  In this paper, we investigate the problems of sum power minimization and sum
rate maximization for multi-cell networks with non-orthogonal multiple access.
Considering the sum power minimization, we obtain closed-form solutions to the
optimal power allocation strategy and then successfully transform the original
problem to a linear one with a much smaller size, which can be optimally solved
by using the standard interference function. To solve the nonconvex sum rate
maximization problem, we first prove that the power allocation problem for a
single cell is a convex problem. By analyzing the Karush-Kuhn-Tucker
conditions, the optimal power allocation for users in a single cell is derived
in closed form. Based on the optimal solution in each cell, a distributed
algorithm is accordingly proposed to acquire efficient solutions. Numerical
results verify our theoretical findings showing the superiority of our
solutions compared to the orthogonal frequency division multiple access and
broadcast channel.
