Dimensional Scaling Laws for Continuous Fluid Antenna Systems

TL;DR

This paper derives asymptotic formulas and scaling laws for the high SNR probability in continuous fluid antenna systems across multiple dimensions, enhancing understanding of their performance in Rayleigh fading channels.

Contribution

It introduces a comprehensive analysis of CFAS in multi-dimensional spaces with spatial correlation, providing exact formulas and scaling laws for high SNR performance.

Findings

Closed-form formulas for high SNR probability in CFAS

Scaling laws for performance improvement with dimensions

Optimal CFAS dimensions for maximizing SNR

Abstract

Consider the signal-to-noise ratio (SNR) of a continuous fluid antenna system (CFAS) operating over a Rayleigh fading channel. In this paper, we extend traditional system assumptions and consider spatially coherent isotropic correlation, continuous positioning of the antenna rather than discrete, and the use of multi-dimensional space (1D, 2D and 3D). By focusing on the upper tail of the received SNR distribution (the high SNR probability (HSP)), we are able to derive asymptotically exact closed-form formulas for the HSP. Finally, these results lead to scaling laws which describe the increase in the HSP as we employ more dimensions and the optimal CFAS dimensions.