  We consider the problem of simultaneous user-scheduling, power-allocation,
and rate-selection in an OFDMA downlink, with the goal of maximizing expected
sum-utility under a sum-power constraint. In doing so, we consider a family of
generic goodput-based utilities that facilitate, e.g., throughput-based
pricing, quality-of-service enforcement, and/or the treatment of practical
modulation-and-coding schemes (MCS). Since perfect knowledge of channel state
information (CSI) may be difficult to maintain at the base-station, especially
when the number of users and/or subchannels is large, we consider scheduling
and resource allocation under imperfect CSI, where the channel state is
described by a generic probability distribution. First, we consider the
"continuous" case where multiple users and/or code rates can time-share a
single OFDMA subchannel and time slot. This yields a non-convex optimization
problem that we convert into a convex optimization problem and solve exactly
using a dual optimization approach. Second, we consider the "discrete" case
where only a single user and code rate is allowed per OFDMA subchannel per time
slot. For the mixed-integer optimization problem that arises, we discuss the
connections it has with the continuous case and show that it can solved exactly
in some situations. For the other situations, we present a bound on the
optimality gap. For both cases, we provide algorithmic implementations of the
obtained solution. Finally, we study, numerically, the performance of the
proposed algorithms under various degrees of CSI uncertainty, utilities, and
OFDMA system configurations. In addition, we demonstrate advantages relative to
existing state-of-the-art algorithms.
