The analytic expressions for the absorption coefficient (ACF) of a weak electromagnetic wave (EMW) caused by confined electrons in the presence of laser radiation modulated by amplitude in doped superlattices (DSL) are obtained by using the quantum kinetic equation for electrons in the case of electron-optical phonon scattering. The dependence of the ACF of a weak EMW on the temperature, frequency and superlattice parameters is analyzed. The results are numerically calculated, plotted and discussed for n-GaAs/p-GaAs DSL. The numerical results show that ACF of a weak EMW in a DSL can get negative values. So, by the presence of laser radiation modulated by amplitude, in some conditions, the weak EMW is increased. The results also show that in some conditions, the ability to increase a weak EMW can be enhanced in comparison with the use of non-modulated laser radiation. This is different from the case of the absence of laser radiation modulated by amplitude.