Performance Analysis of HAPS-RIS-Assisted MIMO Systems Under Phase-Dependent Amplitude Response Using Saddle Point Approximation

This letter proposes a novel mathematical framework for the statistical characterization of reconfigurable intelligent surface (RIS)-mounted high-altitude platform station (HAPS)-assisted MIMO systems over cascaded Rician fading channels. Due to the inherent coupling introduced by the RIS, the resulting cascaded channel does not satisfy the independence assumptions required for conventional Wishart-based modeling, which motivates a tractable alternative approach. By adopting a line-of-sight (LoS)-aligned precoding strategy, the received signal-to-noise ratio (SNR) is represented as a non-central quadratic form with a structured covariance matrix. Exploiting this structure, a saddle point approximation (SPA)-based framework is developed to characterize the SNR distribution. Closed-form expressions for the probability density function (PDF), cumulative distribution function (CDF), and outage probability are derived. The proposed framework further incorporates practical RIS hardware impairments, including discrete phase shifts and phase-dependent amplitude responses. The accuracy of the proposed analysis is validated through Monte Carlo simulations.

Space-Time Coded RIS-Assisted Wireless Systems with Practical Reflection Models: Error Rate Analysis and Negative Moment-Based Optimization with Saddle Point Approximation

RIS-assisted communication has recently attracted significant attention for enhancing wireless performance in challenging environments, making accurate error analysis under practical hardware constraints crucial for future multi-antenna systems. This paper presents a theoretical framework for SER analysis of RIS-assisted multiple antenna systems employing OSTBC under practical reflection models with amplitude-dependent and quantized phase responses. By exploiting the Gramian structure of the cascaded channel f, we derive exact MGF expressions of the nonzero eigenvalue of f'f for small RIS sizes. For large-scale RIS deployments, where closed-form analysis becomes intractable, we employ Saddle Point Approximation 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.

Joint Phase Shift Optimization and Precoder Selection for RIS-Assisted 5G NR MIMO Systems

By intelligently reconfiguring wireless propagation environment, reconfigurable intelligent surfaces (RISs) can enhance signal quality, suppress interference, and improve channel conditions, thereby serving as a powerful complement to multiple-input multiple-output (MIMO) architectures. However, jointly optimizing the RIS phase shifts and the MIMO transmit precoder in 5G and beyond networks remains largely unexplored. This paper addresses this gap by proposing a singular value ($\lambda$)-based RIS optimization strategy, where the phase shifts are configured to maximize the dominant singular values of the cascaded channel matrix, and the corresponding singular vectors are utilized for MIMO transmit precoding. The proposed precoder selection does not require mutual information computation across subbands, thereby reducing time complexity. To solve the $\lambda$-based optimization problem, maximum cross-swapping algorithm (MCA) is applied while an effective rank-based method is utilized for benchmarking purposes. The simulation results show that the proposed precoder selection method consistently outperforms the conventional approach under $\lambda$-based RIS optimization.