## 4 Performance Evaluation
### Real Data Experiment  
We utilize a set of sea clutter measured data with a range resolution of 60 m from the IPIX database in 1998, named \"19980204_223753_ANTSTEP.mat\", including 60,000 pulses and 28 range cells. We selected the 13 th range cell as the CUT, divided the data within it into 200 equally spaced segments, and used the histogram density estimation method to plot the empirical PDF and CDF curves of the real data. To verify the rationality of the selected measured data, we used the fractional moment estimation method (MoFM) [34; 35; 36] for the real data to calculate the parameters of three common compound-Gaussian distributions, namely, the shape parameters and scale parameters of K distribution, Pareto and CG-IG distributions, and plotted the amplitude PDF and CDF curves of the three compound-Gaussian distributions. Specifically, to reduce the error caused by abnormal samples, for K-distributed clutter, we use the first moment and the half-order moment of the clutter  
Figure 4: PD versus SCR without signal mismatch with simulated data for different \(v\). Figure 3: PD versus \(\cos^{2}\!\phi\) with signal mismatch with simulated data. SCR = 35 dB. samples for parameter estimation, which are denoted by \(\hat{m}_{1}\) and \(\hat{m}_{0,5}\), with the expressions as follows  
\[\left\{ \begin{array}{l}\hat{m}_{0,5}=\frac{\Gamma(1.25)\Gamma(v+0.25)}{\Gamma( v)}(2u)^{\frac{1}{2}}\\ \hat{m}_{1}=\frac{\Gamma(1.5)\Gamma(v+0.5)}{\Gamma(v)}(2u)\end{array} \right. \tag{47}\]  
where (47) serves as an implicit function of \(v\). It is worth mentioning that the gamma function is defined as \(\Gamma(z)=\int_{0}^{+\infty}t^{z-1}e^{-t}dt\). So we can eliminate \(u\), unfold, and simplify (47), learning that \(v\) has a unique solution. Next, we use the lookup table method or employ the \(fsolve(\cdot)\) function in MATLAB to find the solution. As shown in Figures 5 and 6, the K distribution provides a better fit to the real data. Figure 5: Compound-Gaussian distribution PDF fitting to empirical PDF of real data. Figure 6: Compound-Gaussian distribution CDF fitting to empirical CDF of real data. To further measure the fitting degree of the three compound-Gaussian distributions mentioned above to the real data, Kolmogorov-Smirnov (KS) distance is commonly used as a metric. In addition, we plot the fitting results of the clutter amplitude distribution of real data in Figure 7. Here, the vertical axis represents the \(1-\)CDF domain, which is equivalent to the meaning of the PFA [37]. As the PFA we set is \(10^{-2}\), we narrow the scope of the KS test to around \(10^{-2}\), and the corresponding expression of the KS distance can be written as  
\[KS(v,u;\hat{v},\hat{u})=\max_{r\in(2,5,4.5)}\left\{\left|\,F(r;v,u)-F(r;\hat{v},\hat{u})\right|\,\right\} \tag{48}\]  
where \(F(r;v,u)\) represents the empirical CDF obtained from the real data and \(F(r;\hat{v},\hat{u})\) represents the fitting CDF obtained through parameter estimation based on the selected distribution model. Table 1 indicates that the KS distance for the K distribution fit is 0.0011 for the PFA we set. As we know, a smaller KS distance indicates a better fit between the empirical CDF of clutter amplitude and the selected clutter model. So, we can draw a conclusion that the K distribution still offers a good fit. It is worth noting that using real data with good fitting results from the K distribution for experiments aims to correspond better with simulation experiments. In this paper, the power mismatch of the training samples obtained through iterative estimation does not need to consider the specific distribution of clutter. We set \(\text{PFA}=10^{-2}\) due to the limited availability of pulses in the real data, and selected the \((13-L/2,12)\) and \((14,13+L/2)\) range cells near the CUT as training samples. The other parameters are consistent with the simulation experiment.