We have investigated the radiative recombination of two-dimensional (2D) electrons with holes bound to acceptors from a \ensuremath{\delta} layer, positioned at a well-defined distance from the interface, in n-type GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As single heterojunctions and have thereby characterized the system by photoluminescence and photoluminescence-excitation techniques. Using magnetotransport and magneto-optics we demonstrate that, under continuous free-carrier generation in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As by laser light, the decrease in the concentration of 2D electrons is accompanied by an enhanced mobility. The magneto-optical results show that the magnetic field dependence of the transition energies is strongly nonlinear just below filling factor 2, which we interpret as mainly due to g-factor enhancement. Finally we present the dependence of the electronic effective mass on the electron concentration, as measured from the Landau-level splitting.