STATISTICS OF PHASE DIFFERENCE AND PRODUCT MAGNITUDE OF MULTI-LOOK PROCESSED GAUSSIAN SIGNALS

The phase difference and the product of two complex Gaussian signals a re important parameters in the study of interferometry and polarimetry . To reduce statistical variations, polarimetric and inteferometric ra dar systems adopted multi-look processing by averaging spatially in th e 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 th e complex Wishart distribution. The procedures involve multiple integr ations of special functions, thus yielding closed-form, easily computa ble solutions for the PDFS. The multi-look phase difference has a Gaus s hypergeometric distribution, and the multi-look product distribution is shown to be a product of two modified Bessel functions. Experiment al results using polarimetric synthetic aperture radar (SAR) data of f orests indicate good agreement between computed histograms and theoret ical distributions.