Further results on the performance of energy detector over generalized fading channels

Abstract

Cognitive radio network requires an efficient and effective means of detecting holes in the spectrum. Energy detection is one of the solutions that have been proposed for enabling opportunistic spectrum access. In this article, we present yet other simplified unified approaches to the analysis of performance of the energy detector under different fading channels. One is based on the k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order derivative of the moment generating function (MGF) of the fading channel and the other is based on the kth moment of the output SNR of the receiver of energy detector. Both methods are derivatives of two complementary alternative series representations of Marcum-Q function using the Laguerre polynomial recently developed by [12]. Due to its faster rate of convergence, we employ the form with kth derivative of MGF of SNR of fade distribution in our computational analysis. However, the same proposed framework is easily applicable to the form requiring k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> moment of SNR of fading channel. The method presented is applicable to common multipath fade distribution (e.g., Rayleigh, Rice and Nakagami-m channels) and composite multipath/shadowing fade distribution. It also has the capability of providing results for fractional fading index, m and half-integer time-bandwidth product, u. Selected numerical results are also provided for the receiver operating characteristics (ROC) of single channel, MRC and SLC diversity energy detectors over Rice channels.