Throughput Maximization with Short-Term and Long-Term Jain's Index Constraints in Downlink OFDMA Systems

We aim to maximize system throughput subject to constraints on both short-term and long-term fairness in terms of Jain's index in single cell downlink OFDMA systems, where the transmission power is fixed. While it is accepted that short-term fairness implies long-term fairness, we find that this is not always true. Noting that long-term performance metric is the average of short-term ones, we point out that it depends on the averaging method and the fairness definition. We prove that short-term throughput Jain's index implies long-term throughput Jain's index. Therefore, we can remove the long-term fairness constraint if it is looser than the short-term constraint. Otherwise, we heuristically replace the long-term fairness constraint by a cumulative fairness constraint. We relax the considered discrete subchannel and slot allocation problem into a continuous convex problem, which can be efficiently solved. Then, the discrete resource allocation is derived by rounding the optimal solution. The analysis indicates that the rounding error is small. Simulation results show that we obtain a good suboptimal solution with small deviations from the optimal relaxed system throughput and the Jain's index constraints. Moreover, comparing with the strategies that take into account only long-term fairness, we guarantee both long-term and short-term fairness.