This paper investigates the performance of a singleuser fluid antenna system (FAS), by exploiting a class of elliptical copulas to describe the structure of dependency amongst the fluid antenna ports. By expressing 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 the 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 without complicated mathematical analysis. Numerical results show that increasing the fluid antenna size 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：本文利用一类椭圆型连接函数描述流体制天线端口间的依赖结构，研究了单用户流体制天线系统（FAS）的性能。通过将Jakes模型表示为高斯连接函数形式，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，我们首先基于多元正态分布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。随后，通过计算中断概率（OP）和延迟中断率（DOR）分析FAS性能。采用Spearman秩相关系数ρ和Kendall秩相关系数τ等常用秩相关度量，我们量化了相关任意衰落信道中的依赖程度，并展示了无需复杂数学分析即可使高斯连接函数与FAS中的Jakes模型精确关联的方法。数值结果表明：增大流体制天线尺寸可降低OP和DOR，但随着天线端口数增加系统性能趋于饱和。此外，研究结果指出，即使流体制天线尺寸较小，FAS相比传统单固定天线系统仍能提供更优性能。