Exact Ergodic Capacity Analysis of Dual-RIS-Aided mmWave Systems With Selection Diversity

Abstract

This paper presents an analytical framework for evaluating the ergodic capacity of dual-reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) systems employing selection diversity over independent, non-identically distributed Nakagami- $m$ fading channels. Unlike prior works that rely on approximations or bounds, our formulation captures the exact statistical characterization of the end-to-end signal-to-noise ratio (SNR) and yields an exact ergodic capacity expression without invoking the central limit theorem or moment-matching techniques. Furthermore, we derive a compact high-SNR asymptotic expression to reveal the fundamental performance limits. The analysis incorporates a comprehensive channel model that accounts for small-scale fading, large-scale path loss, atmospheric attenuation under various weather conditions, and phase errors arising from imperfect channel state information. Based on the derived expressions, we investigate the impact of key system parameters—including the number of reflecting elements, fading severity, transmission distance, and weather conditions—on system performance. Numerical results, validated by Monte Carlo simulations, demonstrate that severe phase estimation error induces a persistent capacity penalty, as it prevents the RIS elements from achieving perfect coherent combining. Furthermore, the dual-RIS architecture provides significant diversity gains, effectively bypassing severely faded links and extending coverage under harsh atmospheric attenuation. Notably, under practical size constraints that limit the number of elements per unit, the dual-RIS architecture significantly outperforms a single-RIS of the same unit size, and offers superior deployment flexibility and resilience.