An experimental observation of a first order phase transition, the critical end point and the restoration of spontaneously broken chiral symmetry is the milestone in our understanding of the phase structure of strongly interacting matter. Herewith, electromagnetic probes (dileptons) play a unique role. An unprecedented interaction rate of the Compressed Baryonic Matter (CBM) experiment at FAIR is the key for high-precision measurements of multi-differential observables of rare dilepton signal. This contribution discusses systematic investigations of lepton pairs over the whole range of invariant masses emitted from a hot and dense fireball. An important part of the research program will be the high-precision measurement of the dilepton invariant mass distribution not only below 1 GeV/c$^2$, but in particular between 1 and 2.5 GeV/c$^2$ for different beam energies. In order to extract the continuum dilepton signals, the physical and combinatorial background of lepton pairs has to be precisely determined. Simulation results in both the di-electron and in the di-muon channel will be presented.
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