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In this letter, we investigate power allocation schemes for OFDM-based cognitive radio (CR) systems while taking errors due to imperfect sensing of primary user (PU) into account. The interference is introduced into PU band by CR user not only because of co-existence in side-by-side bands but also by missed detection due to imperfect sensing. We propose an optimal scheme such that the transmission capacity of CR users is maximized while keeping the total interference within a prescribed threshold and keeping the total power within a budget. As the optimal scheme can have a high complexity, low complexity suboptimal schemes have also been proposed. The performance of the proposed schemes is compared to the schemes that do not take sensing errors into consideration. Presented numerical results demonstrate the strength of our proposed schemes.