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.