Reconfigurable Electromagnetic Environments: A General Framework

The recent introduction of the smart radio environments (SREs) paradigm, facilitated by reconfigurable intelligent surfaces (RISs) and large surface antennas, has highlighted the need for physically consistent models and design tools in communication systems that integrate information theory (IT) and electromagnetic (EM) theory. In this paper, we present a comprehensive framework for characterizing and designing programmable EM environments, based on rigorous EM arguments and represented through a linear graph employing matrix operators. The framework enables the determination of the EM transfer function of the system and the channel matrix used in IT, along with their relationship as functions of the programmable parameters. Considering that the mapping of EM quantities into IT signals occurs through the presence of ports in antenna structures, using the framework, we analyze the constraints imposed by the ports in terms of potential degrees-of-freedom (DoF) and establish the fundamental limits on the DoF of large surface antennas. To demonstrate the utility and validity of the framework, we provide examples specifically related to the characterization and optimization of RISs.