## 1 Introduction  
Ultra-wideband (UWB) through-wall radar (TWR), as an emerging technology, is used to detect targets blocked by obstacles. It has wide application prospects in military and civil fields, such as urban combat, antiterrorism, vigilance, security inspection, disaster rescue, and so on [1; 2; 3; 4; 5; 6]. According to the working mode, TWR can be divided into synthetic aperture radar (SAR) systems and MIMO radar systems [7; 8; 9; 10; 11; 12; 13]. Conventionally, to get a high azimuth resolution, the synthetic aperture method (SAR) is extensively used. The transceiver of a SAR system is sequentially sled on a rail to provide synthetic aperture scanning imaging. However, this method requires long data acquisition times and its azimuth resolution is limited by the length of the rail. In addition, the TWR of the SAR mode has the disadvantage of large scale and high cost [10; 11; 12; 13]. In this case, the MIMO radar technology provides a new platform to solve the above problems [7; 8; 9; 14; 15; 16; 17; 18; 19; 20]. The MIMO radar technology was proposed in 2003 and 2004 [14; 15]. It uses multiple transmitting and receiving antennas and transmits orthogonal waveforms, which can expand the aperture of the actual array elements and confer a better spatial sampling ability. In addition, the sparse MIMO array design of switched antenna can also meet the requirements of high scanning speed and detection ability in the practical application of through-wall imaging. Therefore, the switched antenna array radar is often considered as the MIMO radar. In recent years, the MIMO radar system has received extensive attention of scholars. [PERSON] et al. [1; 4] proposed the 'co-array'. The azimuth resolution of the imaging is improved by expanding the aperture of the virtual array which is formed by the transceiver array. [PERSON] et al. [18; 19] studied the equivalence of a UWB MIMO array using the point spread function (PSF). It is pointed out that the equivalent array is the spatial convolution of the PSF of the transmitting array and the receiving array in the far field. Based on this, a linear array design was proposed. [PERSON] et al. [20] developed a MIMO array-based radar system using a SFCW signal, which can effectively improve the data sampling speed, maintain the azimuth resolution, and reduce the hardware costs. However, due to the high frequency range of the antenna used, the penetration depth of the radar system is too shallow for through-wall imaging. [PERSON] et al. [6] designed and manufactured a uniform array radar system to detect and image targets behind a wall with a monostatic configuration controlled by a switcher. However, the effect of the wall on the refraction of EM waves, which produces a position shift of the targets behind the wall, was ignored. Based on the advantages and limitations of the above research results, a UWB MIMO sparse array radar system with eight pairs of transmitting and receiving miniaturized Vivaldi antennas is studied in this paper and is mainly used for 2D imaging of multiple targets behind a wall. The UWB MIMO system combines UWB technology with MIMO technology. On one hand, UWB technology can improve range resolution [21; 22]. On the other hand, the sparse topology of the MIMO system can obtain larger array aperture and smaller element spacing by using fewer antennas. Moreover, higher azimuth resolution and better main/side lobe control are obtained. Therefore, the MIMO radar system only needs a few physical elements to achieve the same imaging effect as SAR. In this way, the number of array elements and the system cost are greatly reduced, while the aperture length is maintained. In addition, the electronic switching mode used in the MIMO radar system can improve the data acquisition speed. In the MIMO radar system, the antenna is of great importance as it radiates power to the wall and detects the signals of the targets. UWB signals are suitable for the radar system while the through-wall penetration losses for general wall materials increase with frequency.