The effect of the imperfect channel state information (CSI) on the system performance of radio resource management is addressed for a downlink OFDMA system. Differing from the previous works, it is shown that the imperfect CSI introduces a signal-and-power dependent noise term, and then a new method is proposed to evaluate the utility function. Numerical simulations show that the signal-and-power dependent noise yields a non-negligible degradation to the system performance.