In this paper, the optimal power allocation algorithm that minimizes the aggregate bit error rate (BER) of the secondary user (SU) in a downlink orthogonal frequency division multiplexing (OFDM) based cognitive radio (CR) system, while subjecting to the interference power constraint and the transmit power constraint, is investigated under the assumption that the instantaneous channel state information (CSI) of the interference links between the secondary transmitter and the primary receiver, and between the primary transmitter and the secondary receiver is perfectly known. Besides, a suboptimal algorithm with less complexity is also proposed. In order to deal with more practical situations, we further assume that only the channel distribution information (CDI) of the interference links is available and propose heuristic power allocation algorithms based on bisection search method to minimize the aggregate BER under the interference outage constraint and the transmit power constraint. Simulation results are presented to verify the effectiveness of the proposed algorithms.