  In this paper, we present the first analytical solution for performance
analysis of proportional fair scheduling (PFS) in downlink non-orthogonal
multiple access (NOMA) systems. Assuming an ideal NOMA system with an arbitrary
number of multiplexed users, we derive a closed-form solution of the optimal
power allocation for PFS and design a low-complexity algorithm for joint power
allocation and user set selection. We develop an analytical model to analyze
the throughput performance of this optimal solution based on stochastic channel
modeling. Our analytical performance is proved to be the upper bound for PFS
and is used to estimate user data rates and overall throughput in practical
NOMA systems. We conduct system-level simulations to evaluate the accuracy of
our data rate estimation. The simulation results verify our analysis on the
upper bound of PFS performance in NOMA and confirm that using the analytical
performance for data rate estimation guarantees high accuracy. The impact of
partial and imperfect channel information on the estimation performance is
investigated as well.
