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.To tackle this problem, we use the so-called improper Gaussian signaling.Particularly, we assume a system with a SU pair working in a half-duplex modethat uses improper Gaussian signaling while the FD PU pair implements theregular proper Gaussian signaling. First, we derive a closed form expressionand an upper bound for the SU and PU outage probabilities, respectively.Second, we optimize the SU signal parameters to minimize its outage probabilitywhile maintaining the required PU quality-of-service based on the averagechannel state information (CSI). Moreover, we provide the conditions to reapmerits from employing improper Gaussian signaling at the SU. Third, we designthe SU signal parameters based on perfect knowledge of its direct linkinstantaneous CSI and investigate all benefits that can be achieved at both theSU and PU. Finally, we provide some numerical results that demonstrate theadvantages of using improper Gaussian signaling to access the spectrum of theFD PU.
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