## 3 MIMO Radar Simulation Platform
### Noise and Data Receiver Module  
Radar targets can reflect electromagnetic waves in space. For different kinds of radar targets, the characteristics of the reflected signals are different. Generally, the radar cross-section (RCS) is used to measure the characteristics of the target. \[\sigma=\frac{4\pi A^{2}}{\lambda^{2}} \tag{17}\]  
The \(\sigma\), \(A\), and \(\lambda\) parameters represent the radar target RCS, the irradiated area, and the operating wavelength of radar, respectively. For most complex scattering targets, RCS represents the equivalent area. The larger \(\sigma\) is, the more likely the target is to be detected by radars. For the opposite condition, it is not easily detected and has excellent stealth performance. If the RCS of targets in the same processing cycle is constant, and different treatment periods are not related to each other, then the radar target falls into the slow fluctuating category; if the pulses are not related to each other, the radar target falls into the rapidly fluctuating category. If the target has no fluctuation characteristics, it is called a \"no fluctuation target\" (also called Swerling 0 type). The radar targets can be roughly divided into four categories according to the type of the fluctuating target and their respective probability density functions, as is shown in Table 1.  
The five radar targets correspond to different target types. In general, Swerling I and II apply to the approximately equal scattering targets at low speed and high speed, respectively. Swerling III and IV apply to the strong dispersion and a plurality of small reflecting targets at low speed and high speed, respectively. Swerling 0 type corresponds to the target in uniform linear motion. In this study, the radar target focused on was the Swerling 0 type, and the rest of the targets were obtained by modifying the target type in the software. In the MIMO radar receiver, the received signal is not only reflected by the target signal, but interfered with by all kinds of noise and clutter. They can be divided into external noise and the internal noise. External noise is mainly caused by the interference from external electromagnetic waves, such as discharge phenomena. Internal noise is mainly caused by materials or internal circuits affects, such as thermal noise. A noise signal can be classified as additive noise and multiplicative noise according to its attributes. Thermal noise and shot noise belong to the additive noise category. If the source signal and the noise signal are represented as \(s(t)\) and \(n(t)\), then the noise signal is usually expressed in the form of \(s(t)+n(t)\). In the process of establishing the system platform, the additive noise is generally regarded as the background noise of the system. Channel-fading and the noise generated by the nonlinear system are multiplicative noise, which is generally expressed in the form of \(s(t)\times[1+n(t)]\). If the source signal disappears, then the multiplicative noise has no effect on the system. The noise and interference in this paper are all additive. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Target Type** & **Fluctuation Type** & **Probability Density Function** \\ \hline Swerling I & Slow & \(P(\sigma)=\frac{1}{\sigma}\exp(-\frac{\sigma}{\sigma})\) \\ Swerling II & Fast & \(P(\sigma)=\frac{\sigma}{\sigma}\exp(-\frac{\sigma}{\sigma})\) \\ Swerling III & Slow & \(P(\sigma)=\frac{\sigma\sigma}{\sigma^{2}}\exp(-\frac{\sigma\sigma}{\sigma^{2}})\) \\ Swerling IV & Fast & \(P(\sigma)=\frac{\sigma\sigma}{\sigma^{2}}\exp(-\frac{\sigma\sigma}{\sigma^{2}})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Different types of radar targets. In this work, the interference module adopted the Rayleigh noise, which is mainly used to describe the statistical laws of the flat fading signals. The envelope of the Rayleigh noise distribution is the sum of the Gaussian noise signal envelopes of two orthogonal distributions.