Analytic Nakagami fading parameter estimation in dependent noise channel using copula
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Analytic Nakagami fading parameter estimation in dependent noise channel using copula Mohammad Hossein Gholizadeh1 , Hamidreza Amindavar1* and James A Ritcey2
Abstract In this paper, the probability density function (PDF) estimation is introduced in the framework of estimating the Nakagami fading parameter. This approach provides an analytic procedure for finding the fading parameter. Using the copula theory, an accurate PDF estimate is obtained even when the desired signal is corrupted in a noisy environment. In the real world, the noise samples could be highly dependent on the main signal. Copula-based models are a general set of statistical models defined for any multivariate random variable. Thus, they depict the statistical behavior of a received signal including two dependent terms, representative of the desired signal and noise. Previous works in the Nakagami parameter determination have mainly examined estimation based on either a noiseless sample model or an independent trivial noisy one. In this paper, we consider a more comprehensive situation about the noise destruction and our investigation is done in low signal-to-noise ratios. The parametric bootstrap method approves the accuracy of the analytically estimated PDF, and simulation results show that the new estimator has superior performance over conventional estimators. Keywords: Nakagami fading; PDF estimation; Dependent noise; Copula theory
1 Introduction The Nakagami-m distribution is considered as one of the most important models among all the statistical ones that have been proposed to characterize the fading envelope due to multipath fading in wireless communications [1]. With a simple exponential family form, the Nakagami-m distribution often leads to closed-form analytical results. The Nakagami fading exploits Nakagami probability density function (PDF) for the envelope of received signal which possesses two parameters: scale and shape parameters. The latter is more important and called the fading parameter or m-parameter. Determining m is a problem in Nakagami PDF estimation. The most prominent conventional procedures used for the estimation of the Nakagami fading parameter, m, are based on either maximum likelihood estimation or moment-based estimators [2,3]. Among *Correspondence: [email protected] 1 Amirkabir University of Technology, Department of Electrical Engineering, P.O. Box 15914, Tehran, Iran Full list of author information is available at the end of the article
maximum likelihood (ML)-based conventional methods, the Greenwood-Durand estimator is well known in mparameter estimation [4]. There are also analytic and bootstrap bias-corrected ML estimators for estimating m that improve conventional ML estimators [5]. On the other hand, the inverse normalized variance and generalized method of moments (GMM) are the moment-based procedures, in which the latter presents the Nakagami parameter estimation in noisy environment with acceptable performance [4]. However, all aforementioned approaches either do not take
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