In this paper, we present a new Cognitive Radio (CR) paradigm based on the Full-Duplex mechanism. In the classical Full-Duplex CR (FD-CR) system, the Secondary User (SU) can examine the availability of a channel while transmitting. This fact leads to enhance the SU transmission rate. However, in this classical secondary network, SU is assumed to adopt frequency or time division duplex. In the proposed work, we analyse the CR performance with an In-Band Full-Duplex communication, i.e. SU can simultaneously receive and transmit at the same band. This scenario is accompanied with a Full-Duplex sensing, i.e. SU performs the Spectrum Sensing while transmitting. The Spectrum Sensing performance is analysed as well as proposing an adaptable detection mechanism that can perform well under such situation. Further, a study on the SU throughputs is developed in order to show the spectral efficiency of the proposed CR paradigm.