  Non-orthogonal multiple access (NOMA) is a part of 5th generation (5G)
communication systems. This article presents the underpinnings and underlying
structures of the problem of NOMA user-channel allocation. Unlike the
heuristics for NOMA user-channel allocation, the presented results are
guaranteed to converge to a solution. In addition, the solutions are stable.
Generally, the results apply to any NOMA system. Unlike the orthogonal
frequency division multiple access (OFDMA) resource allocation problem, the
core matching is not the solution to NOMA resource allocation. The conditions
under which the fix-point NOMA resource allocation is guaranteed to be stable
from the viewpoint of both the base station and the NOMA users are described.
In addition, relationships of NOMA user-channel resource allocation to game
models and subgame perfect Nash equilibria are elucidated.
