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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.
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