Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices

TL;DR

This paper derives a more accurate limiting distribution for the eigenvalue ratio in Wishart matrices, improving cooperative spectrum sensing in cognitive radio by enhancing detection accuracy over previous asymptotic methods.

Contribution

It introduces a novel exact distribution for the eigenvalue ratio in Wishart matrices, leading to improved spectrum sensing performance in non-asymptotic scenarios.

Findings

Enhanced detection accuracy in spectrum sensing.

Better threshold calculation for false alarm control.

Significant performance gains over existing eigenvalue-based methods.

Abstract

Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. Most of such techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far in this field are based on asymptotical assumptions, due to the difficulties in characterizing the exact distribution of the eigenvalues ratio. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then straightforwardly applied to calculate the decision threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial performance improvement compared to the other eigenvalue-based algorithms.