# Bistatic Sea Clutter Suppression Method Based on Compressed Sensing Optimization
## 2 Overview of Signal Modelling and Compressed Sensing
### Signal Modelling  
The generation mechanism of bistatic sea clutter is similar to that of monostatic sea clutter, both of which are generated by Bragg scattering. The Bragg scattering mechanism is shown in Figure 1.  
According to the Bragg scattering theory, the bistatic sea clutter echo spectrum is primarily made up of two narrow first-order Bragg peaks, as well as the surrounding continuously broadened second-order and higher-order sea clutter. The first-order Bragg peak can be approximately described by two sine signals, while the intensity of second-order and higher-order sea clutter is approximately 10-40 dB lower than that of the first-order Bragg peak [13]. The latter can be simplified with white Gaussian noise. The theoretical value of the Doppler shift of the bistatic first-order Bragg peak is:  
\[f_{\text{Bragg\_B}}=\pm\sqrt{\frac{g}{\pi\lambda}}\sqrt{\frac{(\cos\Delta_{ \text{in}}+\cos\Delta_{\text{sc}})}{2}\cos\left(\frac{\varphi}{2}\right)} \tag{1}\]  
where \(g\) is the acceleration of gravity, \(\lambda\) is the radar working wavelength, \(\Delta_{in}\) is incident angle, \(\Delta_{\text{sc}}\) is scattering angle, and \(\varphi\) is a bistatic angle. Figure 1: Bragg scattering mechanism. In practical scenarios, bistatic sea clutter is influenced by various parameters, including ocean current, bistatic angle, and the ionosphere, all of which have a significant impact on the sea clutter spectrum. The current affects the relative speed of the targets on the sea surface. This impact on the sea clutter spectrum can be approximated as a process of spectrum shifting. The ionosphere has non-stationary characteristics, and its influence on electromagnetic waves can be approximated as a modulation effect [14]. As a result, the sea clutter spectrum will be a combination of multiple signal spectra. In addition, the bistatic angle is a variable for each clutter unit, and it affects the formation of first-order sea clutter by causing all sea waves that meet the Bragg resonance condition to undergo Bragg resonance. Then, the corresponding Doppler shift will be superimposed on the sea clutter spectrum, which will inevitably exacerbate spectrum peak splitting and spectrum broadening [15]. Considering the influence of ocean current, the Doppler shift of the bistatic first-order Bragg peak is:  
\[f_{\text{Bragg\_B}}=\sqrt{\frac{g}{\pi\lambda}}\sqrt{\frac{(\cos\Delta_{ \text{in}}+1)}{2}\cos(\frac{\varphi}{2})}+\frac{2\
u_{\text{oc}}\cos(\frac{ \varphi}{2})}{\lambda} \tag{2}\]  
where \(\
u_{\text{oc}}\) refers to the radial velocity of the current velocity, which is the velocity component of the current velocity vector on the bisector of the bistatic angle of the scattering point, towards or away from the baseline. Considering that the height of the receiver is usually very low, which is negligible compared with the height of the spaceborne or satellite radiation source. Therefore, the scattering angle is approximated as \(0^{\circ}\), and \(\Delta_{\text{sc}}\) is replaced by \"1\". Considering the combined effects of ionosphere and bistatic angle, the sea clutter spectrum will be the superposition of multiple signal spectra:  
\[S_{c}(f)=\sum_{i=1}^{K}A_{i}\big{(}f_{\text{Bragg\_B}}-f_{i}\big{)} \tag{3}\]  
where \(S_{c}(f)\) is the sea clutter spectrum, \(K\) is number of sea clutter, \(A_{i}\) is amplitude of the \(i\)th clutter, and \(f_{i}\) is frequency deviation. Figure 2 shows the comparison between the ideal bistatic first-order sea clutter spectrum and the spectrum affected by interference. It can be clearly seen that the sea clutter spectrum has a spectrum shift and a slight spectrum broadening at this time. Figure 2: The comparison between the ideal bistatic first-order sea clutter spectrum and the spectrum affected by interference. For the ship target on the sea, its speed is generally slow, and it can be regarded as a uniform motion in a short time. Therefore, the target echo can also be modelled as a sinusoidal signal.