Unified Analytical Framework for Emergency RIS-UAV Networks Under Practical Impairments

Heterogeneous unmanned aerial vehicle (UAV) networks embedded with reconfigurable intelligent surfaces (RISs) present a promising paradigm for emergency wireless communications (EWC), offering enhanced coverage and resilience in harsh environments. However, extreme conditions in disaster areas necessitate robust performance evaluation under practical impairments, including outdated/imperfect channel state information (CSI) and discrete RIS phase shifts. Existing works lack a unified analytical framework for modeling CSI errors, employing inconsistent approaches that treat errors either as channel gain or as equivalent interference, leading to ambiguous benchmarks. To address this, we propose the $ζ$-Model, a unified receiver-equivalent signal-to-noise (SNR) framework that continuously parameterizes residual-error exploitability via $ζ$. This framework unifies the information-theoretic model (ITM) and the engineering baseline model (EBM) as the optimistic and pessimistic benchmark receiver treatments, while incorporating the simplified engineering model (SEM) as a tractable approximation. By employing the Fisher-Snedecor $\mathcal{F}$ distribution to capture severe fading and shadowing, we derive moment-matching-based closed-form or finite-sum approximate expressions and asymptotic expressions for average capacity (AC), effective capacity (EC), and outage probability (OP) under the proposed unified framework and its boundary cases. Validated by Monte Carlo simulations, our framework quantifies performance limits and provides crucial insights for designing robust and efficient EWC systems under various channel conditions and system impairments.