Full-Duplex (FD) transceiver has been proposed to be used in Cognitive Radio (CR) in order to enhance the Secondary User (SU) Data-Rate. In FD CR systems, in order to diagnose the Primary User activity, SU can perform the Spectrum Sensing while operating. Making an accurate decision about the PU state is related to the minimization of the Residual Self Interference (RSI). RSI represents the error of the Self Interference Cancellation (SIC) and the receiver impairments mitigation such as the Non-Linear Distortion (NLD) of the receiver Low-Noise Amplifier (LNA). In this manuscript, we deal with the RSI problem by deriving, at the first stage, the relation between the ROC curves under FD and Half-Duplex (HD) (when SU stops the transmission while sensing the channel). Such relation shows the RSI suppression to be achieved in FD in order to establish an efficient Spectrum Sensing relatively to HD. In the second stage, we deal with the receiver impairments by proposing a new technique to mitigate the NLD of LNA. Our results show the efficiency of this method that can help the Spectrum Sensing to achieve a closed performance under FD to that under HD.