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The authors devise an optimization framework for Generalized Proportional Fairness (GPF) under different time scales for Amplify-and-Forward (AF) relay networks. In GPF scheduling, a single input parameter is used to change the fairness from throughput optimal, to proportionally fair and asymptotically to max-min fair. They extend the GPF scheduling to include a new input parameter, which determines the time-scale of fairness from short-term GPF to long-term GPF. They devise a low-complexity near-optimal algorithm to find schedules satisfying the given fairness criteria in a given time-scale. Simulations show that the proposed algorithm indeed allows the flexibility to change the fairness and its time-scale.
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