Rate Loss Analysis of Reconfigurable Intelligent Surface-Aided NOMA With Limited Feedback

The design of feedback channels in frequency division duplex (FDD) systems is a major challenge because of the limited available feedback bits. We consider non-orthogonal multiple access (NOMA) systems that incorporate reconfigurable intelligent surfaces (RISs). In limited feedback RIS-aided NOMA systems, the RIS-aided channel and the direct channel gains should be quantized and fed back to the transmitter. We investigate the rate loss of the overall RIS-aided NOMA systems suffering from quantization errors under Rayleigh and Rician fading channel models. We first consider random vector quantization for the overall RIS-aided channel and identical uniform quantizers for the direct channel gains. We then obtain an upper bound for the rate loss in Rayleigh fading, due to the quantization error, as a function of the number of feedback bits and the size of RIS. In addition, we determine the channel gain values for which NOMA is advantageous under full channel state information (CSI) but not with the quantized feedback. We perform a similar analysis assuming Rician models by approximating the extremely complicated probability density function (pdf) of a RIS-aided double-Rician channel. Our numerical results indicate that, for a small RIS size, the sum rate performance of the limited feedback system approaches that of the system with full CSI as the number of feedback bits increases. However, as the size of RIS enlarges, the sum rate improvement slows down. Further, by increasing the number of feedback bits and the transmit power, the probability that NOMA should be chosen over OMA increases.