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Sharing the spectrum with in-band full-duplex (FD) primary users (PU) is achallenging and interesting problem in the underlay cognitive radio (CR)systems. The self-interference introduced at the primary network maydramatically impede the secondary user (SU) opportunity to access the spectrum.In this work, we attempt to tackle this problem through the use of theso-called improper Gaussian signaling. Such a signaling technique hasdemonstrated its superiority in improving the overall performance ininterference limited networks. Particularly, we assume a system with a SU pairworking in half-duplex mode that uses improper Gaussian signaling while the FDPU pair implements the regular proper Gaussian signaling techniques. First, wederive a closed form expression for the SU outage probability and an upperbound for the PU outage probability. Then, we optimize the SU signal parametersto minimize its outage probability while maintaining the required PUquality-of-service based on the average channel state information. Finally, weprovide some numerical results that validate the tightness of the PU outageprobability bound and demonstrate the advantage of employing the improperGaussian signaling to the SU in order to access the spectrum of the FD PU.

Sharing the Licensed Spectrum of Full-Duplex Systems using Improper Gaussian Signaling