  The parameterization of the nucleon structure through Generalized Parton
Distributions (GPDs) shed a new light on the nucleon internal dynamics. For its
direct interpretation, Deeply Virtual Compton Scattering (DVCS) is the golden
channel for GPDs investigation. The DVCS process interferes with the
Bethe-Heitler (BH) mechanism to constitute the leading order amplitude of the
$eN \to eN\gamma$ process. The study of the $ep\gamma$ reaction with polarized
positron and electron beams gives a complete set of unique observables to
unravel the different contributions to the $ep \gamma$ cross section. This
separates the different reaction amplitudes, providing a direct access to their
real and imaginary parts which procures crucial constraints on the model
dependences and associated systematic uncertainties on GPDs extraction. The
real part of the BH-DVCS interference amplitude is particularly sensitive to
the $D$-term which parameterizes the Gravitational Form Factors of the nucleon.
The separation of the imaginary parts of the interference and DVCS amplitudes
provides insights on possible higher-twist effects. We propose to measure the
unpolarized and polarized Beam Charge Asymmetries (BCAs) of the $\vec{e}^{\pm}p
\to e^{\pm}p \gamma$ process on an unpolarized hydrogen target with {\tt
CLAS12}, using polarized positron and electron beams at 10.6 GeV. The azimuthal
and $t$-dependences of the unpolarized and polarized BCAs will be measured over
a large $(x_B,Q^2)$ phase space using a 100 day run with a luminosity of
0.66$\times 10^{35}$cm$^{-2}\cdot$s$^{-1}$.
