Statistics of phase difference and product magnitude of multi-look processed Gaussian signals

Abstract

The phase difference and the product of two complex Gaussian signals are important parameters in the study of interferometry and polarimetry. To reduce statistical variations, polarimetric and inteferometric radar systems adopted multi-look processing by averaging spatially in the complex interferogram. The statistical characteristics of these two parameters are different from those of the single-look processing. In this paper, we derive their probability density functions (PDFs), and establish their statistical properties. These PDFS are derived from the complex Wishart distribution. The procedures involve multiple integrations of special functions, thus yielding closed-form, easily computable solutions for the PDFs. The multi-look phase difference has a Gauss hypergeometric distribution, and the multi-look product distribution is shown to be a product of two modified Bessel functions. Experimental results using polarimetric synthetic aperture radar (SAR) data of forests indicate good agreement between computed histograms and theoretical distributions.