Impact of Residual Hardware Impairments on Non-Orthogonal Multiple Access Based Amplify-and-Forward Relaying Networks

Abstract

We quantify the impact of residual hardware impairments (RHI) on a non-orthogonal multiple access (NOMA)-based relaying network, where a source communications simultaneously with multiple users via an amplify-and-forward relay. Specifically, exact and asymptotic expressions for the outage probability are first derived in closed-form over Nakagami- $m$ fading channels, accounting for RHI at the source, relay, and all users. Our results show that the outage performance loss induced by RHI is small in the low signal-to-noise ratio (SNR) regime or/and at low target rates, however it is significant at high SNRs or/and target rates. Furthermore, we present new tight analytical approximated and asymptotic expressions for the system ergodic sum rate (ESR). For comparison, we also discuss the ESR of the conventional hardware-impaired relaying system employing orthogonal multiple access (OMA) transmission and obtain the asymptotic high-SNR expression of the ESR. The provided numerical results demonstrate that in the absence of RHI, the ESR in either the NOMA or the OMA system increases monotonically with the increase of SNR, whereas an unavoidable ESR ceiling is introduced in the hardware-impaired scenario for both systems. Notably, since the ESR ceiling value is only depended on the RHI levels, the NOMA-based and OMA-based systems achieve the same ESR performance in high SNRs.