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In this letter, we consider a more practical scenario when the primary user (PU) transmits with multiple levels of power in a cognitive radio (CR) network. The optimal spectrum sensing algorithm at the secondary user (SU) that could discriminate the PU's' transmitting power is proposed and the related performance is analyzed. We also designed a new SU transmission strategy where one transmit power is found for each estimation of the PU's power. The strategy is further optimized according to the SU's achievable rate. In the end, we validate our study by various simulations.