RIS Assisted Short-Packet NOMA Systems with Discrete Phase Shifts and Hardware Impairments

Reconfigurable intelligent surface (RIS) and non-orthogonal multiple access (NOMA) are two promising technologies for future wireless communication networks. This paper proposes a new transmission design for short-packet communications (SPCs) in a downlink RIS-assisted NOMA system, considering hardware impairments at the transceiver nodes, non-optimal continuous phase shifts (CPSs) and discrete phase shifts (DPSs) at the RIS, and imperfect successive interference cancellation (SIC) for a pair of NOMA users. Using the method of moment matching, we approximate the end-to-end channel gain with a Gamma distribution, and derive the closed-form approximate expressions for the average block error rates (BLERs) for NOMA users, along with the diversity order and the asymptotic expressions for the average BLERs at the high signal-to-noise ratio (SNR) region. Inspired by the asymptotic average BLER, the minimum blocklength is derived, and the optimal power allocation factor is obtained. Then, the system throughput is obtained to characterize the transmission efficiency of the RIS-assisted short-packet NOMA network. Analytical results of the proposed scheme indicate that: 1) The phase estimation error of the RIS has a significant impact on the system performance, and thus the non-optimal CPSs should be used in the theoretical analysis; 2) The DPSs with 3-bit quantization can effectively achieve a comparable performance to the optimal CPS scheme in practical applications. Numerical results validate our theoretical analysis, and clearly show the performance improvement of transmission reliability and effectiveness of the proposed scheme, as compared to existing transmission schemes.