Certified Outage Dimensioning of Fluid Antenna Receivers: Required SNR, Aperture, and Port Count

Abstract: We study the SNR, aperture, and port count needed to meet a target outage in a single-user downlink with a fixed transmit antenna and a single-RF fluid antenna receiver. For known spatially correlated Rayleigh channels and ideal port selection, a sampling-free residual certificate controls reduced-rank outage error over a continuous SNR interval. Positive Bessel features support large arrays, and bounded importance sampling converts the certificate into simultaneous design intervals. At 1 bit/s/Hz and outage $10<sup>{-5}$, a four-wavelength, ten-port receiver requires 4.40--4.55 dB. Reducing its port count from 256 to ten costs 0.70--1.25 dB under a joint 95\% probability statement. At 3.5 wavelengths, ten ports require 4.90--5.05 dB. Integer-port screening across 3--8 dB shows how aperture and port requirements change with available SNR; an effective-SNR transformation extends these decisions to other rates. The reported intervals include model and sampling uncertainty under checked Gaussian covariance inputs. A constructive slow-growth rank bound and a 16--1024-port study support compact evaluation as port count grows.