Outage Performance Analysis of Improper Gaussian Signaling for Two-User Downlink NOMA Systems with Imperfect Successive Interference Cancellation

The improper Gaussian signaling (IGS) technique can improve the achievable rate of an interference-limited network by fully exploiting the second-order statistics of complex signaling. This paper addresses the outage performance analysis of a two-user downlink non-orthogonal multiple access (NOMA) system using the IGS technique in the presence of imperfect successive interference cancellation (SIC). The strong channel user (SU) adopts the IGS, while the weak channel user (WU) adopts the traditional proper Gaussian signaling (PGS). Considering a practical scenario where the transmitter has obtained the statistics of the channel coefficients instead of the instantaneous channel state information (CSI), the expressions of the achievable rates of both users under residual interference due to imperfect SIC are derived, together with their outage probabilities, subject to predetermined target rates and channel statistics. Given a fixed transmit power of the WU, both the transmit power and the degree of impropriety of the SU are optimized to minimize the outage probability subject to the outage constraint of the WU. Numerical results are provided to assess the benefits of the proposed IGS-based downlink NOMA system, which are consistent with the analysis.