  Many practical wireless communications systems select their transmit rate
from a finite set of modulation and coding schemes, which correspond to a set
of discrete rates. In this paper, we therefore formulate a joint coordinated
precoding and discrete rate selection problem for multiple-input
multiple-output (MIMO) multicell networks. Compared to the common assumption of
using the continuous Shannon rates as the user utilities, explicitly accounting
for the discrete rates more accurately models practical wireless communication
systems. The optimization problem that we formulate is combinatorial and
non-convex, however, and is thus hard to solve. We therefore rewrite the
problem using a discontinuous rate function, which we then bound using its
concave envelope in some domain. Based on block coordinate descent, we provide
a convergent resource allocation algorithm which can be implemented in a
semi-distributed fashion. Numerical performance evaluation shows performance
gains when the discrete rates are optimized using our model, as compared to the
traditional methods which use the continuous Shannon rates as the user
utilities.
