This paper investigates the effect of imperfect channel state information (CSI) on the performance of radio resource management for the uplink OFDMA system. First, we prove that the imperfect CSI introduces a constellation-point dependent and error-floor symbol error rate (SER), which correspondingly yields the nonconvex and nondifferentiable throughput function in real communication systems. Then, in the uplink OFDMA system, a bisection algorithm and BA-based algorithm are proposed for single-user and multi-user cases, respectively, for the adaptive resource allocation to minimize the total transmit power.