Channel Eigenvalues and Effective Degrees of Freedom of Reconfigurable Intelligent Surfaces

Abstract: As a promising candidate technology for the next-generation wireless communications, reconfigurable intelligent surface (RIS) has gained tremendous research interest in both the academia and industry in recent years. Only limited knowledge, however, has been obtained about the channel eigenvlaue characteristics and degrees of freedom (DoF) of systems containing RISs. In this paper, we focus on a wireless communication system where both the transmitter and receiver are respectively equipped with an RIS. Features of eigenvalues, such as their summation and individual behavior, are investigated for both the correlation matrix of an RIS and the composite channel matrix encompassing the two RISs and the wireless channel. Furthermore, the concept of effective degrees of freedom (EDoF), i.e., the number of subchannels actively contributing to conveying information, is revisited for RIS-enabled systems. Analytical and numerical results demonstrate that the EDoF depends upon various factors including the operating SNR, physical parameters of RISs, and propagation environment.