## 5 Discussion  
In this paper, a linear sparse MIMO radar system which can be used for through-wall detection was designed and analyzed. The array design methods can reduce the number of antennas while maintaining the azimuth resolution. The traditional Vivaldi antenna was improved by antenna miniaturization technology, so that the characteristics of high gain, ultra-wideband, and low frequency were realized. This miniaturization approach may also be utilized to improve the bandwidth characteristics of other similar printed antennas. Concerning the imaging, the TDBP imaging algorithm based on cross correlation was presented in detail. The experimental results in Figures 15 and 16 show that the proposed CC-TDBP algorithm can suppress artifacts better than the traditional TDBP algorithm. In addition, we considered the effect of the wall on the refraction of EM waves and the changes of velocity in the through-wall detection experiment (Section 4.2). Based on the principle of [PERSON]'s law and ray tracing, a new through-wall imaging model is established in Figure 12. The improved BP algorithm with cross-correlation compensates for the wall's influence and effectively focuses the targets behind the wall. Figure 19 shows that the targets' locations are closer to the real positions measured by meter stick. Finally, the significance and characteristics of this research are discussed in the following four points. (1). The direct significance of the MIMO radar system studied in this paper is to improve traditional synthetic aperture methods. The designed radar system with optimized UWB Vivaldi antennas has the characteristics of fast data acquisition speed, required azimuth resolution, low cost, and can be applied to through-wall detection. The Vivaldi antenna has been designed, simulated, manufactured, and successfully used in through-wall imaging, which is one of the contributions to the through-wall radar technology. The period data (64 channels data) acquisition time of the MIMO radar system is approximately 35 s. However, this relatively long sampling time is due to the specific VNA that operated as the transceiver. It is an old model (Agilent N9925a) which is not designed for fast acquisition. In fact, the MIMO radar does not have mechanical moving parts, so it can acquire data much faster than synthetic aperture radar (SAR) based on the movement of the transceiver along a rail [17]. In addition, compared with the current research [9; 37] which is limited to simulation and validation, we developed the actual radar system to carry out experimental verification, which is more conducive to illustrate the effectiveness of the proposed system design and imaging algorithm. (2). Generally, the dielectric constant of the wall is larger than that of the air. The transmitted EM waves have to pass the wall twice to reach the radar receivers, which further reduces the energy of the received target signal. In terms of amplitude attenuation, the first reflection from the front wall is the strongest and the higher-order reflection can be neglected. The signal information of the targets hidden behind walls, such as back walls and human targets, are mainly conveyed by the first transmission. It is worth noting that the reflection of the human body is relatively low compared with wall reflection and the direct coupling between the antennas. Moreover, the attenuation of the wall makes the collected human target signal weaker, which certainly increases the difficulty of through-wall imaging [38]. Therefore, in the third experiment, background removal is used to improve the imaging performance. (3). Based on the VNA platform, the system is more flexible. For example, we can properly change the operating frequency range and frequency points of the system according to the specific application scenario. Thus, the range resolution and maximum ambiguity range can be improved. In particular, when the wall is thicker, the low-frequency UWB range can be chosen to improve the penetration of EM waves. (4).