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Orthogonal frequency division multiplexing (OFDM) is a promising technology for high data rate transmission in wideband wireless systems for achieving high downlink capacities in future cellular systems. In this paper, first each user is assigned one subcarrier (channel) with best channel-to-noise ratio for the channel and random power for each channel. The goal is to minimize the overall transmission power ensuring the optimum allocation of subcarriers for users. We used a simple genetic algorithm to improve the power requirements in a multiuser environment. The simulation results indicate that the proposed genetic algorithm performs better than the Wong's (1999) subcarrier, bit, and power allocation algorithm.