In cognitive radio networks, acquiring the position information of the primary user is critical to the communication of the secondary user. Localization of primary users can help improve the efficiency with which the spectrum is reused, because the information can be used to avoid harmful interference to the network while simultaneity is exploited to improve the spectrum utilization. Despite its inherent inaccuracy, received signal strength based on range has been used as the standard tool for distance measurements in the location detection process. Most previous works have employed the path-loss propagation model with a fixed value of the path loss exponent. However, in actual environments, the path loss exponent for each channel is different. Moreover, due to the complexity of the radio channel, when the number of channel increases, a larger number of RSS measurements are needed, and this results in additional energy consumption. In this paper, to overcome this problem, we propose using the Bayesian compressive sensing method with a calibrated path loss exponent to improve the performance of the PU localization method.