## 1 Introduction  
Nowadays, wide-beam antennas have a range of applications requiring wide coverage [1; 2; 3; 4; 5; 6; 7], such as satellite systems [8], radar detection [9; 10], and 5G wireless communication [11; 12; 13]. Although wide beamwidth can be obtained by reducing antenna gain, the directivity of the antenna will also be reduced and cause a large loss of radiation energy. To solve this contradiction between high directivity and wide beamwidth, beam broadening technology is worth studying. In most of the reported studies, beamwidth widening is only aimed at either one or both of the E- and H-planes, while few pieces of research focus on all cut-planes to achieve a quasi-hemispherical radiation pattern, especially for end-fire antennas. Meanwhile, to achieve the goal of beam broadening, most of the reported studies have paid the cost of overall size and structural complexity increase. All of these insufficiencies limit the applications of wide-beam antennas. In recent years, a large number of techniques have been investigated to broaden beamwidth. In [14], a binary coding technique was proposed to determine the complex metal patterns of a patch antenna. In this way, the beamwidth in the H\(-\)plane for port 1 was effectively broadened. However, it also significantly increased the design complexity. The authors of [15] employed four separated microstrip patches to load on a dielectric substrate as the radiators. By adjusting the distance between these patches, the beamwidth in the E-plane could be widened. Unfortunately, the antenna suffered from design complexity, and beam broadening in all cut-planes could not be achieved. In [16], a new aperture-coupled cylindrical dielectric resonator antenna was designed. By means of exciting the basic and high-order modes in the dielectric resonator, a widened beam could be realized in the E- and H-planes. Nonetheless, the overall size of the antenna was enlarged due to the dielectric resonator loading, and the stacking of multi-layered cylindrical disks also increased the manufacturing difficulty. Another dielectric resonator antenna was also proposed in [17]. Owing to the loading of the engraved groove and comb-like metal wall, the HPBW in the E- and H- planes could be widened, but at the cost of the size and design complexity. In [18], a magnetoelectric dipole could achieve a stable wide beam in the H-plane; regrettably, however, the HPBW extension was not large enough and the structure was complex. The authors of [19] combined a U-shaped reflector with L-shaped metal arms as a magnetic dipole and added a parasitic patch to the L-shaped metal arms as an electric dipole. Thereby, the impedance bandwidth and the antenna HPBW were broadened. Nevertheless, a larger antenna size was needed and fabrication at high frequencies was not easy. In [20], to achieve a broad beamwidth, the authors combined a parasitic strip with a rectangular microstrip magnetic dipole antenna (MMDA). The MMDA was equivalent to a magnetic dipole toward the y-axis direction, and the parasitic strip worked as an electric dipole toward the x-axis direction. The beamwidth in the _yoz_ cut-plane could be widened from about 70\({}^{\circ}\) to 180\({}^{\circ}\) due to the superposition of multiple complementary sources. However, the beamwidth was basically widened in a single cut-plane. In [21], a subarray, including a main radiant patch and two parasitic patches, was created to widen the beamwidth in the E-plane. By adjusting the spacing between the patches, the amplitude and phase of the coupling energy from the main patch to the parasitic patches could be controlled and the superposed radiation patterns could be affected. Nevertheless, this also only widened beamwidth in a single cut-plane. In [22], the mushroom structure and a pair of equal-amplitude and out-of-phase Huygens sources were introduced into the dielectric resonator antenna. The beamwidth was widened from 90\({}^{\circ}\) to 194\({}^{\circ}\). However, the beamwidth could only be widened within one cut-plane.