Polarization Jones Vector Distance Statistics-Based Full-Duplex Primary Signal Extraction for Cognitive Radios

Abstract

The problem of full-duplex primary user (PU) signal space extraction is studied for cognitive radios, and polarization Jones vector distance (PJVD) under generalized likelihood ratio test (GLRT) paradigm is used as the extraction metric. Based on the orientation and magnitude difference of the signal samples from different PUs, the GLRT-based PJVD (GLRT-PJVD) method can efficiently detect each PU’s signal space by calculating the PJVD between any two samples. It is found that the samples from the same PU experience smaller PJVD in comparison with those from different PUs. Due to the Gaussian distributed noise, the resulting PJVD is non-central chi-squared distributed. Based on the distribution, the extraction metric is constructed as the likelihood ratio of PJVD. A closed-form expression of the optimal threshold is derived under the large argument assumption for amplitude modulated primary signals. Theoretical analysis shows that the proposed GLRT-PJVD method outperforms the polarization similarity-based method in terms of both error probability and computational complexity. It is revealed that the performance gain is proportional to the SUs’ antenna number, the PUs’ polarization angle, and the signal amplitude difference. The analytical results are verified by the Monte Carlo simulation, and the performance of GLRT-PJVD is validated.