  We consider the problem of scheduling and power allocation for the downlink
of a 5G cellular system operating in the millimeter wave (mmWave) band and
serving two sets of users: fix-rate (FR) users typically seen in
device-to-device (D2D) communications, and variable-rate (VR) users, or high
data rate services. The scheduling objective is the weighted sum-rate of both
FR and VR users, and the constraints ensure that active FR users get the
required rate. The weights of the objective function provide a trade-off
between the number of served FR users and the resources allocated to VR users.
For mmWave channels the virtual channel matrix obtained by applying fixed
discrete-Fourier transform (DFT) beamformers at both the transmitter and the
receiver is sparse. This results into a sparsity of the resulting multiple
access channel, which is exploited to simplify scheduling, first establishing
an interference graph among users and then grouping users according to their
orthogonality. The original scheduling problem is solved using a graph-coloring
algorithm on the interference graph in order to select sub-sets of orthogonal
VR users. Two options are considered for FR users: either they are chosen
orthogonal to VR users or non-orthogonal. A waterfilling algorithm is then used
to allocate power to the FR users.
