Macroscopic model and statistical model to characterize electromagnetic information of a digital coding metasurface

A digital coding metasurface is a platform connecting the digital space and electromagnetic wave space, and has therefore gained much attention due to its intriguing value in reshaping wireless channels and realizing new communication architectures. Correspondingly, there is an urgent need for electromagnetic information theory that reveals the upper limit of communication capacity and supports the accurate design of metasurface-based communication systems. To this end, we propose a macroscopic model and a statistical model of the digital coding metasurface. The macroscopic model uniformly accommodates both digital and electromagnetic aspects of the meta-atoms and predicts all possible scattered fields of the digital coding metasurface based on a small number of simulations or measurements. Full-wave simulations and experimental results show that the macroscopic model is feasible and accurate. A statistical model is further proposed to correlate the mutual coupling between meta-atoms with covariance and to calculate the entropy of the equivalent currents of digital coding metasurface. These two models can help reconfigurable intelligent surfaces achieve more accurate beamforming and channel estimation, and thus improve signal power and coverage. Moreover, the models will encourage the creation of a precoding codebook in metasurface-based direct digital modulation systems, with the aim of approaching the upper limit of channel capacity. With these two models, the concepts of current space and current entropy, as well as the analysis of information loss from the coding space to wave space, is established for the first time, helping to bridge the gap between the digital world and the physical world, and advancing developments of electromagnetic information theory and new-architecture wireless systems.