Quickest Eigenvalue-Based Spectrum Sensing using Random Matrix Theory

TL;DR

This paper explores eigenvalue-based spectrum sensing methods using random matrix theory, deriving analytical detection formulas and proposing quickest detection algorithms for improved primary user detection in cognitive radio networks.

Contribution

It introduces new eigenvalue-based quickest detection algorithms and provides analytical expressions for their performance, advancing spectrum sensing techniques.

Findings

Analytical PDF of maximum-minimum eigenvalue for K=2 SUs.

Proposed CUSUM and GLR-based quickest detection algorithms.

Numerical results show faster detection with quickest detection methods.

Abstract

We investigate the potential of quickest detection based on the eigenvalues of the sample covariance matrix for spectrum sensing applications. A simple phase shift keying (PSK) model with additive white Gaussian noise (AWGN), with $1$ primary user (PU) and $K$ secondary users (SUs) is considered. Under both detection hypotheses $\mathcal{H}_0$ (noise only) and $\mathcal{H}_1$ (signal + noise) the eigenvalues of the sample covariance matrix follow Wishart distributions. For the case of $K = 2$ SUs, we derive an analytical formulation of the probability density function (PDF) of the maximum-minimum eigenvalue (MME) detector under $\mathcal{H}_1$. Utilizing results from the literature under $\mathcal{H}_0$, we investigate two detection schemes. First, we calculate the receiver operator characteristic (ROC) for MME block detector based on analytical results. Second, we introduce two eigenvalue-based quickest detection algorithms: a cumulative sum (CUSUM) algorithm, when the signal-to-noise ratio (SNR) of the PU signal is known and an algorithm using the generalized likelihood ratio, in case the SNR is unknown. Bounds on the mean time to false-alarm $\tau_\text{fa}$ and the mean time to detection $\tau_\text{d}$ are given for the CUSUM algorithm. Numerical simulations illustrate the potential advantages of the quickest detection approach over the block detection scheme.