  Sharing the licensed spectrum of full-duplex (FD) primary users (PU) brings
strict limitations on the underlay cognitive radio operation. Particularly, the
self interference may overwhelm the PU receiver and limit the opportunity of
secondary users (SU) to access the spectrum. Improper Gaussian signaling (IGS)
has demonstrated its superiority in improving the performance of interference
channel systems. Throughout this paper, we assume a FD PU pair that uses proper
Gaussian signaling (PGS), and a half-duplex SU pair that uses IGS. The
objective is to maximize the SU instantaneous achievable rate while meeting the
PU quality-of-service. To this end, we propose a simplified algorithm that
optimizes the SU signal parameters, i.e, the transmit power and the circularity
coefficient, which is a measure of the degree of impropriety of the SU signal,
to achieve the design objective. Numerical results show the merits of adopting
IGS compared with PGS for the SU especially with the existence of week PU
direct channels and/or strong SU interference channels.
