Space-Time Coded RIS-Assisted Wireless Systems With Imperfect CSI and Practical Reflection Models: Error Rate Analysis and Optimization With Saddle Point Approximation

Abstract

Reconfigurable Intelligent Surface (RIS)-assisted communication has recently attracted significant attention for enhancing wireless performance in challenging environments, making accurate error analysis under practical hardware constraints and imperfect channel state information (CSI) conditions crucial for future multi-antenna systems. This paper presents a unified theoretical framework for the symbol error rate (SER) analysis of RIS-assisted multiple-antenna systems employing orthogonal space-time block codes (OSTBC), considering practical reflection models with amplitude-dependent and quantized phase responses under channel estimation errors (CEEs). By exploiting the Gramian structure of the cascaded channel f, we derive exact moment-generating function (MGF) expressions of the nonzero eigenvalue of ff for small RIS sizes. For large-scale RIS deployments, where closed-form analysis becomes intractable, we employ Saddle Point Approximation (SPA) to approximate the eigenvalue distribution. Using these results, we derive unified SER expressions using exact and SPA-based MGF formulations, applicable to arbitrary RIS sizes, phase configuration, and both identical and non-identical amplitude responses. Extensive Monte Carlo simulations confirm the accuracy of the proposed SER expressions, demonstrating very close agreement for all configurations and under imperfect channel state information (CSI) scenarios. In addition, by applying asymptotic SNR analysis on the SPA-based SER formulation, we mathematically establish that the coding gain is inversely proportional to the N-t-th negative moment of the SPA-approximated probability density function (PDF) corresponding to the nonzero eigenvalue of the cascaded RIS-receiver Gram matrix. This insight motivates a negative moment minimization algorithm that efficiently identifies hardware-constrained RIS phase configurations, achieving near-optimal SER performance with low complexity.