Log-normal approximation of chi-square distributions for signal processing

Abstract

We investigate in this paper a Log-Normal approximation of X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> distributions. Our study is motivated by the analysis of ratios of random variables where both, Log-Normal and X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> distributions are involved. Such ratios appear, for instance, when dealing with an energy detector while only an imperfect knowledge of the noise level is available. In order to characterize the distribution of the ratio, an accurate approximation of the X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> distribution by a Log-Normal distribution would highly simplify this problem known to be analytically intractable otherwise.