Spectrum Sensing For Cognitive Radios Through Differential Entropy

In this work, we present a novel Goodness-of-Fit Test driven by differential entropy for spectrum sensing in cognitive radios, under three different noise models – Gaussian, Laplacian and mixture of Gaussians. We analyze the proposed detector under Gaussian noise which models the worst-case. We then analyze by considering the Laplacian noise process which has tails heavier than that of the Gaussian. We generalize the analysis considering the noise to be a mixture of Gaussians, which is often the case with noise and interference in communication systems. We analyze the performance under each of these cases for a large class of practically relevant fading channel models and primary signal models, with emphasis on low Signal-to-Noise ratio regimes. Towards this end, we derive closed form expressions for the distribution of the test statistic under the null hypothesis and the detection threshold that satisfies a constraint on the probability of false-alarm. Through Monte Carlo simulations, we demonstrate that our detection strategy outperforms an existing spectrum sensing technique based on order statistics.