Full Waveform Inversion (FWI) is an optimization method that retrieves high-quality images of the ground's internal electromagnetic properties, such as permittivity, permeability, or conductivity. FWI requirements include an initial subsurface image of the parameters (starting point models), a wave propagation model, a cost function, and the source wavelet used during data acquisition. Usually, the source wavelet is estimated from the acquired data, or modelled from the antenna characteristics. In this study, the materials of the shielded antenna of a commercial Ground Penetrating Radar (GPR), developed by GSSI, are estimated using a global optimization method, from the observation measurements of the source signal. The estimated source is then used to model the wave propagation of the electromagnetic signal, and to estimate the electromagnetic parameters of the SEAM model via FWI. Experimental results show that the soil characteristics with the estimated source and pattern radiations retrieve better quality images than the inversion when the radiation pattern is neglected. In fact, the impact of using the correct source during the inversion is more evident when the initial model is distant from the correct solution.