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Journal of Emerging Trends in Computing and Information Sciences >> Call for Papers Vol. 8 No. 3, March 2017

Journal of Emerging Trends in Computing and Information Sciences

On the Performance of “Improved” Energy Detector for Random Signals in Gaussian Noise

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Author O. Olabiyi, A. Annamalai
ISSN 2079-8407
On Pages 584-590
Volume No. 4
Issue No. 6
Issue Date July 01, 2013
Publishing Date July 01, 2013
Keywords Energy detector, detection probability, false alarm probability, spectrum sensing


Abstract

This article shows that the non-coherent detector for random signals which maximizes the generalized likelihood function is the same as the detector that maximizes the probability of correct detection at any specified false alarm probability by deriving the exact statistics for |Y|°(where Y is a Gaussian random variable and p is a positive real number) for the following two cases: (i) sample size L = 1 but for arbitrary real p > 0; (ii) arbitrary L but for p = 1, 2 or 4. This observation is in stark contrast to all earlier studies on the “improved” energy detector (that replaces the squaring operation of the signal amplitude in the classical energy detector with an arbitrary positive power p operation). Our analytical results are in excellent agreement with those obtained via Monte-Carlo simulations, and also highlight the inaccuracies with the Gamma density approximation for |Y|° employed by Chen [2]. Since analytical characterization of the “improved” energy detector becomes very cumbersome for other real values of p when L > 1, we also resort to the Monte-Carlo simulation technique to investigate those cases. Although different choices of p and L will yield distinct receiver operating characteristics (ROC) curves, the optimum p remains 2 (i.e., no gain over the classical energy detector) regardless of the values of the signal-to-noise ratio and/or the sample size L.
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