We consider the problem of power allocation for the down-link of a 5G cellular system operating in the mm-wave band and serving two sets of users: fix-rate (FR) users (transmitting data at fixed rate), typically seen in device-to-device communications, and variable-rate (VR) users (that can change their transmission data rate), typically requiring high data rate services. The power allocation objective is the maximization of the spectral efficiency of VR users while ensuring that FR users get the required rate. In contrast with the existing literature on power allocation, we exploit the sparsity of the virtual mm-wave channel matrix, obtained by applying fixed discrete-Fourier transform beamformers at both the transmitter and the receiver. Exploiting the channel partial orthogonality, users are first grouped based on the mutual interference and then the power is allocated among and within groups.