  Dileptons are considered as one of the cleanest signals of the quark-gluon
plasma (QGP), however, the QGP radiation is masked by many 'background' sources
from either hadronic decays or semileptonic decays from correlated charm pairs.
In this study we investigate the relative contribution of these channels in
heavy-ion collisions from $\sqrt{s_{\rm NN}}=$ 8 GeV to 5 TeV with a focus on
the competition between the thermal QGP radiation and the semileptonic decays
from correlated $D-$meson pairs. As a 'tool' we employ the parton-hadron-string
dynamics (PHSD) transport approach to study dilepton spectra in Pb+Pb (Au+Au)
collisions in a wide energy range incorporating for the first time a fully
microscopic treatment of the charm dynamics and their semileptonic decays. We
find that the dileptons from correlated $D-$meson decays dominate the 'thermal'
radiation from the QGP in central Pb+Pb collisions at the intermediate masses
(1.2 GeV $< M <$ 3 GeV) for $\sqrt{s_{\rm NN}} > $ 40 GeV, while for
$\sqrt{s_{\rm NN}}=$ 8 to 20 GeV the contribution from $D,{\bar D}$ decays to
the intermediate mass dilepton spectra is subleading such that one should
observe a rather clear signal from the QGP radiation. We, furthermore, study
the $p_T$-spectra and the $R_{AA}(p_T)$ of single electrons at different
energies as well as the excitation function of the inverse slope of the $m_T$-
spectra for intermediate-mass dileptons from the QGP and from charm decays. We
find moderate but characteristic changes in the inverse slope parameter for
$\sqrt{s_{\rm NN}} > $ 20 GeV which can be observed experimentally in high
statistics data. Additionally, we provide detailed predictions for dilepton
spectra from Pb+Pb collisions at $\sqrt{s_{\rm NN}} = $ 5.02 TeV.
