Imperfect CSI and Improper Gaussian Noise Effects on SSK: Optimal Detection and Error Analysis

Space shift keying (SSK) has many advantages through its unique transmission manner as compared to other multiple-input multiple-output (MIMO) techniques. Nevertheless, the practicality of SSK in the presence of real-time imperfections such as channel estimation errors and hardware impairments (HWIs) is still an open research problem. On the other hand, the effects of HWIs are assumed as zero-mean circularly-symmetric complex Gaussian random variable (RV) in the literature. However, this model does not reflect the asymmetric characteristics of different HWIs. Therefore, the aim of this paper is to shed light on the joint effect of improper Gaussian noise (IGN) and imperfect channel state information (ICSI) on the performance of SSK receiver. Particularly, an optimal maximum likelihood (ML) detector is designed, and pairwise error probability (PEP) expression is derived. Additionally, an exact closed-form Cramer-Rao bound expression is calculated for evaluating the channel estimation accuracy under the effect of IGN. The results obtained by using computer simulations prove that the proposed optimal detector is superior to the traditional ML detector in the presence of IGN and ICSI.