Statistics of the Polarimetric Weibull-Distributed Electromagnetic Wave

The statistical properties of partially polarized light in Gaussian stochastic plane wave fields have been reported in the literature. In this paper, we examine the statistics of the stochastic plane electromagnetic (EM) wave fields that are Weibull distributed. The polarimetric Weibull-distributed wave is characterized by three parameters: the sum of the intensities of the two electric vector components, the orientation angle that the major axis makes with the reference coordinate system, and the ratio of the minor to the major axis. The joint and marginal probability densities of these random variables are determined as a function of the covariance matrix. The main properties of this important distribution are shown. Then, the statistical properties of the normalized Stokes parameters are described in detail in Weibull-distributed stochastic fields. The joint and marginal probability density functions of the three components of the normalized Stokes parameters are presented. Numerical simulations are operated, which coincide with the theoretical derivations. Comparisons between Gaussian and Weibull stochastic fields have been made. The presented statistics of the Weibull polarimetric wave will be useful to random medium scattering and speckle filtering, which can also be extended to deal with the characterization of the scattering matrix elements in radar polarimetry.