On α-proportional fair packet scheduling in OFDMA downlink

We consider resource allocation in block fading downlink Orthogonal Frequency Division Multiple access systems with infinitely divisible resources. The proportional fairness of the scheduler is characterized by a parameter α. In block-fading channels, one-shot utility maximization may be performed. We investigate properties of resulting α-Proportionally Fair scheduling decisions. We find that an optimal schedule is cycle free: no K users share K resources so that each gets a fraction of at least two resources. Most scheduling weights vanish. For N users sharing M resources, there are at most N +M - 1 non-zero scheduling weights.