Sigmoid Approximation to the Gaussian <i>Q</i>-function and its Applications to Spectrum Sensing Analysis



Lopez-Benitez, Miguel ORCID: 0000-0003-0526-6687 and Patel, Dhaval
(2019) Sigmoid Approximation to the Gaussian <i>Q</i>-function and its Applications to Spectrum Sensing Analysis. In: 2019 IEEE Wireless Communications and Networking Conference (WCNC), 2019-4-15 - 2019-4-18.

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Abstract

Most of the existing approximations for the Gaussian Q-function have been developed bearing in mind applications that require high estimation accuracy for large argument values (e.g., derivation of the bit/symbol error rates of digital communication systems, which are typically in the order of 10-6to 10-12). Such values correspond to positive arguments of the function and consequently most of the existing approximations are valid for positive arguments only. However, other relevant problems where the Gaussian Q-function can appear do not require such a level of accuracy (e.g., derivation of the detection probability of a signal detector, where accuracies of two or three decimal figures are sufficient) and, more importantly, require the evaluation of the Q-function over the whole range of values (i.e., both positive and negative arguments). In this context, this paper analyses a sigmoid approximation to the Q-function that provides adequate levels of accuracy for any real argument. As an illustrative example, this approximation is employed to obtain new closed-form expressions for the probability of detection of an energy detector under Rayleigh and Nakagami-m fading channels.

Item Type: Conference or Workshop Item (Unspecified)
Depositing User: Symplectic Admin
Date Deposited: 23 Jan 2019 15:58
Last Modified: 16 Oct 2023 22:46
DOI: 10.1109/wcnc.2019.8886061
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3031701