Sensing and Recognition When Primary User Has Multiple Transmit Power Levels In this paper, a new cognitive radio (CR) scenario called Multiple Primary Transmit Power (MPTP) is investigated where the primary user (PU) could possibly work on more than one discrete transmit power levels. Different from most existing literatures where PU is assumed to operate with a constant transmit power only, this new consideration well matches the practical standards, e.g., IEEE 802.11 Series, GSM, LTE, LTE-A, etc., as well as the adaptive powering concept that a user would vary its transmit power under different situations. The primary target of CR under MPTP may still be detecting the presence of PU. However, there emerges a secondary target as to identify the PU’s transmit power level. Compared to the existing sensing strategy where the secondary user (SU) only detects the “on-off” status of PU, recognizing the transmit power level of PU achieves more “cognition” and makes the CR more intelligent. Meanwhile, SU could utilize the power level information of PU and make the subsequent design. We derive quite many closed-form results for either the threshold expressions or the performance analysis in this new CR scenario, from which many interesting points and discussions are raised. We then study the cooperative sensing schemes under MPTP and demonstrate their significant differences from traditional cooperative algorithms. Lastly, numerical examples are provided to corroborate the proposed studies.