A Minimum Error Probability NOMA Design

Non-orthogonal multiple access (NOMA) enables massive connectivity and achieves high spectral efficiency. The vast majority of the NOMA literature has adopted the ideal information rate as performance metric assuming perfect successive interference cancellation (SIC) without any error propagation, which, however, may lead to NOMA designs adverse to SIC. In this paper, we take into account imperfect SIC and practical modulation schemes for power-domain NOMA design. To characterize the error propagation, we derive the bit error rates (BERs) of the users for arbitrary-order quadrature amplitude modulation (QAM) schemes. Then, we propose a minimum error probability NOMA (MEP-NOMA) design, minimizing the average BER of the users via power allocation. Considering the complicated error probability expressions of the MEP-NOMA design, we derive lower and upper bounds on the average BER, based on which a simple closed-form power allocation is obtained. We show that the proposed power allocation minimizes both the lower and upper bounds on the average BER for a sufficiently large power budget and provides near-optimal error performance. On this basis, we theoretically prove the superiority of MEP-NOMA over existing OMA and NOMA schemes in terms of error performance. Comprehensive numerical results are provided to verify the accuracy of the error probability analysis of the considered practical NOMA scheme with imperfect SIC and to demonstrate the efficacy of the proposed MEP-NOMA design.