Eigenvalue-based cooperative spectrum sensing with finite samples/sensors

Abstract

Eigenvalue-based spectrum sensing techniques have drawn lots of attention recently. Research are mainly based on the asymptotic or limiting distributions of extreme eigenvalues, which require large numbers of samples and sensors. Here we probe into the question of what will happen when the sample size or number of sensors is small. Exploiting a recent result on multivariate analysis of variance, under the presence of primary user's signal, we give a new expression for the distribution of the largest eigenvalue of the sample covariance matrix. It turns out to be much more accurate than existing approximations under asymptotic or limiting assumptions. Noticing the connection between the Moment Generating Function of the distribution of the largest eigenvalue and the certain form of Lauricella function, compact expressions for the Probability Density Function as well as Cumulative Distribution Function of largest eigenvalue of non-central Wishart matrix are given. These results are then applied to analyse the detection performance of our test. Simulations show the proposed method outperform other eigenvalue based spectrum sensing techniques for finite number of samples and sensors.