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.

翻译：本文研究了在非理想信道状态信息下，可重构智能表面辅助的空间移位键控无线通信系统的性能。具体而言，我们分析了基于智能反射和盲反射两种模式的RIS-SSK系统的平均误比特率。对于智能RIS-SSK方案，首先通过最大似然检测推导了复合信道的条件成对错误概率，进而得到了复合信道的概率密度函数。由于复合信道公式的复杂性，直接推导无法获得精确的闭合式ABEP表达式。为此，我们采用高斯-切比雪夫求积法进行结果估计，并利用Q函数近似推导了存在信道估计误差时的非精确闭合表达式。对于盲RIS-SSK方案，基于ML检测器推导了非理想CSI下的闭合式ABEP表达式与渐进ABEP表达式。为深入分析，我们探讨了离散反射相位偏移对RIS-SSK系统性能的影响。最后，通过蒙特卡洛仿真全面验证了所有解析推导结果。