Outage Balancing in Phase Hopping Based Reconfigurable Intelligent Surface-Aided Downlink NOMA Systems

For reconfigurable intelligent surface (RIS)-aided wireless communications, the phase hopping scheme forces the wireless channel to experience multiple channel conditions and thus improves the system reliability. In this paper, we propose a phase hopping based RIS-aided downlink non-orthogonal multiple access system. For the proposed system, we study the outage balancing problem, where the closed-form expression of ergodic capacity, an increasing function with respect to the variance of overall channels, is theoretically derived. One challenge to solve the outage balancing problem is to obtain the cumulative distribution function (CDF) of the variance of overall channels. For Rayleigh fading channels, the CDF is obtained using the characteristic function of the product of channel gains and the inverse theorem. For Rician fading channels, we approximate the variance of overall channels as a Gamma distributed random variable. The outage balancing problem is solved by a bisection search. To show the advantages to the phase hopping scheme, we also solve the outage balancing problem for a static random phases based system. Simulation results show that at moderate and high signal-to-noise ratio, the proposed phase hopping based system is superior to the static random phases based one.