Abstract
In many applications such as multiuser radar communications and astrophysical imaging processing, the encountered noise is usually described by the finite sum of -stable variables. In this paper, a new parameter estimator is developed, in the presence of this new heavy-tailed noise. Since the closed-form PDF of the -stable variable does not exist except and , we take the sum of the Cauchy () and Gaussian () noise as an example, namely, additive Cauchy-Gaussian (ACG) noise. The probability density function (PDF) of the mixed random variable, can be calculated by the convolution of the Cauchy's PDF and Gaussian's PDF. Because of the complicated integral in the PDF expression of the ACG noise, traditional estimators, e.g., maximum likelihood, are analytically not tractable. To obtain the optimal estimates, a new robust frequency estimator is devised by employing the Metropolis-Hastings (M-H) algorithm. Meanwhile, to guarantee the fast convergence of the M-H chain, a new proposal covariance criterion is also devised, where the batch of previous samples are utilized to iteratively update the proposal covariance in each sampling process. Computer simulations are carried out to indicate the superiority of the developed scheme, when compared with several conventional estimators and the Cramér-Rao lower bound.
Highlights
Heavy-tailed noise is commonly encountered in a variety of area such as wireless communication and image processing [1,2,3,4,5,6,7,8]
Typical models of impulsive noise are α-stable, Student’s t and generalized Gaussian distributions [9,10,11,12], which cannot represent all kinds of the noise types in the real-world applications
The density parameters of additive Cauchy-Gaussian (ACG) noise are set to γ = 0.05 and σ 2 = 0.5
Summary
Heavy-tailed noise is commonly encountered in a variety of area such as wireless communication and image processing [1,2,3,4,5,6,7,8]. Typical models of impulsive noise are α-stable, Student’s t and generalized Gaussian distributions [9,10,11,12], which cannot represent all kinds of the noise types in the real-world applications. CMC, 2022, vol., no.1 the weighted sum of the corresponding components’ PDF. These mixture models still cannot describe all impulsive noise types, especially for the case where the interference is caused by both channel and device. In astrophysical imaging processing [15], the observation noise is modelled as the sum of a symmetric α-stable (SαS) and a Gaussian noise, caused by the radiation from galaxies and the satellite antenna, respectively. A new description of the mixture impulsive noise model is proposed, referring to as the sum of SαS and Gaussian random variables in time domain
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