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Power control plays a critical role in cognitive radio (CR) system to achieve a balance between efficient sharing of licensed spectrum and interferences to primary system (PU). Most of the existing works considered power control under perfect knowledge of system state (such as channel state information (CSIT) and sensing information (SIT)). In this paper, we shall focus on the design and analysis of power control scheme under imperfect knowledge of system state for SISO and OFDM systems. We obtained asymptotically optimal power control policy, taking into account of imperfect system state knowledge and packet errors due to channel outage. In addition, we found that system parameters affect asymptotic average goodput by O(-ln(rhopRp)e-sigma e 2 /1-sigma e 2) and O(e-rho p R pe-sigma e 2 /1-sigma e 2) under low and high PU activities respectively where rhopRp, sigmae 2 represents PU activity level and CSIT quality respectively.