Cognitive radio (CR) is a key solution for the problem of inefficient usage of spectral resources. Spectrum sensing in each CR aims at detecting whether a preassigned spectrum band is occupied by a primary user or not. Conventional techniques do not allow the CR to communicate with its own base station during the spectrum sensing process. So, only a part of the frame can be used for cognitive data transmission. In this paper, we introduce a new spectrum sensing framework that combines a blind source separation technique with conventional spectrum sensing techniques. In this way, the cognitive transmitter can continue to transmit during spectrum sensing, if it was in operation in the previous frame. Moreover, the accuracy is improved since the decision made by the spectrum unit in each frame depends on the decision made in the previous frame. We use Markov chain tools to model the behavior of our spectrum sensing proposal and to derive the parameters that characterize its performance. Numerical results are provided to confirm the superiority of the proposed technique compared to conventional spectrum sensing techniques.