Optimum CFAR detection against correlated K-distributed clutter

The K-distributed clutter can be described as the product model of a texture variable, representing the properties of the observed surface, times an exponential component, usually named speckle, representing the effect of the coherent radar sensor. The performance of usual CFAR schemes for the detection of radar targets embedded in this clutter depends strictly on the algorithm used to select the detection threshold. In particular Watts (1985) pointed out that the exact knowledge of the texture value at each instant allows an ideal adaptive threshold to be set only on the speckle component. This selection, named `ideal CFAR´, is shown to widely outperform the fixed threshold detection scheme, especially for spiky clutter. The performance of the ideal CFAR defines an upper bound to the detection probability in K-distributed clutter, but it is purely theoretical since the knowledge of the texture variable is not available in practice. We derive two estimators of the local texture value on the basis of the echoes received from the N range cells closest to the cell under test and use the estimated texture value, instead of the exact one, to set the detection threshold. The performance is clearly highly dependent on the range correlation, which determines the texture estimation accuracy, and its analysis allows us to assess how far is the `ideal CFAR´ from the practical implementation in the different conditions