Performance Analysis of MIMO Full-Duplex NOMA Networks with Max-Min Relay Selection for Short-Packet Communications

Abstract

This paper investigates the performance of a multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) network, enhanced by a pool of full-duplex (FD) relays, for short-packet communications (SPC). We propose a combined framework where the source and destinations are equipped with multiple antennas, and a max-min relay selection criterion is employed to choose the best relay among multiple candidates. This criterion maximizes the end-to-end link quality by selecting the relay that offers the best bottleneck signal-to-interference-plus-noise ratio (SINR). We derive novel, exact analytical expressions for the average block error rate (BLER) for two NOMA users, meticulously accounting for the joint effects of MIMO diversity, relay selection diversity, residual self-interference (RSI) at the FD relay, and imperfect successive interference cancellation (SIC). To facilitate computation, we also provide a highly accurate closed-form approximation of the BLER using Gauss-Chebyshev quadrature. The analysis reveals that the max-min selection strategy effectively overcomes the performance bottleneck of simpler selection schemes, ensuring that the system's diversity order scales with the number of available relays. Numerical results validate our rigorous theoretical analysis, demonstrating the significant reliability gains achieved by the proposed framework. The findings offer crucial insights into the interplay between key system parameters, providing a comprehensive guide for designing robust ultra-reliable low-latency communication (URLLC) systems.