Performance Analysis of MR-NOMA with Arbitrary Number of Users and Symbol Rates
This paper analytically investigates the bit error rate (BER) performance of downlink multi-rate (MR)-non-orthogonal multiple access (NOMA) over Nakagami-m fading channels for an arbitrary number of users and symbol rates. The analysis is first developed for a three-user case, then generalized to systems with more than three users, yielding an exact BER expression for the first detected user and an accurate closed-form approximations for the remaining users under the perfect-successive interference cancellation (SIC) assumption. These results are further unified into a general average-BER expression over Nakagami-m fading for arbitrary user numbers and symbol-rate configurations. A symbol-pattern-dependent signal-to-interference plus noise ratio (SINR) analysis further shows how the symbol-duration diversity enables inherent interference cancellation, explaining the BER advantage of MR-NOMA over conventional single-symbol rate (SR)-NOMA. An average BER minimization problem is also formulated and numerically solved to optimize the users' power allocation, with simulation results corroborating the analytical findings. Overall, MR-NOMA is shown to offer greater flexibility in user pairing while maintaining reliable BER performance and accommodating diverse quality-of-service (QoS) requirements.