# Adaptive Clutter Intelligent Suppression Method Based on Deep Reinforcement Learning
## 3 MTI Filter Based on the Eigenvector Method  
It is usually assumed that the power spectrum of the clutter obeys a Gaussian distribution, \(f_{0}\) is the spectral center, \(\sigma_{f}\) is the spectral width, and its power spectrum is expressed as  
\[C(f)=\frac{1}{2\pi\sigma_{f}}\exp(-\frac{(f-f_{0})}{2\sigma_{f}^{2}}) \tag{4}\]  
According to Wiener filtering theory, clutter is usually regarded as a smooth random process, and its frequency domain suppression characteristics can be analyzed using the power spectral function. There is a Fourier transform relationship between the power spectral function and the autocorrelation function. Therefore, the clutter autocorrelation function is represented by the following Equation (5):  
\[r_{c}(m,n)=\int_{-\infty}^{+\infty}C(f)e^{\text{j}2\pi f(t_{m}-t_{n})}df=\int _{-\infty}^{+\infty}\frac{1}{2\pi\sigma_{f}}\exp(-\frac{(f-f_{0})}{2\sigma_{f }^{2}})e^{\text{j}2\pi f(t_{m}-t_{n})}df \tag{5}\]from equation \(\frac{1}{2\pi}\int_{-\infty}^{+\infty}e^{-ax^{2}}e^{\beta x}df=\frac{1}{\sqrt{2a}} \exp\frac{\zeta^{2}}{4a}\), we can derive Equation (6) as  
\[r_{c}(m,n)=e^{-2\pi^{2}c_{f}^{2}\tau_{nm}^{2}}e^{2\pi f_{0}\tau_{mn}} \tag{6}\]  
where \(\tau_{mn}=t_{m}-t_{n}\) is time-dependent. The power spectral center \(\hat{f}_{0}\) estimated based on FFT selection [24] and the spectral width \(\hat{\sigma}_{f}\) estimated based on integration method [24] are substituted into Equation (6), and the clutter autocorrelation matrix \(R_{c}\) is constructed according to the following Equation (7):  
\[\mathbf{R_{c}}= \begin{bmatrix}r_{c}(0,0)&r_{c}(0,1)&\cdots&r_{c}(0,N-1)\\ r_{c}(1,0)&r_{c}(1,1)&\cdots&r_{c}(1,N-1)\\ \vdots&\vdots&\ddots&\vdots\\ r_{c}(N-1,0)&r_{c}(N-1,1)&\cdots&r_{c}(N-1,N-1)\end{bmatrix}  \tag{7}\]  
from the eigenequation \(R_{c}w_{n}=\lambda_{n}w_{n}\), \(n=0,1,\cdots,N\), the eigenvalue decomposition of \(R_{c}\) is calculated to compute the eigenvalues and eigenvectors, where \(w_{n}\) is the eigenvector corresponding to the eigenvalue \(\lambda_{n}\). Ranking the eigenvalues \(\lambda_{n}\) in ascending order yields \(\lambda_{0}\leq\lambda_{1}\leq\cdots\lambda_{n}\). Article [18] proved that the eigenvector \(w_{0}\), corresponding to the smallest eigenvalue \(\lambda_{0}\) obtained by the eigenvalue decomposition of the clutter autocorrelation matrix, is the optimal weight coefficients \(W_{opt}=[w_{1},w_{2},\cdots,w_{m}]\) of the filter, and \(m\) is the filter orders; using the optimal weight coefficients \(W_{opt}\) obtained above to filter the echo data matrix, the output signal is expressed as  
\[\mathbf{Y_{ij}}=\mathbf{X}\cdot W_{opt}^{T} \tag{8}\]  
In the above Equation (8), \(\mathbf{X}=[x_{i,j},x_{(i+1),j},\cdots,x_{(i+m-1),j}]\) represents the echo sequence of successive \(m\) pulses from the \(i\)th pulse to the \(i+m-1\) pulse at the \(j\)th range cell of the echo data matrix; \(\mathbf{Y_{ij}}\) represents the filtered value of the radar echo data of the \(i\)th pulse, the \(j\)th range cell. According to the above analysis, the performance of the MTI filter based on the eigenvector method in the time domain is the clutter signal multiplied by the optimal weight coefficient \(W_{opt}\) to achieve clutter suppression. In the frequency domain, according to the spectrum characteristics of the clutter signal, the filter notch is in the center of the clutter frequency \(f_{0}\), and the notch width is \(\sigma_{f}\). The wider the spectral width of the clutter, the wider the width of the filter notch is designed, and the shallower the notch depth will be. The narrower the spectral width of the clutter, the narrower the width of the filter notch, and the deeper the notch depth will be. When the filter notch is consistent with the spectrum width of the clutter, the filtering effect is optimal, and the filter parameters are the optimal parameters for this range cell. In practical applications, the MTI filter based on the eigenvector method is highly dependent on the a priori knowledge of the clutter information.