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

TL;DR

This work tackles the analytical challenge of evaluating single-antenna fluid antenna systems under fully correlated Rayleigh fading by casting the FAS channel, $|h_{ m FAS}|$, as the maximum of correlated port channels and modeling its distribution with extreme value distributions. It first employs the Gumbel distribution, deriving ML-based parameter maps $a_N,b_N$ as functions of port count $N$ and antenna size $W$, and provides closed-form OP and EC under Rayleigh fading. To improve accuracy, it extends to the generalized extreme value (GEV) distribution, estimating the shape parameter $\xi$ and corresponding location/scale parameters, with a practical rule $\tilde\xi=2\xi$ to relate the $|h_{ m FAS}|$ and $C=\ln(1+\bar{\gamma}|h_{ m FAS}|^2)$ fits. Simulation results show that the GEV-based framework achieves higher accuracy than the Gumbel model while maintaining low computational complexity compared to existing methods, making it a practical tool for evaluating FAS performance in realistic fading conditions. The approach enables fast, tractable performance analysis and offers insight into how port count and aperture size influence reliability via extreme-value modeling.

Abstract

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.

Figures (13)

• Figure 1: The flowchart of the Monte Carlo simulation process.
• Figure 2: The CDFs of $|h_{\rm FAS}|$ obtained from the Monte-Carlo simulations and the fitted Gumbel distribution under $N=10$ and $N=20$, respectively, for selected values of $W$.
• Figure 3: The Q-Q plot of the empirical distribution versus the fitted Gumbel distribution.
• Figure 4: The OPs of FAS obtained from Monte-Carlo simulations and the fitted Gumbel distribution versus the transmit SNR $\bar{\gamma}$ under $N=10$ and $N=20$, respectively, for selected values of $W$.
• Figure 5: The ECs of FAS obtained from Monte-Carlo simulations and the fitted Gumbel distribution versus the transmit SNR $\bar{\gamma}$ and the number of ports $N$, respectively.

Theorems & Definitions (11)

• Remark 1
• Lemma 1
• Lemma 2
• Lemma 3
• Remark 2
• Remark 3
• Lemma 4
• Theorem 1
• Theorem 2
• Theorem 3