A Gaussian Copula Approach to the Performance Analysis of Fluid Antenna Systems

TL;DR

This paper models the performance of fluid antenna systems using Gaussian copulas to describe dependence among antenna ports, deriving analytical performance metrics for correlated fading scenarios, and demonstrating performance improvements over fixed antennas.

Contribution

It introduces a Gaussian copula-based framework for analyzing fluid antenna systems, deriving new analytical expressions for performance metrics under correlated fading.

Findings

Increasing FAS size reduces outage probability and delay outage rate.

Performance saturates as the number of antenna ports grows large.

FAS outperforms conventional fixed antennas even at small sizes.

Abstract

This paper investigates the performance of a single-user fluid antenna system (FAS), by exploiting a class of elliptical copulas to describe the dependence structure amongst the fluid antenna positions (ports). By expressing the well-known Jakes' model in terms of the Gaussian copula, we consider two cases: (i) the general case, i.e., any arbitrary correlated fading distribution; and (ii) the specific case, i.e., correlated Nakagami-$m$ fading. For both scenarios, we first derive analytical expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the equivalent channel in terms of multivariate normal distribution. Then we obtain the outage probability (OP) and the delay outage rate (DOR) to analyze the performance of FAS. By employing the popular rank correlation coefficients such as Spearman's $\rho$ and Kendall's $\tau$ , we measure the degree of dependency in correlated arbitrary fading channels and illustrate how the Gaussian copula can be accurately connected to Jakes' model in FAS. Our numerical results demonstrate that increasing the size of FAS provides lower OP and DOR, but the system performance saturates as the number of antenna ports increases. In addition, our results indicate that FAS provides better performance compared to conventional single-fixed antenna systems even when the size of fluid antenna is small.