The challenge of scheduling user transmissions on the downlink of a long term evolution (LTE) cellular communication system is addressed. A maximum rate algorithm which does not consider fairness among users was proposed in . Here, a multiuser scheduler with proportional fairness (PF) is proposed. Numerical results show that the proposed PF scheduler provides a superior fairness performance with a modest loss in throughput, as long as the user average SINRs are fairly uniform. A suboptimal PF scheduler is also proposed, which has a much lower complexity at the cost of some throughput degradation.