An Approach for Reconfigurable Intelligent Surface (RIS) design for MIMO-NOMA Transmission: theoretical study

The approach (Paradigm) presented hereafter was inspired by two basic ideas: assuming the MIMO-RIS-NOMA communication channel as a dispersive channel with fading and representing the later by means of Generalized Kroneker Channel model (GKCM) applying the so-called “Orthogonalization Approach” based on the utilization of the “universal” eigenbasis in the form of Prolate  Spheroidal Wave Functions (PSWF). In other words, the essence of the approach lies in representing the MIMO-RIS-NOMA channel by means of the finite set of artificially created orthogonal trajectories for wave propagation (PSWF eigenbasis) depending to the Planar Antenna(PA) patterns at the Transmitting and Receiving terminals of MIMO systems, being connected between themselves by the so-called Coupling Matrix (CM) of the RIS. Certainly, the goal for RIS (by certain choice of the elements of CM) is to provide the system for the decoding of the NOMA users with the required values of SNR for each user to guarantee its successful decoding processing. Theoretical analysis of this paradigm is presented in the following material.