  Non-orthogonal multiple access (NOMA) is a technology proposed for next
generation cellular networks because of its high spectral efficiency and
enhanced user connectivity. However, in the literature the optimal joint power
and sub-carrier allocation for NOMA has been proposed for single cell only.
Consequently, a global optimal algorithm for the joint power and sub-carrier
allocation for NOMA system in multi-cell scenario is still an open problem. In
this work, we propose a polyblock optimization based algorithm for obtaining a
global optimal solution. It has reduced complexity due to a necessary and
sufficient condition for feasible successive interference cancellation (SIC).
Besides, we can adjust its optimization approximation parameter to serve as
benchmark solution or to offer suitable practical solution for multi-cell
multi-carrier NOMA systems. Numerical studies have shown its effectiveness.
