Throughput maximization with short- and long-term Jain's index guarantees in OFDMA systems

In wireless resource allocation, improving system throughput and simultaneously enhancing user fairness are two fundamental but contradictory objectives. As for fairness, both short-term and long-term fairness are of significant importance. However, less effort has been dedicated to explore the optimal tradeoff between system throughput and the two mentioned fairness in terms of widely used Jain's index. In this context, we aim to maximize system throughput subject to constraints on both short-term and long-term fairness in single cell downlink OFDMA systems. The difficulty of this issue lies in that the considered subchannel and slot allocation problem is a nonlinear integer programming problem, and furthermore seems to be non-causal. To overcome these challenges, we first relax the integer variables. Second, we prove that short-term fairness ensures long-term fairness so that the long-term fairness constraint is redundant and can be removed. Third, the problem is decomposed into a sequence of short-term convex optimization problems that can be easily solved. Numerical results show that the proposed method achieves a good suboptimal solution with small deviations from the optimal relaxed system throughput and the Jain's index constraint.