Sharing the spectrum with in-band full-duplex (FD) primary users (PU) is a challenging and interesting problem in the underlay cognitive radio (CR) systems. The self-interferenceudintroduced at the primary network may dramatically impede the secondary user (SU) opportunity to access the spectrum. In thisudwork, we attempt to tackle this problem through the use of the so-called improper Gaussian signaling. Such a signaling technique has demonstrated its superiority in improving the overall performance in interference limited networks. Particularly, we assume a system with a SU pair working in half-duplex mode that usesudimproper Gaussian signaling while the FD PU pair implements the regular proper Gaussian signaling techniques. First, we deriveuda closed form expression for the SU outage probability and an upper bound for the PU outage probability. Then, we optimize the SU signal parameters to minimize its outage probability while maintaining the required PU quality-of-service based on the average channel state information. Finally, we provide someudnumerical results that validate the tightness of the PU outage probability bound and demonstrate the advantage of employingudthe improper Gaussian signaling to the SU in order to access the spectrum of the FD PU.
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