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) |
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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 |