I. Introduction
When a radar system illuminates a large area of the sea, the probability density function (pdf) of the amplitude of the returned signal is well approximated by the Rayleigh distribution [1], i.e., the echo can be modeled as a complex-Gaussian process. That distribution is a good approximation. This can be proved theoretically by the central limit theorem, since the returned signal can be viewed as the sum of the reflection from a large number of randomly phased independent scatterers. However, in high-resolution and low-grazing-angle radar, the real clutter data show significant deviations from the complex Gaussian model, see [2], because only a small sea surface area is illuminated by the narrow radar beam. The behavior of the small patch is nonstationary [1] and the number of scatterers is random, see [3]. Due to the different waveform characteristics and generation mechanism, the sea surface wave, i.e., the roughness of the sea surface, is often modeled in two scales [4], [5]. To take into account different scales of roughness, a two-scale sea surface scattering model was developed, see [6]–[8]. In this two-scale model—a compound-Gaussian model—the fast-changing component, which accounts for local scattering, is referred to as speckle . It is assumed to be a stationary complex Gaussian process with zero mean. The slow-changing component, texture is used to describe the variation of the local power due to the tilting of the illuminated area, and it is modeled as a nonnegative real random process. The complex clutter can be written as the product of these two components $${\mmb e}(t)=\sqrt{u(t)}{\mmb\chi}(t).\eqno{\hbox{(1)}}$$The compound-Gaussian model is a model widely used to characterize the heavy-tailed clutter distributions in radar, especially sea clutter, see [2], [6], [9], and Section II. It belongs to the class of the spherically invariant random process (SIRP), see [10] and [17]. Note that the compound-Gaussian distribution is also often used to model speech waveforms and various radio propagation channel disturbance, see [10] and the references therein.