## 2 Methodology  
### Vi-Cfar  
VI-CFAR is an adaptive CFAR detector, and its calculation block diagram can be shown in Figure 1.  
In Figure 1, the homogeneous signal \(I\) and the orthogonal signal \(Q\) are processed by the envelope detector and stored in the samples \(X_{i}\), \(i=1\), \(2\),..., \(N\), in the leading window A and the lagging window B, respectively, sorted in ascending order. Based on the sample values in the leading window A and the lagging window B, the variability index (_VI_) and the mean ratio (_MR_) are calculated. By comparing _VI_ and _MR_ with threshold values, the current environmental type can be determined. Based on this determination, VI-CFAR selects different detection algorithms for target detection. The selected detection algorithm calculates the background clutter estimate \(T\cdot Z_{VI}\), and the threshold coefficient \(T\) is determined based on the false alarm probability (\(P_{FA}\)). If \(X_{0}\) is greater than or equal to \(T\cdot Z_{VI}\), it indicates the presence of a target. Conversely, if \(X_{0}\) is less than \(T\cdot Z_{VI}\), it indicates no target. The _VI_ is a second-order statistic and its value is jointly determined by the overall mean and the overall variance. For a reference window, _VI_ can be calculated as:  
\[VI=1+\frac{\phi^{2}}{\hat{\mu}^{2}}=1+\frac{1}{n-1}\cdot\sum\frac{\left(X_{i} -\overline{X}\right)^{2}}{\left(\overline{X}\right)^{2}} \tag{1}\]  
where, \(n=N/2\), and \(\overline{X}\) is the arithmetic mean of \(n\) cell samples in the reference window. The variability index \(VI_{A}\) of the leading window and the variability index \(VI_{B}\) of the lagging window are calculated, respectively. The homogeneity of the background environments in the leading window or the lagging window is assessed by the hypothesis testing in (2):  
\[\left\{ \begin{array}{l}VI\leq K_{VI}\Rightarrow Nonvariable\\ VI>K_{VI}\Rightarrow Variable\end{array} \right. \tag{2}\]  
Figure 1: Calculation block diagram of VI-CFAR. where, \(K_{VI}\) is a threshold. If the test result is nonvariable, it indicates that there is no interference target in the reference window. In contrast, if the test result is variable, it indicates the existence of interference targets in the reference window. The \(MR\) is the sample mean ratio between the leading window and the lagging window, and it can be calculated as:  
\[MR=\frac{\overline{X_{A}}}{\overline{X_{B}}}=\frac{\sum_{i\leq S}X_{i}}{\sum_{ i\leq B}X_{i}} \tag{3}\]  
Whether sample means of reference cells in the leading window and the lagging window are the same, is determined using (4):  
\[\left\{ \begin{array}{l}K_{MR}^{-1}\leq MR\leq K_{MR}\Rightarrow\textit{ Same Means}\\ MR<K_{MR}^{-1}\textit{ or }MR>K_{MR}\Rightarrow\textit{Different Means}\end{array} \right. \tag{4}\]  
where, \(K_{VI}\) is a threshold. If the test result is the same, it indicates that the clutter levels in the leading window and the lagging window are the same. In contrast, if the test result is different, it indicates that the clutter levels in the leading window and the lagging window are different. Algorithm selection rules of VI-CFAR are given in Table 1.  
In Table 1, \(T_{N}\) and \(T_{n}\), respectively, represent the threshold coefficient of the entire sliding window and the half sliding window. From Table 1, the adaptability of VI-CFAR is effectively improved by using different detection algorithms in different background environments. However, in VI-CFAR, homogeneous environments and multiple-target environments are frequently misjudged as clutter edge environments, and the detection performance of the GO algorithm is sensitive to the background environment. Therefore, the use of the GO algorithm in a clutter edge environment may potentially reduce the detection performance of VI-CFAR. In addition, the detection performance of CA and SO algorithms in a multiple-target environment is not satisfactory, which will further reduce the detection performance of VI-CFAR. For this, an improved VI-CFAR is proposed.