## 2 MIMO Radar Principle  
The complexity of the MIMO radar system is a major impediment to its development of wide applications. The cost of the RF chains and power consumption is increased by the number of the antenna element arrays. For such circumstances, a MIMO system with a single RF link chain is proposed, which not only reduces the dimensions and cost, but shows better performance compared to the traditional complex MIMO system. A single RF link MIMO radar first generates a control signal through two random digital signals. One of the signals is the control signal of the initial orthogonal basis, and the result obtained by the two signal XOR operations controls the opening direction of the single pole double throw(SPDT) switch. Assuming that \(\widetilde{A}_{R}\) and \(\widetilde{A}_{T}^{H}\) represent the projection of the two orthogonal digital signals of the scatter directions [33; 34], the virtual channel representation can be expressed as:  
\[H=\sum\limits_{q=-\widetilde{Q}}^{\widetilde{Q}}\sum\limits_{p=-\widetilde{p} }^{\widetilde{p}}H_{V}(q,p)a_{R}(\widetilde{\theta}_{R},q)a_{T}^{H}( \widetilde{\theta}_{T},p)=\widetilde{  
As for the single RF MIMO transmitter, the transmitting version pattern can be described as:  
\[P_{T}(\varphi)=\sum_{n=0}^{Neff-1}s_{bs,n}\Phi_{n}(\varphi) \tag{2}\]  
\(\widetilde{A}_{R}\widetilde{A}_{T}^{H}=\Phi_{T}=\left[\varphi_{0,T}\ \varphi_{1,T}\dots\varphi_{Neff-1,T}\right]\) can be considered as the sampled transmitting pattern of the MIMO radar. As for the single receiver port, it is not possible to realize the spatial sampling of the incident wave. \(N_{\mathit{eff}}\) denotes the number of the symbol period division for different patterns. The received vector at the end of the period can be described as:  
\[y_{bs}=\Phi_{R}^{H}H_{g}\Phi_{T}s_{bs}+n_{bs} \tag{3}\]  
The MIMO radar system adopts a series of transmitting antennas to construct orthogonal signals in the time domain and transmits them to air space at the same time. The reflection on the target of the electromagnetic wave is received by multiple antennas at the receiver. The space position and motion state information of the target are extracted by a comprehensive process of the reflection wave. A schematic diagram of MIMO radar is shown in Figure 1. The whole MIMO radar system consists of \(M\) transmitting antennas and \(N\) receiving antennas. The \(M\) transmitting antennas can work simultaneously to transmit orthogonal signals and the \(N\) receiving antennas can receive all the target echoes simultaneously, thus forming \(M\times N\) observation channels. The introduced observation channels are far more than the actual number of physical array elements and, ultimately, multichannel information acquisition capability is realized using this method. Accordingly, the multiple MIMO RF links make signal processing more complicated than traditional radar. False alarm is the phenomenon that occurs when, even if there is no signal at the input of the radar receiver, it still judges that the signal existed. Since radar performance has always been affected by outside interferences, such as sea surface and internal receiver thermal noise, it is necessary for radar to acquire a certain signal-to-noise ratio (SNR) when extracting a signal from the received waveform. As for the adaptive detection algorithms for radar targets, two adaptive detectors were proposed in [35], which eliminated the need for matched filtering for colocated MIMO radar target detection. In [36], the persymmetric generalized likelihood ratio test (PGLRT) for distributed MIMO radar was studied, which has a simpler form and a more efficient computation process. Figure 1: Schematic diagram of the multiple-input multiple-output (MIMO) radar model. There are \(M\) elements in the transmitting array and \(N\) elements in the receiving array. The transmitted signal is reflected by the radar target and received by the receiving antenna. multichannel signal detection in homogeneous Gaussian disturbance was discussed in [37].