Proportional fairness in multi-carrier system with multi-slot frames: Upper bound and user multiplexing algorithms

Optimal Proportional Fair Scheduling (PFS) in a multi-carrier system is a prohibitively complex combinatorial problem. In this paper we consider practical time frames with multiple time slots, where this optimal allocation becomes even more complex. Therefore, we derive bounds for the optimal proportional fair allocation, by means of convex optimization, and propose approximation algorithms where several users can be time-multiplexed on a same subchannel. With a much lower complexity than the optimal allocation, these algorithms achieve an excellent tradeoff between throughput and proportional fairness, even with the increased signaling overhead.