Approximation of the central Chi-square distributions for on-line computation of the false alarm probability for energy detector

Lesnikov, V.A.; Chastikov, A.V.; Naumovich, T.V.; Dubovcev, D.V.

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Approximation of the central Chi-square distributions for on-line computation of the false alarm probability for energy detector

Authors

Date of publication

2016

Abstract

Despite the simplicity of the energy detector, its use in cognitive radio systems is limited by the need of a priori information about the noise level. In the absence of such information it is necessary various ways to estimate the variance of the noise and recalculate the detection threshold on false alarm. The statistics compared to a threshold in the absence of a signal has the central chi-square distribution. For on-line calculation of the threshold using this distribution is straightforward, it is therefore of interest to approximate the distribution of Chi-square.
This paper describes the next approximations:
• Normal approximations:
o Simple normal approximation [9], [10],
o Fisher approximation [12],
o Wilson and Hilferty approximations [14],
o Kelley approximation [11],
o Hawkins and Wixley approximation [15],
o Peizer and Pratt approximation [16],
o Canal approximation [17],
• Log-normal approximation [18].
The assessment of accuracy of the considered types of approximation is presented.

Keywords

Cognitive radio, energy detector, false alarm probability, central Chi-square distributions.

Library reference

Lesnikov V.A., Chastikov A.V., Naumovich T.V., Dubovcev D.V. Approximation of the central Chi-square distributions for on-line computation of the false alarm probability for energy detector // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part 1. P. 230-235.

URL of paper

http://www.mes-conference.ru/data/year2016/pdf/D177.pdf