# ISAR Imaging Analysis of Complex Aerial Targets Based on Deep Learning
## 2 ISAR Model  
### Principles of Electromagnetic Analysis  
In the study of scattering characteristics of complex air targets, the scattering center refers to the region on the target that produces the main scattering effect on electromagnetic waves [15]. Key elements for describing the scattering center include its position, amplitude and geometric type. These elements are essential for accurately understanding and predicting the scattering behavior of a target. Currently, methods for determining the scattering center are mainly divided into two categories: non-parametric methods and parametric methods. The non-parametric method primarily relies on Fourier analysis, which extracts relevant information about the scattering center by analyzing the spectral characteristics of the target's scattered signal. This method does not require a predefined model of the scattering center; rather, it identifies the existence and characteristics of the scattering center through data analysis. In contrast, the parameter method is a model-based parameter estimation technique that typically necessitates defining the scattering center model in advance. It estimates the model parameters through optimization algorithms to ascertain the location, amplitude and geometric type of the scattering center. While this approach generally demands more prior knowledge and computational resources, it offers the advantage of providing a more accurate description of the scattering center. Through theoretical calculation and experimental verification, the total electromagnetic scattering of complex targets can be attributed to a series of local scattering sources. These local scattering sources, known as equivalent multiple scattering centers (EMscs), are one of the core elements of a target's scattering characteristics. The translational component is that the target attitude remains unchanged relative to the radar ray, while the rotational component is that the target rotates around a certain reference point. By compensating for the translational component, the target can be equivalent to a planar turntable model, and then the two-dimensional image of the target can be obtained by using the Doppler effect and signal processing techniques. The plane wave takes the frequency \(f\) as the irradiation target and the incidence angle \(\theta\) as the irradiation target. The expression of the function \(g(x,y;k,\theta)\) that defines the two-dimensional scattering image of the target is as follows:  
\[E_{s}(x,y;k)=E_{i}(x,y;k)\frac{\exp(j2\pi ft-j2 kR(t))}{R(t)}g(x,y;k,\theta) \tag{1}\]  
where: \(E_{s}\)--backscattered electric field,  
\(E_{i}\)--incident electric field;  
\(R(t)\)--Distance from radar to target  
\(\theta\)--beam, \(k=2\pi/\lambda=2\pi f/C\)  
\(g(x,y;k,\theta)\) represents the two-dimensional scattering center distribution of the target, i.e., the two-dimensional scattering image, which is not only about the coordinate relationship of \((x,y)\), but also includes the function of radar frequency \(f\) and incidence angle \(\theta\). The scattering characteristics can be equivalently regarded as the vector superposition of the backward scattering from \(p\) scattering centers:  
\[g(k,\theta)=\sum\limits_{i=1}^{p}A_{i}(k,\theta)\cdot\exp(-j2\pi ft_{i}) \tag{2}\]  
where \(A_{i}(k,\theta)\) is the backscatter intensity of the \(i\) th scattering center, and \(t_{i}\) is twice the time delay from the \(i\) th scattering center to the rotation center \(O\), namely:  
\[t_{i}=2(x_{i},\sin\theta+y_{i}\cos\theta)/C \tag{3}\]  
Substitute the above formula into Formula (2) to obtain the following:  
\[ \begin{array}{l}g(k,\theta)=\sum\limits_{i=1}^{p}A_{i}(k,\theta)\exp(-j4\pi( x_{i}f\sin\theta+y_{i}f\cos\theta)/C)\\ =\sum\limits_{i=1}^{p}A_{i}(k,\theta)\exp\left[-2j(x_{i}k_{x}+y_{i}k_{y})\right] \end{array}  \tag{4}\]  
where \(k_{x}=\frac{2\pi f}{C}\sin\theta\), \(k_{y}=\frac{2\pi f}{C}\cos\theta\).