基于相依赖幅度响应的HAPS-RIS辅助MIMO系统性能分析
Performance Analysis of HAPS-RIS-Assisted MIMO Systems Under Phase-Dependent Amplitude Response Using Saddle Point Approximation
AI总结：
本文基于相依赖幅度响应，提出利用鞍点近似分析HAPS-RIS辅助MIMO系统在级联Rician信道中的性能，推导出SNR分布及 outage 概率的闭式表达式，并验证了实际RIS硬件缺陷的影响。
摘要：
本文提出了一种新的数学框架，用于统计表征基于RIS的高空平台站（HAPS）辅助MIMO系统在级联Rician衰落信道中的性能。由于RIS引入的固有耦合，所得到的级联信道不满足传统Wishart基模型所需的独立性假设，这促使了可操作的替代方法。通过采用视线对齐预编码策略，接收信噪比（SNR）被表示为具有结构化协方差矩阵的非中心二次型。利用这一结构，开发了基于鞍点近似（SPA）的框架来表征SNR分布。推导出概率密度函数（PDF）、累积分布函数（CDF）和 outage 概率的闭式表达式。所提出的框架进一步纳入了实际RIS硬件缺陷，包括离散相位偏移和相依赖幅度响应。所提出的分析的准确性通过蒙特卡洛模拟进行了验证。
英文摘要：
The integration of HAPS, RISs, and MIMO technologies is emerging as a promising paradigm for extending the coverage and reliability of future wireless communication networks. However, in a HAPS-mounted RIS-assisted MIMO (HAPS-RIS-MIMO) system, the received SNR statistics become difficult to characterize due to the cascaded Rician small-scale fading and log-normal large-scale shadowing effects. To address this challenge, this paper develops a tractable analytical framework for the SNR characterization of HAPS-RIS-MIMO systems under LoS-aligned precoding. Specifically, saddlepoint approximation is employed to characterize the distribution of the small-scale effective channel power, while Gauss-Hermite quadrature is used to incorporate the composite log-normal large-scale fading effect. Based on the resulting cumulative distribution function, the outage probability expression is derived and validated through Monte Carlo simulations. The numerical results provide both theoretical validation and practical design insights by analyzing the effects of transmit power, HAPS altitude, transmit antenna number, RIS size, RIS amplitude response, and RIS phase resolution. It is shown that optimizing the RIS phases to enhance the LoS power contribution provides substantial transmit-power savings compared with random RIS phase configurations. Moreover, LoS-aligned precoding achieves a performance close to eigenmode precoding when the RIS phases are properly optimized, indicating a promising low-complexity alternative for practical HAPS-RIS-MIMO deployments. Furthermore, sufficiently large RIS deployments with LoS-aware phase optimization can mitigate the degradation caused by increased HAPS altitude and limited transmit-power budgets, while practical RIS hardware improvements in amplitude response and phase resolution provide additional transmit-power gains of approximately 3-5 dB.
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