On the Performance of Spectrum Sensing Algorithms using Multiple Antennas

TL;DR

This paper derives the asymptotic distributions of eigenvalues and condition numbers for spectrum sensing algorithms using multiple antennas, focusing on fixed small antenna numbers and large sample sizes, to improve detection performance analysis.

Contribution

It provides new asymptotic distribution results for eigenvalues and condition numbers with fixed small antenna counts, extending previous large-antenna assumptions.

Findings

Derived asymptotic distributions for fixed small K and large N.

Validated results with computer simulations.

Enhanced understanding of detection probabilities in practical scenarios.

Abstract

In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the test statistics of the EBD algorithms. Two EBD algorithms using sample covariance matrices are considered: maximum eigenvalue detection (MED) and condition number detection (CND). The earlier studies usually assume that the number of antennas (K) and the number of samples (N) are both large, thus random matrix theory (RMT) can be used to derive the asymptotic distributions of the maximum and minimum eigenvalues of the sample covariance matrices. While assuming the number of antennas being large simplifies the derivations, in practice, the number of antennas equipped at a single secondary user is usually small, say 2 or 3, and once designed, this antenna number is fixed. Thus in this paper, our objective is to derive the asymptotic distributions of the eigenvalues and condition numbers of the sample covariance matrices for any fixed K but large N, from which the probability of detection and probability of false alarm can be obtained. The proposed methodology can also be used to analyze the performance of other EBD algorithms. Finally, computer simulations are presented to validate the accuracy of the derived results.