  In this paper, we investigate upper and lower bounds on the capacity of
two-user fading broadcast channels where one of the users has a constant
(non-fading) channel. We use the Costa entropy power inequality (EPI) along
with an optimization framework to derive upper bounds on the sum-capacity and
superposition coding to obtain lower bounds on the sum-rate for this channel.
For this fading broadcast channel where one channel is constant, we find that
the upper and lower bounds meet under special cases, and in general, we show
that the achievable sum-rate comes within a constant of the outer bound.
