Probability Density Function of Logarithmic Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power

摘要

In this work, we study the statistical properties of a parameter △, which is defined as the logarithmic ratio of the arithmetic mean to the geometric mean for the Nakagami-m fading power. This parameter is useful in studying the maximum-likelihood (ML) based estimation of the Nakagami m fading parameter. Closed-form expressions are derived for the moment generating function and the probability density function (PDF) of the parameter △. For large sample size, it is found that the PDF of the parameter △ can be well approximated by a two-parameter Gamma PDF. This approximation is validated by the Kolmogorov-Smirnov test.