Reconfigurable Intelligent Surface Aided Space Shift Keying With Imperfect CSI

In this paper, we investigate the performance of reconfigurable intelligent surface (RIS)-aided spatial shift keying (SSK) wireless communication systems with imperfect channel state information (CSI). Specifically, we study the average bit error probability (ABEP) of two RIS-SSK systems based on intelligent reflection and blind reflection modes. For the intelligent RIS-SSK scheme, we first derive the conditional pairwise error probability of the composite channel through maximum likelihood (ML) detection. Subsequently, we derive the probability density function of the combined channel. Due to the intricacies of the composite channel formulation, an exact closed-form ABEP expression is unattainable through direct derivation. To this end, we resort to employing the Gaussian-Chebyshev quadrature method to estimate the results. Additionally, we employ Q-function approximation to derive the non-exact closed-form expression in the presence of channel estimation errors. For the blind RIS-SSK scheme, we derive both closed-form ABEP expression and asymptotic ABEP expression with imperfect CSI by adopting the ML detector. To offer deeper insights, we explore the impact of discrete reflection phase shifts on the performance of the RIS-SSK system. Lastly, we extensively validate all the analytical derivations via Monte Carlo simulations.