An Improved and More Accurate Expression for a PDF Related to Eigenvalue-Based Spectrum Sensing

TL;DR

This paper introduces a more precise integral expression for the probability density function of the eigenvalue ratio used in cooperative spectrum sensing, improving detection accuracy by removing previous independence assumptions.

Contribution

It derives an improved, more accurate integral solution for the eigenvalue ratio's PDF, advancing the theoretical foundation of eigenvalue-based spectrum sensing.

Findings

Enhanced detection performance in spectrum sensing

More accurate probability density function expression

Removes incorrect independence assumption

Abstract

Cooperative spectrum sensing based on the limiting eigenvalue ratio of the covariance matrix offers superior detection performance and overcomes the noise uncertainty problem. While an exact expression exists, it is complex and multiple useful approximate expressions have been published in the literature. An improved, more accurate, integral solution for the probability density function of the ratio is derived using order statistical analysis to remove the simplifying, but incorrect, independence assumption. Thereby, the letter makes an advance in the rigorous theory of eigenvalue-based spectrum sensing.