On the Distribution of Matched Filtering with Continuous Aperture Arrays

TL;DR

This paper develops precise analytical models for the SNR distribution of continuous aperture arrays in correlated Rayleigh fading, enabling better performance evaluation and demonstrating their superiority over discrete arrays.

Contribution

It introduces accurate closed-form expressions for the SNR distribution of CAPAs in correlated Rayleigh environments using the Karhunen-Loeve expansion and hypoexponential approximation.

Findings

The derived models closely match simulation results.

CAPAs outperform discrete antenna arrays in the analyzed scenarios.

The approach improves accuracy over standard gamma approximations.

Abstract

Continuous aperture arrays (CAPAs) provide a theoretical upper bound on the performance of densely packed antenna arrays, but their analysis is limited by the lack of closed-form signal-to-noise ratio (SNR) distributions under realistic fading conditions. This paper derives accurate analytical expressions for the matched-filter SNR distribution of one-dimensional CAPAs in correlated Rayleigh environments under both the sinc and Jakes correlation models using the Karhunen-Loeve expansion. By applying a truncated hypoexponential model, we obtain accurate approximations for the probability density function and cumulative distribution function of the SNR that closely match simulations, including the outage probability region where precise characterization is critical. Compared to a standard gamma approximation, our approach provides significantly improved accuracy in this regime. Additionally, the CAPA system considered is shown to outperform discrete antenna arrays. The derived expressions enable tractable and accurate evaluation of CAPAs under practical channel models.