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The antenna of a zero-offset off-ground ground-penetrating radar can be accurately modeled using a linear system of frequency-dependent complex scalar transfer functions under the assumption that the electric field measured by the antenna locally tends to a plane wave. First, we analyze to which extent this hypothesis holds as a function of the antenna height above a multilayered medium. Second, we compare different methods to estimate the antenna phase center, namely, 1) extrapolation of peak-to-peak reflection values in the time domain and 2) frequency-domain full-waveform inversion assuming both frequency-independent and -dependent phase centers. For that purpose, we performed radar measurements at different heights above a perfect electrical conductor. Two different horn antennas operating, respectively, in the frequency ranges 0.2-2.0 and 0.8-2.6 GHz were used and compared. In the limits of the antenna geometry, we observed that antenna modeling results were not significantly affected by the position of the phase center. This implies that the transfer function model inherently accounts for the phase-center positions. The results also showed that the antenna transfer function model is valid only when the antenna is not too close to the reflector, namely, the threshold above which it holds corresponds to the antenna size. The effect of the frequency dependence of the phase-center position was further tested for a two-layered sandy soil subject to different water contents. The results showed that the proposed antenna model avoids the need for phase-center determination for proximal soil characterization.