## 3 Signal Model  
The model of the MIMO radar mounted on a flying platform was taken into consideration. The MIMO radar consists of an \(M\)-element array of transmitting antennas and an \(N\)-element array of receiving antennas. Each element of a uniform linear array (ULA) is isotropic. The distances between the elements of the array of the transmitting antennas are equal to \(d_{t}\), and the distances between the elements of the receiving antenna array are equal to \(d_{r}\). The model assumes the transmission of orthogonal signals with time division multiplexing (TDM). The construction of the MIMO antenna array is shown in Figure 1.  
Figure 2 shows the geometry of the radar system mounted on a flying platform moving along a straight line at a speed, \(V_{a}\). The distance from the radar to the object is \(R_{s}\). The radar observes the target at an angle, \(\alpha\). The radar system modeled in this way operates at a specific wavelength, \(\lambda\), and transmits a sequence, \(C\), of coherent pulses with a pulse repetition rate, \(f_{r}\). The presence of \(P\) targets was assumed, where the elevation angle between the radar and the \(p\)th object is \(\theta_{p}\) (\(p\) = 1, 2..., \(P\)). Figure 1: Example of MIMO array obtained via M = 2 and N = 4 antennas. Figure 2: Geometry of MIMO radar system. There are \(M\)-matched filters in each of the \(N\)-receiving antennas to receive orthogonal signals from \(M\)-transmitting antennas. Hence, the total number of received signals is equal to the product of \(MN\). The matrix of received data can be represented as [1; 2; 3; 4]:  
\[\mathbf{X}=\mathbf{AS}+\mathbf{Z} \tag{1}\]  
\[\mathbf{A}=\mathbf{A_{r}}\odot\mathbf{A_{t}} \tag{2}\]  
where denotes virtual array antennas, \(\mathbf{A_{t}}\) denotes the transmit steering matrix with the \(p\)th transmit steering vector, \(\mathbf{a_{t}}\) (\(\theta_{p}\)), and \(\mathbf{A_{r}}\) denotes the receive steering matrix with the \(p\)th receive steering vector, \(\mathbf{a_{r}}\) (\(\theta_{p}\)). \[\mathbf{A_{r}}=\left[\mathbf{a_{r}}(\theta_{1}),\mathbf{a_{r}}(\theta_{2}),\dots,\mathbf{a_{r }}(\theta_{p})\ \right] \tag{3}\]  
\[\mathbf{a_{r}}(\theta_{p})=\left[1,e^{-2\pi\frac{d_{s}\sin\theta_{p}}{\lambda}}, \dots,e^{-2\pi(N-1)\frac{d_{s}\sin\theta_{p}}{\lambda}}\right]^{T} \tag{4}\]  
\[\mathbf{A_{t}}=\left[\mathbf{a_{t}}(\theta_{1}),\mathbf{a_{t}}(\theta_{2}),\dots,\mathbf{a_{t }}(\theta_{p})\ \right] \tag{5}\]  
\[\mathbf{a_{t}}(\theta_{p})=\left[1,e^{-2\pi\frac{d_{s}\sin\theta_{p}}{\lambda}}, \dots,e^{-2\pi(M-1)\frac{d_{s}\sin\theta_{p}}{\lambda}}\right]^{T} \tag{6}\]  
\(S\) denotes the data matrix from the received target; it also includes the clutter and jammer. \(\mathbf{X}\) is the data matrix corresponding to a virtual array, with \(x_{m,n}\) being the output data of the \((n-1)\times M+m\)th virtual array element, where \(m=1\),\(2\),..., \(M\) and \(n=1\),\(2\),..., \(N\). \(\mathbf{Z}\) represents the white Gaussian noise matrix, with \(z_{m,n}\) being the noise vector of the \((n-1)\times M+m\)th virtual element. \[S=\left[\mathbf{s_{1}},\ \mathbf{s_{2}},\dots,\mathbf{s_{C}}\right] \tag{7}\]  
Figure 1:0  
Figure 1:1  
Figure 1:2  
Figure 1:3  
The covariance matrix of the received data is given as [1]:  
Figure 1:4  
Figure 1:5  
Figure 1:6  
where \(\mathbf{R_{s}}\) denotes the covariance matrix of the received signal, and \(\mathbf{R_{N}}\) denotes the covariance matrix of the noise. The STAP processor is a linear filter, so ultimately, the STAP processor is designed to remove noise and detect the target. The relationship describing these activities is given as [1; 2; 3; 4]:  
Figure 1:7where \(\mathbf{w}\) denotes the vector of weights given by the formula [1]:  
Figure 1:8  
In order to realize the essence of the issues discussed, it seems very helpful to present the STAP scheme. Hence, the following figure highlights the most important stages of the STAP radar signal processing (Figure 3).