  We consider a virtualized RAN architecture for 5G networks where the Remote
Units are connected to a central unit via a mid-haul. To support high data
rates, the midhaul is realized with a Passive Optical Network (PON). In this
architecture, the data are stored at the central unit until the scheduler
decides to transmit it through the mid-haul to an appropriate remote unit, and
then over the air at the same slot. We study an optimal scheduling problem that
arises in this context. This problem has two key features. First, multiple
cells must be scheduled simultaneously for efficient operation. Second, the
interplay between the time-varying wireless interface rates and the fixed
capacity PON needs to be handled efficiently. In this paper, we take a
comprehensive look at this resource allocation problem by formulating it as a
utility-maximization problem. Using combinatorial techniques, we derive useful
structural properties of the optimal allocation and utilize these results to
design polynomial-time approximation algorithms and a pseudopolynomial-time
optimal algorithm. Finally, we numerically compare the performance of the
proposed algorithms to heuristics which are natural generalizations of the
ubiquitous Proportional Fair algorithm.
