Maximum-Likelihood Based Estimation of the

Abstract— Maximum-likelihood estimation of the Nakagamiparameter is considered. Two new estimators are proposed and ex-amined. The sample mean and the sample variance of the new es-timators are compared with the best reported estimator. The newestimators offer superior performance.Index Terms— Fading channels, multipath fading, parameter es-timation. I. I NTRODUCTION E XTENSIVE empirical measurements have confirmed theusefulness of the Nakagami- distribution for modelingradio links [1], [2]. The probability density function (PDF) ofthe Nakagami- distribution is given by [1](1)where is the second moment, i.e., , and theparameter, also known as the fading figure, is defined as(2)The Nakagami- distribution covers a wide range of fadingconditions; when , it is a one-sided Gaussian distri-bution and when , it is a Rayleigh distribution. In thelimit as approaches infinity, the channel becomes static, anditscorrespondingPDFbecomesanimpulsivefunctionlocatedat. The th moment of the Nakagami- distribution is givenby(3)where is the standard Gamma function.In order to use the Nakagami- distribution to model a givensetofempiricaldata,onemustdetermine,orestimate,thefadingfigure from the data. Knowledge of the parameter is alsorequired by the receiver for optimal reception of signals in Nak-agami fading [3]. Estimators of the parameter have been pro-