A Novel Full-Duplex Primary Signal Extraction Method Based on Polarization Vector Distance in Cognitive Radio Networks

In this paper, a polarization vector distance based signal extraction (PVD-SE) method for full-duplex primary users (FD-PUs) oriented cognitive radio networks (CRN) is studied. The problem of primary signal extraction in FD-PUs oriented CRN boils down to a finite hypotheses testing problem. Based on the orientation and magnitude difference of the signal samples from different FD-PUs, the proposed PVD-SE method can efficiently detect each PU's signal space by calculating polarization vector distance (PVD) between any two samples. It is found that the samples from the same PU experience relatively smaller PVD in comparison with those from different FD-PUs. As a result of the Gaussian distributed noise, the resulting PVD is non-central chi-squared distributed, which depends on the modified Bessel function of the first kind without closed-form expressions. Using large argument (LA) and small argument closed-form approximations of modified Bessel functions, the optimal extraction threshold that minimizes the extraction error probability is investigated, and analytical expressions of optimal threshold under the LA assumption are derived for amplitude modulated and non-amplitude modulated primary signals. The presented analytical results are verified by Monte Carlo simulation and the performance of PVD-SE is validated.