## 1 Introduction
Lens antennas have been used for radar systems because they can convert a spherical wave into a plane wave to produce high gain. A convex-plane lens using low-loss dielectric material with a relative permittivity greater than 1 can be used. A Luneburg lens, a spherical dielectric lens with a graded index of refraction (increasing toward the center), can create multiple beams using multiple feed antennas. Lens antennas offer several advantages, such as a wide scan angle, a very low sidelobe, and low feed blockage, compared to reflector antennas. Still, they are very thick and heavy at microwave frequencies, and the attenuation caused by the loss tangent of the dielectric material is significant. Various array antennas using different array elements, such as dipoles, waveguide slots, horns, and microstrip patches, have also been widely used to achieve high gain for radar systems. Various planar microstrip patch array antennas are mainly used for commercial semiconductor-integrated radar sensors. The microstrip patch array antenna configurations are based on the feed network [10; 11]. There are three types of feed networks for the microstrip patch array antennas: series, parallel (or corporate), and series-parallel combination. In the parallel feed network, input power is distributed to all radiating elements using power dividers. Larger frequency bandwidths can be achieved, and the configuration is modular. Since the path length to each array element is the same, each element has the same power and phase. However, the parallel feed network requires a very large space; a long length in the feed network causes high feed losses, and discontinuity between line corners causes large mutual coupling effects that distort the radiation patterns resulting in a high cross-polarization level. In the series feed network, array elements are serially fed from a single transmission line, and the total lengths of the feed line can be minimized with reduced losses and lower sidelobes. The series feed network can be divided into in-line and shunt-connected. For the in-line series feed network, array elements are placed in series and are connected by an intervening transmission line. Therefore, it is most compact in size and efficient in space usage. For the connection between array elements, direct connection or coupled connection can be employed. Since the electrical length of the transmission line between the elements changes as the frequency changes, the main beam direction changes and can be used for frequency beam scanning. In addition, the frequency bandwidth of the in-line series feed network is narrower, compared to the corporate network. The shunt-connected series feed network is the same as the in-line series feed network, but the array elements branch out from the transmission line, and each element has only one transmission line. The lengths of the paths between the elements can be adjusted to make the array insensitive to frequency variation. The series-parallel combination feed network can compensate for the disadvantages of series and parallel feed networks. According to the radar equation, maximum detection range varies as a square root of the antenna gain. Therefore, we can double the maximum detection range by increasing the antenna gain by four times (6 dB) [8]. Various gain enhancement methods for microstrip patch antennas have been attempted. Fabry-Perot cavity (FPC) antennas, formed by the ground plane of the feed patch antenna and a partially reflective surface (PRS) located above the ground plane with some spacing, have been extensively studied for gain enhancement [12; 13; 14; 15; 16]. The PRS is also called the superstrate, and it consists of arrays of periodic metallo-dielectric or pure dielectric elements. Gain in the FPC antenna is proportional to the reflection magnitude and the dimensions of the PRS. Hemispherical, extended hemispherical with a cylinder, elliptical, or planar graded index dielectric lenses have been used for gain enhancement [17; 18; 19; 20].