# MIMO Radar Imaging Method with Non-Orthogonal Waveforms Based on Deep Learning
## 3 Imaging Method of Non-Orthogonal Waveform MIMO Radar Based on Deep Learning
### Training Data Generation  
In order to train the above MIMO-LI-Net, sufficient training samples need to be generated. Considering that it is difficult to obtain a large number of MIMO radar measured data in practice, this paper constructs a training data set from simulation data. It can be seen from Figure 2 that the training data include the MIMO radar target echo and the ideal target image. For the MIMO radar target echo, this paper generates the simulated MIMO radar target echo based on the parameterized attribute scattering center model and MIMO radar echo signal model in Section 2.1. For a multi-scattering center target, its frequency domain echo at the \(n\)th receiver of the MIMO radar can be generated by the following formula  
\[\boldsymbol{y}_{n}=\sum_{m}\sum_{q}\boldsymbol{e}_{q,m,n}\cdot\boldsymbol{ \varphi}_{m} \tag{9}\]  
where \(\boldsymbol{y}_{n}\) is the vector composed of echoes in different frequencies, \(\boldsymbol{\varphi}_{m}\) is the vector form of the transmission waveform \(\varphi_{m}(t)\) in the frequency domain, \(\boldsymbol{e}_{q,m,n}\) is the frequency-related vector composed of the scattering field generated by the \(q\)th scattering center in the \(m\)th transmitting and \(n\)th receiving channel, and \(\cdot\) denotes the point-to-point multiplication between two vectors. Considering the centralized MIMO imaging scene, the scattering center has stable scattering characteristics within the observation angle range of the MIMO array, and according to the attribute scattering center model [33], \(\boldsymbol{e}_{q,m,n}\) can be generated by the following formula  
\[\boldsymbol{e}_{q,m,n}=\sigma_{q}\left(1j\frac{\boldsymbol{f}}{f_{c}}\right)^{ a_{q}}\cdot\sin c\left(\frac{2\pi\boldsymbol{f}}{c}L_{q}\sin\left(\varphi_{q,m,n}- \overline{\varphi}_{q}\right)\right)\cdot\exp\left(-2\pi\boldsymbol{f}\gamma _{q}\sin\phi_{q,m,n}\right)\cdot\exp\left(1j\frac{4\pi\boldsymbol{f}}{c} \Delta R_{q,m,n}\right) \tag{10}\]  
where \(\boldsymbol{f}\) is a vector that contains all the frequency points of echoes, \(f_{c}\) is the center frequency, and \(\phi_{q,m,n}\) is the azimuth angle between the \(q\)th scattering center and the equivalent transceiver of the \(m\)th transmitter and \(n\)th receiver. \(\Delta R_{q,m,n}\) is the sum of the wave path from the \(q\)th scattering center to the \(m\)th transmitter and \(n\)th receiver. \(\left\{\sigma_{q},\boldsymbol{a}_{q},L_{q},\overline{\varphi}_{q},\gamma_{q}\right\}\) is the parameter related to the \(q\)th scattering center: \(\sigma_{q}\) is the scattering coefficient; \(\alpha_{q}\) is a parameter describing the frequency and geometric relationship of the scatterer;  
Figure 2: Network structure of MIMO-LI-Net.  
represent the length and direction angle of the distributed scattering center; \(\gamma_{q}\) describes the relationship between the local scattering center and the direction. Through the above methods, MIMO radar echoes containing both local and distributed scattering mechanism targets can be simulated.  
In addition to the MIMO radar target echo, network training also requires the corresponding output target image. In this paper, the target imaging result under the condition of an ideal orthogonal waveform is used as the target image. The specific method is as follows: using the equivalent transceiver array echo to replace the MIMO array echo shown in Formula (9), at this time, the echoes of different transmitted waveforms are not aliased and there is no coupling interference; the back-projection algorithm is used to image the echo of the equivalent transceiver array. Even if there is migration though resolution cells, the algorithm can still obtain the focused image; the sidelobe is suppressed by two-dimensional windowing, and the image resolution is improved by doubling the array length and doubling the signal bandwidth.