  Experimental 21 cm cosmology aims to detect the formation of the first stars
during the cosmic dawn and the subsequent epoch of reionization by utilizing
the 21 cm hydrogen line transition. While several experiments have published
results that begin to constrain the shape of this signal, a definitive
detection has yet to be achieved. In this paper, we investigate the influence
of uncertain antenna-sky interactions on the possibility of detecting the
signal. This paper aims to define the level of accuracy to which a simulated
antenna beam pattern is required to agree with the actual observing beam
pattern of the antenna to allow for a confident detection of the global 21 cm
signal. By utilising singular value decomposition, we construct a set of
antenna power patterns that incorporate minor, physically motivated variations.
We take the absolute mean averaged difference between the original beam and the
perturbed beam averaged over frequency ($\Delta D$) to quantifying this
difference, identifying the correlation between $\Delta D$ and antenna
temperature. To analyse the impact of $\Delta D$ on making a confident
detection, we utilize the REACH Bayesian analysis pipeline and compare the
Bayesian evidence $\log \mathcal{Z}$ and root-mean-square error for antenna
beams of different $\Delta D$ values. Our calculations suggest that achieving
an agreement between the original and perturbed antenna power pattern with
$\Delta D$ better than -35 dB is necessary for confident detection of the
global 21 cm signal. Furthermore, we discuss potential methods to achieve the
required high level of accuracy within a global 21~cm experiment.
