This paper studies the problem of power allocation for a two-way orthogonal frequency division multiplexing (OFDM) based cognitive radio (CR) network to maximize the ergodic capacities of the secondary users (SUs). Under the assumption that the SUs know the channel state information (CSI) of the interference links between the SUs and the primary user (PU) perfectly, the optimal power allocation algorithm under the interference and transmit power constraints is derived. In addition, we further assume that the SUs only know the channel distribution information (CDI) of the interference links and propose a heuristic algorithm under the interference outage and transmit power constraints based on Gaussian approximation. It is shown that the ergodic capacity with CDI is not degraded compared to that with perfect CSI under tight transmit power constraint. Moreover, it is shown that the interference outage constraint is satisfied even for very small number of subcarriers if an interference power margin is adopted for Gaussian approximation.