Performance Analysis of Single-Antenna Fluid Antenna Systems via Extreme Value Theory

In single-antenna fluid antenna systems (FASs), the transceiver dynamically selects the antenna port with the strongest instantaneous channel to enhance link reliability. However, deriving accurate yet tractable performance expressions under fully correlated fading remains challenging, primarily due to the absence of a closed-form distribution for the FAS channel. To address this gap, this paper develops a novel performance evaluation framework for FAS operating under fully correlated Rayleigh fading, by modeling the FAS channel through extreme value distributions (EVDs). We first justify the suitability of EVD modeling and approximate the FAS channel through the Gumbel distribution, with parameters expressed as functions of the number of ports and the antenna aperture size via the maximum likelihood (ML) criterion. Closed-form expressions for the outage probability (OP) and ergodic capacity (EC) are then derived. While the Gumbel model provides an excellent fit, minor deviations arise in the extreme-probability regions. To further improve accuracy, we extend the framework using the generalized extreme value (GEV) distribution and obtain closed-form OP and EC approximations based on ML-derived parameters. Simulation results confirm that the proposed GEV-based framework achieves superior accuracy over the Gumbel-based model, while both EVD-based approaches offer computationally efficient and analytically tractable tools for evaluating the performance of FAS under realistic correlated fading conditions.