Error Probability Analysis of Non-Orthogonal Multiple Access for Relaying Networks with Residual Hardware Impairments

In this paper, we quantify the effect of residual hardware impairments (RHI) on the error rate performance of a relay-based non-orthogonal multiple access (NOMA) system, where the communication between a source node and multiple users is completed via an amplify-and-forward (AF) relay node. In particular, we focus on the pairwise error probability (PEP) analysis and derive an accurate PEP approximation to characterize the performance of NOMA users under Rayleigh fading channels. The derived PEP expression is then exploited to investigate the diversity gain and the union bound on the bit error rate (BER) of the underlying system. Our results demonstrate that the presence of RHI causes an error floor at high signal-to-noise ratio (SNR) values. This error floor yields a detrimental effect on the achievable diversity order of NOMA users, where it is shown that the diversity order of all users converges to zero.