  A limiting systematic effect in 21-cm interferometric experiments is the
chromaticity due to the coupling between the sky and the instrument. This
coupling is sourced by the instrument primary beam; therefore it is important
to know the beam to extremely high precision. Here we demonstrate how known
beam uncertainties can be characterized using databases of beam models. In this
introductory work, we focus on beam errors arising from physically offset
and/or broken antennas within a station. We use the public code OSKAR to
generate an "ideal" SKA beam formed from 256 antennas regularly-spaced in a
35-m circle, as well as a large database of "perturbed" beams sampling
distributions of broken/offset antennas. We decompose the beam errors ("ideal"
minus "perturbed") using Principal Component Analysis (PCA) and Kernel PCA
(KPCA). Using 20 components, we find that PCA/KPCA can reduce the residual of
the beam in our datasets by 60-90% compared with the assumption of an ideal
beam. Using a simulated observation of the cosmic signal plus foregrounds, we
find that assuming the ideal beam can result in 1% error in the EoR window and
10% in the wedge of the 2D power spectrum. When PCA/KPCA is used to
characterize the beam uncertainties, the error in the power spectrum shrinks to
below 0.01% in the EoR window and <1% in the wedge. Our framework can be used
to characterize and then marginalize over uncertainties in the beam for robust
next-generation 21-cm parameter estimation.
