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In this paper, we propose a spectrum sensing based joint rate and power allocation scheme for Cognitive Radio (CR) systems. By exploiting both its sensing result and sensing accuracy, the Secondary User (SU) adaptively determines its transmission policy to maximize its effective throughput which is achievable without requiring any Primary User's (PU's) true state information and thus is more practical than the performance metric of ergodic capacity used by . We propose an efficient algorithm to find the optimal SU rate and power allocation policy by exploiting the special structure of the problem. Based on the optimal policy, we further quantify sufficient conditions under which it is beneficial for the SU to use the PU channel even the SU sensing result indicates that the PU is busy by anticipating the happening of sensing error (but still with the PU interference constraint satisfied). Our results validate the advantages of exploiting both the information on sensing result and sensing accuracy in the overlay secondary spectrum access.