  In this work, we propose a globally optimal joint successive interference
cancellation (SIC) ordering and power allocation (JSPA) algorithm for the
sum-rate maximization problem in downlink multi-cell non-orthogonal multiple
access (NOMA) systems. The proposed algorithm is based on the exploration of
base stations (BSs) power consumption, and closed-form of optimal powers
obtained for each cell. Although the optimal JSPA algorithm scales well with
larger number of users, it is still exponential in the number of cells. For any
suboptimal decoding order, we propose a low-complexity near-optimal joint rate
and power allocation (JRPA) strategy in which the complete rate region of users
is exploited. Furthermore, we design a near-optimal semi-centralized JSPA
framework for a two-tier heterogeneous network such that it scales well with
larger number of small-BSs and users. Numerical results show that JRPA highly
outperforms the case that the users are enforced to achieve their channel
capacity by imposing the well-known SIC necessary condition on power
allocation. Moreover, the proposed semi-centralized JSPA framework
significantly outperforms the fully distributed framework, where all the BSs
operate in their maximum power budget. Therefore, the centralized JRPA and
semi-centralized JSPA algorithms with near-optimal performances are good
choices for larger number of cells and users.
