We consider a scheduling and resource allocation problem for the downlink of an OFDMA-based wireless network, where the channel estimation error is modeled by a self-noise term in the decoding process. During each time-slot this involves selecting a subset of users for transmission, determining the assignment of available subcarriers to selected users, and for each subcarrier determining the transmission power and the coding and modulation scheme used. We address this in the context of a utility-based scheduling scheme presented in earlier papers. This results in an optimization problem, which is convex for a reasonable model of the feasible rates. By exploiting the structure of this problem, we develop optimal and sub-optimal algorithms for its solution. We provide simulation results comparing different algorithms and parameter settings.