Resource allocation in the uplink of orthogonal frequency‐division multiple access systems is investigated. The problem of ergodic utility maximisation with discrete rates is formulated and solved using dual Lagrangian techniques. Suboptimal algorithms based on equal power allocation over the subcarriers are proposed. Results are presented and compared for the continuous and discrete rates scenario, using both the optimal solutions and the suboptimal algorithms. Equal power allocation is shown to approximate well the optimal solution in the continuous rates case, as well as in the discrete rates scenario when the number of modulation and coding schemes increases. Copyright © 2011 John Wiley & Sons, Ltd.