# Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging
## 2 Gnlcsa
### Block Diagram of GNLCSA  
The blocks diagram of the proposed GNLCSA is shown in the Figure 3.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Coefficients** & **Value** \\ \hline \(A_{1}(q_{2},q_{3},q_{4},q_{5},X_{3},X_{4},X_{5})\) & \(0\) \\ \hline \(A_{2}(q_{2},q_{3},q_{4},q_{5},X_{3},X_{4},X_{5})\) & \(-\frac{\pi}{K_{\text{sinc}}-\text{sinc}}\) \\ \hline \(A_{3}(q_{2},q_{3},q_{4},q_{5},X_{3},X_{4},X_{5})\) & \(\frac{\pi(R_{0}+K_{\text{sinc}},X_{5})}{(K_{\text{sinc}}+\text{sinc})}\) \\ \hline \(A_{4}(q_{2},q_{3},q_{4},q_{5},X_{3},X_{4},X_{5})\) & \(\frac{\pi}{4(K_{\text{sinc}}+q_{3})}\big{(}4(K_{\text{LENWC}}+q_{2})(q_{4}+K_{ \text{ENWC}}^{2}X_{4})-\vartheta_{3}^{2}+2K_{\text{ENWC}}^{2}q_{3}X_{3}-K_{ \text{ENWC}}^{2}q_{2}X_{3}^{2}\big{)}\big{)}\) \\ \hline \(A_{5}(q_{2},q_{3},q_{4},q_{5},X_{3},X_{4},X_{5})\) & \(\frac{\pi}{4(K_{\text{sinc}}+q_{3})}\bigg{(}\begin{array}{c}4(K_{\text{LENWC} }+q_{2})^{2}(q_{3}+K_{\text{ENWC}}^{2}X_{5})+2\vartheta_{3}(q_{3}+K_{\text{ENWC }}X_{3})^{2}\\ +24(K_{\text{LENWC}}+q_{2})\bigg{(}\begin{array}{c}-q_{3}(q_{4}+K_{\text{ENWC }}^{2}X_{4})\\ +K_{\text{ENWC}}^{2}X_{3}(-q_{4}+K_{\text{ENWC}}^{2}t_{2}X_{4})\end{array} \bigg{)}+27K_{\text{LENWC}}^{2}X_{3}(q_{3}-K_{\text{ENWC}}^{2}t_{2}X_{3})^{2} \end{array}\bigg{)}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coefficients values in Equation (33).  
Figure 3: Block diagram of proposed generalized nonlinear chirp scaling (GNLCSA).  
The steps of the proposed algorithm for high-resolution highly squint SAR are as follows:  
1. A range FFT is used to transfer the raw data to the range frequency domain. The data is multiplied with the filter of LRWC to achieve the processing of \"equivalent broadside\" in range direction.
2. range IFFT is implemented to transfer the data after LRWC into the range time domain. The modified CSA proposed in [18; 21], is introduced to process the former high-resolution squint data, which has the advantages of eliminating the coupling between the range and azimuth dimensions and enhancing the focusing precision for the range dimension at any ratio of \(B_{r}/f_{0}\) (\(B_{r}\) is the bandwidth of the transmitting pulse).
3. The high order compensation filter is multiplied with the data after the processing of step 2. It reduces the deteriorations of focusing caused by the high order phase error.
4. A turbulent compensation filter is multiplied with the data after the processing of step 3 to achieve a coincident FM rate form of different slant range along the azimuth direction.
5. The MSR is implemented in the azimuth IFFT for the data after the processing of step 4. Then a nonlinear chirp scaling filter is applied to compensate the azimuth variance.
6. After the processing of the nonlinear chirp scaling, the MSR is also applied in the azimuth FFT for the data. The azimuth compression filter is used to achieve the focusing of the squint data. Then an IFFT is applied for the focusing data in the RD domain.
7. The geometric correction is applied in the final step to obtain images matching the geometry of the signal acquisition.