The dielectric resonator antenna is actually derived from the dielectric resonator (DR), which was previously used for miniaturization of the active and passive microwave circuit components such as filters and oscillators. The DRs have various advantages such as the compact size, light weight, high radiation efficiency, ease of excitation, high power handling capability, and wideband capability. The coaxial probe and aperture coupled excited cylindrical DRAs have shown wide-bandwidth and broadside radiation patterns. A DRA that radiates pure monopole like patterns is of great interest. The investigations results are presented of a cylindrical dielectric resonator antenna (DRA) with a central air gap and fed in using a coaxial probe connected to a wire monopole. The central air gap and monopole height were determined after parametric studies which offer controllable impedance bandwidth S11≤ -10dB between 40% to 67%. The DRA provides monopole like omni-directional radiation patterns with low cross-polarization levels over a wide impedance bandwidth. Prototype DRA with a selected air gap and monopole height was fabricated and experimentally verified. Simulated and measured impedance bandwidths of 67%, and 64%, respectively, were obtained with acceptable peak realized gain over the bandwidth. The simulated and measured radiation patterns also show monopole like omni-directional radiation patterns within the bandwidth. The investigation results on the beam focusing properties of a dielectric resonator antenna (DRA) array consisting of four-elements on a finite ground plane are also presented. Each of the DRA provides pure omni-directional radiation patterns while possessing 67% impedance bandwidth. One DRA is excited at a time while other DRAs in the array are either short circuited to ground, open circuited, or matched terminated. The best option among the short circuit, open circuit and matched terminated case is selected. The antenna beam provides both horizontal and vertical plane beam coverage with 60% fractional bandwidth. This type of antenna can find applications in Digital Radio Broadcast (DRB), mobile terrestrial communications, and smart adaptive antennas, where switched sector beams are desired. The beam focusing property study was further extended for a case with ground plane having skirt. The array is having six-elements, the center one being fed and one open circuited and rest short circuited to the ground plane surrounding the center element. This work can be carried out further and can be done as a future study of the work presented here.