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

TL;DR

This work tackles the problem of modeling and analyzing fluid antenna system (FAS) performance under realistic spatial correlation among ports. It introduces a Gaussian copula framework that expresses Jakes' correlation as a copula parameter, enabling analytical derivation of the CDF/PDF of the maximum-port channel and closed-form outage-related metrics for arbitrary fading and for Nakagami-\(m\) fading. Key contributions include: (i) joint distributions and OP/DOR formulas expressed via multivariate normal CDFs; (ii) mapping between Gaussian-copula parameters and rank correlations (Spearman's ρ, Kendall's τ); (iii) Nakagami-\(m\) extensions with explicit CDF/PDF; and (iv) numerical results showing that increasing fluid antenna size \(W\) reduces OP and DOR while gains saturate with more ports, with FAS outperforming conventional SISO. The framework provides a tractable, accurate tool for designing FAS port layouts and sizing in 6G/URLLC contexts, balancing diversity gains against correlation-induced limits.

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 $ρ$ and Kendall's $τ$ , 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.

Figures (9)

• Figure 1: Exemplary illustration of FAS when the fluid antenna is implemented by reconfigurable pixels.
• Figure 2: Scatterplots describe the structure of dependency between two arbitrary correlated fading channels $|h_1|$ and $|h_2|$ with uniform marginal distributions $u_1$ and $u_2$ under Gaussian copula that includes correlation matrix $\mathbf{R}_{h_1,h_2}$.
• Figure 3: Scatterplots describe the structure of dependency between two correlated Nakagami-$m$ fading channels $|h_1|$ and $|h_2|$ when $m=1$ under: (a)--(d) Gaussian copula, and (e)--(h) Jakes' model.
• Figure 4: (a) CDF and (b) PDF of FAS for selected values of $K$ and $W$ when $m=3$ and $\mu=1$.
• Figure 5: OP versus average transmit SNR $\bar{\gamma}$ for selected values of $W$ and $K$ when $\gamma_\mathrm{th}=10$dB, $m=1$, and $\mu=1$.

Theorems & Definitions (25)

• Definition 1: $d$-dimensional copula
• Theorem 1: Sklar's theorem
• Definition 2: $d$-dimension Gaussian copula
• Theorem 2
• proof
• Theorem 3
• proof
• Remark 1
• Remark 2
• Remark 3