Differential Entropy Driven Goodness-of-Fit Test for Spectrum Sensing

Abstract

We present a novel Goodness-of-Fit Test driven by differential entropy for spectrum sensing in cognitive radios. When the noise-only observations are Gaussian, it exploits the fact that the differential entropy of the Gaussian attains its maximum. We obtain in closed form the distribution of the test statistic under the null hypothesis and the detection threshold that satisfies a constraint on the probability of false-alarm using the Neyman-Pearson approach. Later, we discuss the use of this technique to the case of the noise process modeled as a mixture Gaussians. Through Monte Carlo simulations, we demonstrate that our detection strategy outperforms the existing technique in the literature which employs an order statistics based detector for a large class of practically relevant fading channel models and primary signal models, especially in the low Signal-to-Noise Ratio regime.