## 1 Introduction
On the other hand, lower working frequency band for antennas can provide better through-wall penetration but this also implies a larger size of the antenna [23]. Hence, the antenna working frequency range of 0.5-2.5 GHz is considered to balance good resolution and strong penetration even for thick walls. In this paper, we apply Vivaldi antennas in a MIMO radar system for through-wall detection because of its many advantages, such as high gain, wide band, steady radiation patterns, simple structure, and simplicity of processing [24]. The low-frequency characteristic of antennas generally results in larger size. Inspired by [25; 26], we use a slotted approach to change the surface current distribution to optimize performance throughout the band, expand the low frequency bandwidth, and reduce its size. Finally, the low-frequency UWB miniaturized Vivaldi antenna was designed and fabricated with dimensions of 250 mm \(\times\) 200 mm \(\times\) 1.6 mm, and a working band (the S11 is less than--10 dB) of 0.5-2.5 GHz, good end-fire radiation behavior, and acceptable gain. The Vivaldi antenna designed in this paper is one of the contributions to the imaging research of through-wall radar technology. The proposed antenna is simple, easy to fabricate, and is made of inexpensive FR4 substrate. The experiments show that the designed antenna has good through-wall penetration ability and resolution. 2D imaging is one of the most important signal processing steps for a through-wall MIMO radar system. The small imaging area is located in the near field of the radar. At the same time, EM waves produce reflections, attenuations, and velocity changes when they penetrate the wall. Therefore, the back projection (BP) imaging algorithm [9; 20], which has no requirement for the array configuration, is one of the most practical through-wall imaging methods due to its convenience and robustness. However, reconstructed images of targets by the BP method may have some artifacts. In this paper, the cross-correlation-based time-domain BP algorithm (CC-TDBP) is applied to suppress artifacts [27; 28]. Moreover, considering the effect of walls on the refraction and velocity of EM waves, an improved BP-based algorithm is proposed in Section 3. The experimental results validate that the designed MIMO radar system with the proposed BP-based algorithm can accurately reconstruct the human locations behind the wall. The structure of the paper is organized as follows: In Section 2, the design process of the UWB MIMO array radar system is described. The imaging signal model and CC-TDBP algorithm are reviewed. The topology, array pattern of the designed MIMO array, and the 2D simulation imaging results are given. Moreover, the design methods of the miniaturized Vivaldi antenna are introduced. Finally, the prototype of the MIMO radar system is presented. In Section 3, the through-wall imaging model is constructed and the improved CC-TDBP algorithm, considering the effect of the wall, is illustrated. In Section 4, three experiments are conducted to assess the effectiveness of the developed MIMO radar system and imaging methods. To summarize, Sections 5 and 6 give discussion and conclusions, respectively.