Exact BER Analysis of NOMA with Arbitrary Number of Users and Modulation Orders

Non-orthogonal multiple access (NOMA) is a promising candidate for future mobile networks as it enables improved spectral-efficiency, massive connectivity and low latency. This paper derives exact and asymptotic bit error rate (BER) expressions under Rayleigh fading channels for NOMA systems with arbitrary number of users and arbitrary number of receiving antennas and modulation orders, including binary phase-shift keying and rectangular/square quadrature amplitude modulation. Furthermore, the power coefficients' bounds, which ensure users' fairness, and solve the constellation ambiguity problem, are derived for N=2 and 3 users cases with any modulation orders. In addition, this paper determines the optimal power assignment that minimizes the system's average BER. These results provide valuable insight into the system's BER performance and power assignment granularity. For instance, it is shown that the feasible power coefficients range becomes significantly small as the modulation order, or N, increases, where the BER performance degrades due to the increased inter-user interference. Hence, the derived expressions can be crucial for the system scheduler in allowing it to make accurate decisions of selecting appropriate N, modulation orders, and power coefficients to satisfy the users' requirements. The presented expressions are corroborated via Monte Carlo simulations.