Improper Gaussian Signaling for Two-User MISO-NOMA Systems Considering Hardware Impairments and Imperfect SIC

In this paper, we study the advantages of improper Gaussian signaling (IGS) with the existence of hardware impairments (HWI) and imperfect successive interference cancellation (SIC) in the downlink two-user power-domain non-orthogonal multiple access (PD-NOMA) systems. We first provide the input-output relationships for the MIMO system with HWIs and then derive the rate expressions for each user. The improper signals are assumed to be generated by widely linear precoding (WLP) and transmitted under the PD-NOMA scheme in the context of imperfect SIC. To exhibit the supremacy of IGS, we formulate two kinds of optimization problems concerned with the max-min rate and maximizing achievable sum rate (ASR) between users under the quality of service (QoS) and the total power constraints (TPC). To deal with the non-convex log-determinant objective functions, we adopt successive concave quadratic programming (SCQP) to obtain suboptimal results by iterations. Simulation results demonstrate that IGS cases outperform ZF precoders and conventional proper Gaussian signaling (PGS) counterparts in both max-min rate and ASR, particularly in high I/Q imbalance (IQI) and less efficient SIC scenarios. Besides, the difference in the performance degradation between imperfect SIC and HWIs is compared. Finally, we briefly classify the conditions where IGS could be preferable for signal transmission.