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In wireless multiuser OFDM systems, dynamic resource allocation has been shown to improve the performance by exploiting the multiuser diversity. In this paper we propose a subcarrier allocation algorithm to increase the total data rate for the downlink of a variable bit rate multiuser OFDM system with proportional rate constraints subject to bit error rate and total transmit power. We assume that the channel is quasi-static where the channel status does not vary within each transmission block and the base station has perfect knowledge of subchannel gains. The proposed algorithm is based on prioritizing the critical (most sensitive) user in the system and the variance of the subchannel gains for each user is used to define the sensitivity of the user to the subcarrier allocation. Simulation results show that this algorithm achieves higher capacity with acceptable proportional fairness compared to the previous suboptimal solutions proposed by Rhee et al. in  and Shen et al. in .