  In this paper, the ergodic sum-rate and outage probability of a downlink
single-antenna channel with K users are analyzed in the presence of Rayleigh
flat fading, where limited channel state information (CSI) feedback is assumed.
Specifically, only 1-bit feedback per fading block per user is available at the
base station. We first study the ergodic sum-rate of the 1-bit feedback scheme,
and consider the impact of feedback delay on the system. A closed-form
expression for the achievable ergodic sum-rate is presented as a function of
the fading temporal correlation coefficient. It is proved that the sum-rate
scales as loglogK, which is the same scaling law achieved by the optimal
non-delayed full CSI feedback scheme. The sum-rate degradation due to outdated
CSI is also evaluated in the asymptotic regimes of either large K or low SNR.
The outage performance of the 1-bit feedback scheme for both instantaneous and
outdated feedback is then investigated. Expressions for the outage
probabilities are derived, along with the corresponding diversity-multiplexing
tradeoffs (DMT). It is shown that with instantaneous feedback, a power
allocation based on the feedback bits enables to double the DMT compared to the
case with short-term power constraint in which a dynamic power allocation is
not allowed. But, with outdated feedback, the advantage of power allocation is
lost, and the DMT reverts to that achievable with no CSI feedback.
Nevertheless, for finite SNR, improvement in terms of outage probability can
still be obtained.
