The Chang’e-5 lunar exploration mission of China is equipped with a Lunar Regolith Penetrating Radar (LRPR) for measuring the thickness and structures of the lunar regolith in the landing area. Since the LRPR is stationary, an ultra-wideband multiple-input multiple-output (MIMO) array is designed as a replacement for conventional mobile subsurface probing systems. The MIMO array, with 12 antenna elements and a switch matrix, operates in the frequency band from 1.0 to 4.75 GHz. In this work, the design and layout of the antenna elements were optimized with respect to the lander. To this end, the antenna elements were designed as miniaturized Vivaldi antennas with quarter elliptical slots (i.e., quarter elliptical slotted antenna, or QESA). QESAs are significantly small while being able to mitigate the impact of the lander on antenna electrical performances. QESAs also have a wide operating bandwidth, flat gain, and excellent time domain characteristics. In addition, a high-temperature resistant ultra-light radome with high transmissivity is designed to protect the external antenna array. After calibration, the MIMO array is used to detect targets embedded in volcanic ash. The detection depth reaches 2.5 m, and the detection effect is good.