circuit framework. Contrary to the conventional view of MC as a performance-limiting factor, our analysis demonstrates that, when properly managed, MC can enhance system efficiency. To this end, we design an optimization algorithm that iteratively updates the RIS phase control matrix and transmits power using gradient ascent combined with successive convex approximation (SCA), ensuring that physical constraints and MC effects are fully integrated. Simulation results demonstrate the proposed model’s ability to accurately predict system behavior and highlight the potential performance gains achievable through MC-aware design, offering a practical foundation for optimizing multi-layer RIS in advanced communication systems.