Cognitive radio (CR) is proposed as a key solution to improve spectral efficiency and overcome the spectrum scarcity. Spectrum sensing is an important task in each CR system with the aim of identifying the spectrum holes and using them for secondary user's (SU) communications. Several conventional methods for spectrum sensing have been proposed such as energy detection, matched filter detection, etc. However, the main limitation of these classical methods is that the CR network is not able to communicate with its own base station during the spectrum sensing period and thus a fraction of the available primary frame cannot be exploited for data transmission. The other limitation in conventional methods is that the SU data frames should be synchronized with the primary network data frames. To overcome the above limitations, here, we propose a spectrum sensing technique based on blind source separation (BSS) that does not need time synchronization between the primary network and the CR. Moreover, by using the proposed technique, the SU can maintain its transmission with the base station even during spectrum sensing and thus higher rates are achieved by the CR network. Simulation results indicate that the proposed method outperforms the accuracy of conventional BSS-based spectrum sensing techniques.