  The design of a scheduling scheme is crucial for the efficiency and
user-fairness of wireless networks. Assuming that the quality of all user
channels is available to a central controller, a simple scheme which maximizes
the utility function defined as the sum logarithm throughput of all users has
been shown to guarantee proportional fairness. However, to acquire the channel
quality information may consume substantial amount of resources. In this work,
it is assumed that probing the quality of each user's channel takes a fraction
of the coherence time, so that the amount of time for data transmission is
reduced. The multiuser diversity gain does not always increase as the number of
users increases. In case the statistics of the channel quality is available to
the controller, the problem of sequential channel probing for user scheduling
is formulated as an optimal stopping time problem. A joint channel probing and
proportional fair scheduling scheme is developed. This scheme is extended to
the case where the channel statistics are not available to the controller, in
which case a joint learning, probing and scheduling scheme is designed by
studying a generalized bandit problem. Numerical results demonstrate that the
proposed scheduling schemes can provide significant gain over existing schemes.
