  The unpolarized and polarized Beam Char\-ge Asymmetries (BCAs) of the
$\vv{e}^{\pm}p \to e^{\pm}p \gamma$ process off unpolarized hydrogen are
discussed. The measurement of BCAs with the CLAS12 spectrometer at the Thomas
Jefferson National Accelerator Facility, using polarized positron and electron
beams at 10.6 GeV is investigated. This experimental configuration allows to
measure azimuthal and $t$-dependences of the unpolarized and polarized BCAs
over a large $(x_B,Q^2)$ phase space, providing a direct access to the real
part of the Compton Form Factor (CFF) ${\mathcal H}$. Additionally, these
measurements confront the Bethe-Heitler dominance hypothesis and eventual
effects beyond leading twist. The impact of potential positron beam data on the
determination of CFFs is also investigated within a local fitting approach of
experimental observables. Positron data are shown to strongly reduce
correlations between CFFs and consequently improve significantly the
determination of $\Re {\rm e} [\mathcal{H}]$.
