  We consider a cooperative non-orthogonal multiple access system with radio
frequency energy harvesting, in which a user with good channel harvests energy
from its received signal and serves as a decode-and-forward relay for enhancing
the performance of a user with poor channel. We here aim at maximizing the
weighted sum rate of the system by optimizing the power allocation coefficient
used at the source and the power splitting coefficient used at the user with
good channel. By exploiting the specific structure of the considered problem,
we propose a low-complexity one-dimensional search algorithm which can provide
optimal solution to the problem. As a benchmark comparison, we derive analytic
expressions and simple high signal-to-noise ratio (SNR) approximations of the
ergodic rates achieved at two users and their weighted sum with fixed values of
the power allocation and the power splitting coefficients, from which the
scaling of the weighted sum in the high SNR region is revealed. Finally, we
provided numerical results to demonstrate the validity of the optimized scheme.
Index Terms-Cooperative NOMA, RF-energy harvesting, weighted sum rate analysis
and optimization.
