Differential Entropy Driven Spectrum Sensing Under Generalized Gaussian Noise

Abstract

We propose a novel goodness-of-fit detection scheme for spectrum sensing, based on differential entropy in the received observations. The noise distribution is known to deviate from the Gaussian in many practical communication settings. We, therefore, permit that the noise process follows the generalized Gaussian distribution, which subsumes Gaussian and Laplacian as special cases. We obtain, in closed form, the distribution of the test statistic under the null hypothesis and compute the detection threshold that satisfies a constraint on the probability of false alarm. Furthermore, we derive a lower bound on the probability of detection in a general scenario, using the entropy power inequality. Through Monte Carlo simulations, we show that for a class of practically relevant fading channel and primary signal models, especially in low SNR regime, our detector achieves a higher probability of detection than the energy detector and the order statistics-based detector. We also demonstrate that the adverse effect of noise variance uncertainty is much less with the proposed detector compared with that of the energy detector.