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.

翻译：本文通过采用一类椭圆Copula来描述流体天线位置（端口）之间的依赖结构，研究了单用户流体天线系统（FAS）的性能。通过将经典的Jakes模型表示为高斯Copula的形式，我们考虑两种情况：（i）一般情况，即任意相关衰落分布；（ii）特定情况，即相关Nakagami-$m$衰落。针对这两种场景，我们首先推导了等效信道的累积分布函数（CDF）和概率密度函数（PDF）的解析表达式，这些表达式以多元正态分布表示。随后，我们获得了中断概率（OP）和延迟中断率（DOR）以分析FAS的性能。通过采用常用的秩相关系数，如Spearman的$\rho$和Kendall的$\tau$，我们测量了相关任意衰落信道中的依赖程度，并阐明了高斯Copula如何能够精确地与FAS中的Jakes模型相关联。我们的数值结果表明，增加FAS的尺寸可以降低OP和DOR，但随着天线端口数量的增加，系统性能趋于饱和。此外，我们的结果表明，即使流体天线的尺寸较小，FAS也能提供比传统的单固定天线系统更好的性能。