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The authors consider the problem of fair resource allocation for multi-carrier systems. Opportunistic scheduling exploits the time-varying, location-dependent channel conditions to achieve multi-user diversity. Previous work in this area has focused on the single-user scheduling in single-carrier systems over a narrowband flat-fading channel, where only one node is scheduled at a time. In wideband multi-carrier systems, multiple nodes can be scheduled concurrently over multiple narrowband channels. In this paper, they analyze Proportional Fair Scheduling (PFS) in multi-carrier systems over a wideband frequency-selective channel. In particular, they first derive analytical expressions for the throughput of opportunistic scheduling under proportional fairness constraints in a frequency-selective channel, for both single-user and multi-user systems.
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