How Many Independent Modes Does a Fluid Antenna Have? A Closed-Form Outage Analysis via Equivalent Degrees of Freedom

TL;DR

This paper introduces a novel eigenmode-based framework for analyzing outage probability in fluid antenna systems, revealing that spatial degrees of freedom depend on aperture size rather than port count.

Contribution

It establishes a spatial eigenmode limit for fluid antennas, derives closed-form outage approximations, and extends analysis to multi-user and planar configurations.

Findings

Spatial correlation matrix has at most 2⎡W⎤+1 significant eigenmodes.

The outage probability can be approximated by a closed-form expression based on these eigenmodes.

The proposed methods are asymptotically exact and never underestimate true outage probability.

Abstract

In a fluid antenna system (FAS), a single reconfigurable antenna is able to activate one of $N$ correlated ports to exploit spatial diversity. However, outage analysis is challenging because exact evaluation requires an $N$-dimensional multivariate integral, while existing closed-form approximations based on block-correlation models tend to underestimate the true outage probability. This paper shows that the spatial correlation matrix of a FAS with a normalized linear aperture length $W$ has at most $K^{*}=2\lceil W\rceil+1$ significant eigenmodes, regardless of the number of deployed ports. This is a spatial counterpart of the Slepian-Landau-Pollak spectral concentration theorem and reveals that the spatial degrees of freedom are determined by aperture size rather than port count. Motivated by this result, we derive an \emph{equivalent degree of freedom} (EDoF) approximation, under which the outage probability can be expressed in closed form as that of selection combining over $K^{*}$ independent branches. We propose a refined \emph{weighted independent modes} (WIM) approximation, to incorporate eigenvalue-dependent branch weights $\{\beta_k\}$ and yield a product-form closed-form expression with improved accuracy at moderate signal-to-noise ratio (SNR). Both approximations achieve the exact diversity order, become asymptotically exact at high SNR, and provably never underestimate the true outage probability by Anderson's inequality. The proposed framework is further extended to obtain closed-form expressions for ergodic capacity, characterize multi-user fluid antenna multiple access (FAMA) with explicit interference-limited outage floors. Besides, we analyze two-dimensional planar FAS, for which the diversity order scales multiplicatively with the aperture dimensions.