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In this paper, we consider resource allocation for downlink OFDMA-based cognitive radio (CR) networks. Instead of using only channel information, the statistics of the sensing information conditioned on the primary user (PU) activity is also incorporated in the design and the optimization of the resource allocation. The objective is to maximize the ergodic weighted sum-rate under total power constraint and a per subcarrier based interference power constraint to protect primary users. We develop an optimal solution method and propose a closed-form suboptimal solution with a complexity of O(KN) for K users and N subcarriers. Simulation results are provided to compare the performance of this method with other allocation schemes and to illustrate the trade-off between maximized ergodic weighted sum rate and the constraints.