  Non-orthogonal multiple access (NOMA) enables power-domain multiplexing via
successive interference cancellation (SIC) and has been viewed as a promising
technology for 5G communication. The full benefit of NOMA depends on resource
allocation, including power allocation and channel assignment, for all users,
which, however, leads to mixed integer programs. In the literature, the optimal
power allocation has only been found in some special cases, while the joint
optimization of power allocation and channel assignment generally requires
exhaustive search. In this paper, we investigate resource allocation in
downlink NOMA systems. As the main contribution, we analytically characterize
the optimal power allocation with given channel assignment over multiple
channels under different performance criteria. Specifically, we consider the
maximin fairness, weighted sum rate maximization, sum rate maximization with
quality of service (QoS) constraints, energy efficiency maximization with
weights or QoS constraints in NOMA systems. We also take explicitly into
account the order constraints on the powers of the users on each channel, which
are often ignored in theexisting works, and show that they have a significant
impact on SIC in NOMA systems. Then, we provide the optimal power allocation
for the considered criteria in closed or semi-closed form. We also propose a
low-complexity efficient method to jointly optimize channel assignment and
power allocation in NOMA systems by incorporating the matching algorithm with
the optimal power allocation. Simulation results show that the joint resource
optimization using our optimal power allocation yields better performance than
the existing schemes.
