Vine Copula-Based Outage Analysis for Fluid Antenna RIS-NOMA Systems Over Nakagami- m Fading Channels

Outage performance in multi-port fluid antenna (FA) systems is governed by the tail dependence between correlated ports, which Gaussian-copula models cannot capture. This paper derives semi-closed-form outage probability expressions for reconfigurable intelligent surface (RIS) assisted fluid antenna (FA) non-orthogonal multiple access (NOMA) downlink systems over Nakagami-mfading channels, using vine copula theory to capture the statistical dependence among correlated FA ports. The existing literature approximates the joint distribution of port gains via a scalar Gaussian copula, which has zero tail dependence and significantly underestimates outage probability in severe-fading regimes (mm/Rayleigh channel, and the vine cumulative distribution function (CDF) is evaluated efficiently via Gauss–Hermite quadrature. It is proved that the vine copula achieves the full diversity order at high signal-to-noise ratio (SNR), whereas the Gaussian copula exhibits a diversity shortfall due to its zero lower tail dependence. A closed-form bound on the Gaussian copula approximation error is also derived that explicitly identifies the parameter regimes where the correction is essential. Monte Carlo (106i.i.d. samples) and quasi-Monte Carlo (220Sobol points) results validate the outage probability expressions, with up to 3.8 dB SNR error from the Gaussian copula atPout= 10−3form= 0.5,L= 30,W= 2. The C-vine is further benchmarked against Frank- and Joe-based PCCs, an asymptotic high-SNR diversity slope is quantified under standard parametric assumptions, and fluid antennas are contrasted against an idealisedL-port selection-combining upper bound over i.i.d. Nakagami branches, providing actionable design guidelines. The framework extends naturally toE-user NOMA systems.