  The existence of a radio synchrotron background (RSB) excess is implied by a
number of measurements, including excess emission seen by the ARCADE~2 and LWA
experiments. Highly sensitive wideband radio arrays, of the kind used to
measure the cosmic 21cm signal, provide a promising way to further constrain
the RSB excess through its anisotropy, providing additional insight into its
origin. We present a framework for evaluating the potential of 21cm arrays to
disentangle different components of the diffuse radio sky based on the
combination of their frequency spectrum and angular power spectrum (APS). The
formalism is designed to calculate uncertainties due to the intrinsic cosmic
variance alone or together with instrumental noise. In particular, we predict
the potential for measuring the anisotropy of a broad generalised class of
excess radio background models using the low-frequency HERA array as an
example. We find that a HERA-like array can distinguish an RSB excess from
other sky components based on its angular clustering and spectral dependence,
even if these are quite similar to one or more of the other components -- but
only in the case that the RSB excess is relatively bright.
