Js. Lee et al., STATISTICS OF PHASE DIFFERENCE AND PRODUCT MAGNITUDE OF MULTI-LOOK PROCESSED GAUSSIAN SIGNALS, Waves in random media, 4(3), 1994, pp. 307-319
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.