  Optimizing non-orthogonal multiple access (NOMA) in multi-cell scenarios is
much more challenging than the single-cell case because inter-cell interference
must be considered. Most papers addressing NOMA consider a single cell. We take
a significant step of analyzing NOMA in multi-cell scenarios. We explore the
potential of NOMA networks in achieving optimal resource utilization with
arbitrary topologies. Towards this goal, we investigate a broad class of
problems consisting in optimizing power allocation and user pairing for any
cost function that is monotonically increasing in time-frequency resource
consumption. We propose an algorithm that achieves global optimality for this
problem class. The basic idea is to prove that solving the joint optimization
problem of power allocation, user pair selection, and time-frequency resource
allocation amounts to solving a so-called iterated function without a closed
form. We prove that the algorithm approaches optimality with fast convergence.
Numerically, we evaluate and demonstrate the performance of NOMA for multi-cell
scenarios in terms of resource efficiency and load balancing.
