Abstract
This letter presents a theoretical analysis of the impact of thermal noise on the statistics of the classical as well as a modified estimator for the cross-correlation coefficient between two receive channels, which follow a noisy compound clutter model. This correlation coefficient, in the synthetic aperture radar (SAR) context often called coherence, is widely used as an important quality parameter in the field of SAR interferometry, SAR change detection, and SAR ground moving target indication. Based on a novel closed-form expressions for the probability density function (pdf) for integer number of averaged samples (or looks), it is shown that, contrary to widespread belief, the clutter texture does not cancel out when the noise contribution is taken into account. It is further demonstrated that the new pdfs can be used to derive the bias and variance of the sample coherence in analytical closed form. Thereby, the impact of the texture on the estimators is analyzed.
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