On Statistics of Log-Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power

Ning WANG  Julian CHENG  Chintha TELLAMBURA  

IEICE TRANSACTIONS on Communications   Vol.E95-B   No.2   pp.647-650
Publication Date: 2012/02/01
Online ISSN: 1745-1345
DOI: 10.1587/transcom.E95.B.647
Print ISSN: 0916-8516
Type of Manuscript: LETTER
Category: Wireless Communication Technologies
Gamma distribution,  maximum likelihood,  moment generating function,  Nakagami m parameter estimation,  

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To assess the performance of maximum-likelihood (ML) based Nakagami m parameter estimators, current methods rely on Monte Carlo simulation. In order to enable the analytical performance evaluation of ML-based m parameter estimators, we study the statistical properties of a parameter Δ, which is defined as the log-ratio of the arithmetic mean to the geometric mean for Nakagami-m fading power. Closed-form expressions are derived for the probability density function (PDF) of Δ. It is found that for large sample size, the PDF of Δ can be well approximated by a two-parameter Gamma PDF.