## 2 Background
### Generalized Pareto Distribution Model  
The generalized Pareto distribution is a kind of composite Gaussian model, which is widely used in the statistical modeling of sea clutter data of high-resolution sea-going radar [30]. The composite Gaussian model is formed by a random process modulating an independent distribution, which can be expressed as the result of the slow-varying structural component \(\tau\) modulating the fast-varying scattering component \(\mu\). In the study of the backscattering mechanism at the sea surface [31], it is known that the structural component is formed by the large-scale steep wave crests and white caps in the sea surface structure, while the scattering component is mainly composed of the small-scale tension waves and surges at the sea surface. The mathematical form of the above stochastic process is as follows:  
\[c(t)=\sqrt{\tau(t)}\mu(t),\qquad t=1,2,\cdots \tag{1}\]  
where the scattered component \(\mu\) is a complex Gaussian random variable with zero mean and unit covariance, the structural component \(\tau\) is a positive random process obeying the inverse gamma distribution, i.e., \(1/\tau\) satisfies the gamma distribution, and the probability density function is defined as  
\[f_{\tau}(\tau;a,b)=\frac{1}{b^{a}\Gamma(a)}\tau^{-(a+1)}e^{-\frac{1}{b\tau}} \tag{2}\]  
where \(a\) is the shape parameter, reflecting the dragging degree of the statistical distribution of sea clutter data, the larger the shape parameter \(a\), the more obvious the dragging phenomenon; \(b\) is the scale parameter, characterizing the intensity level of the echo signal. According to the product form of two random processes in Equation (1), the amplitude probability density function (PDF) of the generalized Pareto distribution can be deduced as  
\[f_{x}(x)=\int_{0}^{\infty}f_{\tau}(\tau;a,b)f_{\mu}(x|\tau)\mathrm{d}\tau \tag{3}\]where \(f_{\tau}(x|\tau)\) is the PDF of the scattered component \(\mu\), which has the following mathematical expression:  
\[f_{u}(x|\tau)=\frac{2x}{\tau}e^{\frac{-x^{2}}{\tau}} \tag{4}\]  
Substituting Equations (2) and (4) into Equation (3) above, the following generalized Pareto distribution magnitude PDF derivation can be obtained:  
\[\begin{array}{rl}f_{x}(x)&=\int_{0}^{\infty}\frac{1}{b^{a}\Gamma(a)}\,r^{-( a+1)}e^{-\frac{1}{1\tau}}\frac{2x}{\tau}e^{\frac{-x^{2}}{\tau}}\text{d}\tau\\ &=\frac{2 xb}{\left(1+bx^{2}\right)^{a+1}\Gamma(a)}\int_{0}^{\infty}y^{a}e^{-y} \text{d}y\\ &\qquad\qquad=\frac{2 xab}{\left(1+bx^{2}\right)^{a+1}}\end{array} \tag{5}\]  
where the variable \(x\) is replaced by \(y=\left(1+bx^{2}\right)/b\tau\). In addition, when the structural component in Equation (3) is in the form of an exponential distribution, the intensity distribution of the generalized Pareto distribution can be deduced as  
\[p(x)=\frac{ab}{\left(1+bx\right)^{\left(a+1\right)}} \tag{6}\]  
From the above Equation (5), it can be seen that the amplitude PDF of the generalized Pareto distribution approximates the Rayleigh distribution when the shape parameter \(a\rightarrow\infty\), and the sea clutter amplitude trailing phenomenon is gradually aggravated when \(a\to 0\). The fixed scale parameter \(b\), the variation of the amplitude PDF curve of the generalized Pareto distribution with the shape parameter \(a\), is shown in Figure 1. As can be seen from Figure 1, when the scale parameter \(b\) is fixed to 1.5, the wave crest of the amplitude PDF curve of the generalized Pareto distribution increases with the increase in the shape parameter, the wave crest gradually moves in the direction of smaller amplitude, and the trailing becomes shorter.