Estimating the Time Difference of Arrival (TDoA), is a simple yet reliable technique to accurately perform an indoor monostatic localization. To implement TDoA estimation, one approach is to utilize a broadband radar system equipped with multiple receiving antenna elements. To obtain the Time of Arrival (ToA) at each antenna element, the round-trip time is required. However, the round-trip time does not only consist of the propagation delay in free space but the propagation delay within the antenna as well. To perform the localization precisely, it is desired that an antenna element introduces a uniform delay in all directions. To this end, a compact rectangular dielectric resonator antenna is designed for the operating frequency of 6.5 GHz with a fractional bandwidth of 20%. Al2O3 with a dielectric constant of 9.8 is used for the substrate as well as the dielectric resonator. The antenna is designed to provide a high correlation between the input and the output pulses. To investigate the correlation, the antenna is excited with a modulated Gaussian pulse and the radiated pulses are studied. The antenna possesses an excellent behavior in terms of pulse preservation for the upper hemisphere. Therefore, when incoming pulses from the same distance but different directions impinge on the antenna, they reach the port of the antenna at a similar time. It is shown that this feature of the proposed antenna allows the utilization of TDoA estimation without the need for a calibration step. The characteristics of the antenna are verified by simulation and measurement.