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As a promising candidate technology for the next-generation wirelesscommunications, reconfigurable intelligent surface (RIS) has gained tremendousresearch interest in both the academia and industry in recent years. Onlylimited knowledge, however, has been obtained about the channel eigenvlauecharacteristics and degrees of freedom (DoF) of systems containing RISs. Inthis paper, we focus on a wireless communication system where both thetransmitter and receiver are respectively equipped with an RIS. Features ofeigenvalues, such as their summation and individual behavior, are investigatedfor both the correlation matrix of an RIS and the composite channel matrixencompassing the two RISs and the wireless channel. Furthermore, the concept ofeffective degrees of freedom (EDoF), i.e., the number of subchannels activelycontributing to conveying information, is revisited for RIS-enabled systems.Analytical and numerical results demonstrate that the EDoF depends upon variousfactors including the operating SNR, physical parameters of RISs, andpropagation environment.

Channel Eigenvalues and Effective Degrees of Freedom of Reconfigurable Intelligent Surfaces