## 2 UWB MIMO Radar System
### MIMO Array Topology Design
Then, the required ideal sidelobe level (SL) is limited by the lower bound \(SL=-20\log(K)\) (dB) [21], which helps to derive the minimal number of the virtual elements \(K=MN\) required within the effective aperture, where \(K\) refers to the channels of the radar array. The next step is to determine the configuration of MIMO array, which is the factorization of a desired equivalent uniform array into topologies of transmitting and receiving MIMO arrays. The number of transmitting and receiving antennas can be obtained from the relation \(K=M\times N\) (the total number of antenna elements is \(Num=M+N\)). The total number of antennas is minimized by selecting an equal or as close as possible number of elements in both transmitting and receiving arrays. For example, the number of virtual elements in the paper is 64; therefore, four different combinations of transmitting and receiving antenna element numbers can be obtained, which are: \(1\times 64\), \(2\times 32\), \(4\times 16\), and \(8\times 8\). The result with the minimal number of antennas is eight transmitters and eight receivers (\(8\times 8\)). At last, based on the polynomial factorization (PF) method in our previous research work [20], a MIMO array with eight pairs of transmitters and receivers was achieved, which satisfies the desired resolution and sidelobe level. The length of aperture is about 1.1 m. The operational center frequency is 1.5 GHz. The array possesses 6.8 cm range resolution and 5.8 rad azimuth resolution, with an equivalent aperture length of 1 m.  
The designed MIMO array with 16 antennas can be used to collect 64 channels of raw data by switching on and off all antennas in a sampling period. This array design method can bring about great  
Figure 3: Schematic diagram of the polynomial factorization (PF) method. reduction in the total number of antenna elements and improve aperture efficiency while maintaining the aperture size. The topology of the designed MIMO array is shown in Figure 4. To assess the capacity of the designed MIMO array, given a point target located at (0,5), the point spread function (PSF) [20] of a sparse array in the azimuth direction is calculated, as given in Figure 5. We can see that the designed MIMO array can achieve low sidelobe level. In order to assess the imaging quality of the above array design results and imaging methods, simple numerical simulations were carried out. The simulation parameters (Table 1) are consistent with the setting parameters of the actual system. Three targets located at different positions, which are (-1,3), (0,1) and (1.5,5), were simulated. Figure 6 shows the 2D imaging performance of the TDBP algorithm and the CC-TDBP algorithm from the designed layout of the MIMO array, respectively. It can be seen that the targets can be well focused. The artifacts in Figure 5(b) are suppressed compared with those in Figure 5(a). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Start frequency & 0.4 GHz \\ Stop frequency & 2.6 GHz \\ Number of frequencies & 256 \\ Number of transmitters/receivers & 8/8 \\ Range resolution & 0.068 m \\ Azimuth resolution & 5.8 rad \\ Maximum range & 17.4 m \\ Length of aperture & 1.1 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. Figure 4: Topology of the designed MIMO sparse array. Figure 5: Point spread function (PSF) of the designed MIMO sparse array in the azimuth direction.