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Cosmic Dawn, the onset of star formation in the early universe, can in principle be studied via the 21cm transition of neutral hydrogen, for which a sky-averaged absorption signal, redshifted to MHz frequencies, is predicted to be {\it O}(10-100)\,mK. Detection requires separation of the 21cm signal from bright chromatic foreground emission due to Galactic structure, and the characterisation of how it couples to instrumental response. In this work, we present characterisation of antenna gain patterns for the Large-aperture Experiment to detect the Dark Ages (LEDA) via simulations, assessing the effects of the antenna ground-plane geometries used, and measured soil properties. We then investigate the impact of beam pattern uncertainties on the reconstruction of a Gaussian absorption feature. Assuming the pattern is known and correcting for the chromaticity of the instrument, the foregrounds can be modelled with a log-polynomial, and the 21cm signal identified with high accuracy. However, uncertainties on the soil properties lead to \textperthousand\ changes in the chromaticity that can bias the signal recovery. The bias can be up to a factor of two in amplitude and up to few \% in the frequency location. These effects do not appear to be mitigated by larger ground planes, conversely gain patterns with larger ground planes exhibit more complex frequency structure, significantly compromising the parameter reconstruction. Our results, consistent with findings from other antenna design studies, emphasise the importance of chromatic response and suggest caution in assuming log-polynomial foreground models in global signal experiments.