  This paper analyzes the power imbalance issue in power-domain NOMA (PD-NOMA)
in the presence of channel correlations, typically encountered on the downlink
of cellular systems when the base station antennas have an insufficient
separation. In a recent paper, the authors analyzed this issue for a typical
uplink scenario with uncorrelated channels, and the study revealed an
astounding result that the optimum in terms of average error probability is
achieved when the user signals are perfectly balanced in terms of power as in
multi-user MIMO with power control. This result led to some questioning of the
concept of PD-NOMA for uncorrelated Rayleigh fading channels. In the present
paper, we make a similar analysis for the downlink, and the study gives a very
clear insight into the influence of the power imbalance at different levels of
channel correlation. First, with full correlation (user signals transmitted
from the same antenna), the PD-NOMA concept reduces to simple signal
constellation design. The optimum is achieved when the power imbalance between
the user signals is such that the resulting constellation has uniform spacing.
Any deviation from this optimum will lead to a hierarchical constellation with
performance loss. Also, this optimum power imbalance is shown to hold for a
range of strong channel correlations, but for moderate and low correlation
values perfectly power balanced NOMA takes over as in the presence of
uncorrelated channels.
