Cognitive radio technology has been proposed as a key solution for the problem of inefficient usage of spectrum bands. Spectrum sensing is one of the most important issues in each cognitive radio system. Classically-used spectrum sensing techniques require that the cognitive transmitter is not in operation while detecting the presence/absence of the primary signal during the sensing period. In this paper, we propose to use blind source separation algorithms such as Kurtosis metric, STFD and TALS with the aim of improving the accuracy of conventional spectrum sensing techniques based on blind source separation. Using blind source separation algorithms, cognitive radio can sense a specific spectrum band while sending its own data in this band. We also introduce a new spectrum sensing framework that combines blind source separation with conventional spectrum sensing techniques. In this way, spectrum sensing can continue to work even when the cognitive transmitter is in operation. Simulation results provided in terms of receiver operating characteristic (ROC) curves indicate that the proposed method also improves the sensing performance achieved with conventional spectrum sensing techniques.