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In this paper, we propose a new blind spectrum sensing method based on the polarization characteristic of the received signal, which is completely represented by the orientation of a polarization vector. We first discuss a spectrum sensing model based on polarization vectors' orientation. Then we develop the directional statistics of polarization vectors that contain both the signal and noise or noise only. The distinctive difference between the two statistics can be used to decide whether the primary signal exists or not. Based on this, by using the well-known generalized likelihood ratio test (GLRT) paradigm, a new polarization sensing algorithm GLRT-polarization vector (GLRT-PV) is proposed. By applying directional statistics, we derive closed-form expressions for the probability of false alarm and the probability of detection under both dual-polarized additive white Gaussian noise (AWGN) and Rayleigh-fading channels. Our numerical simulation and experimental results show that the proposed method exhibits better performance than other existing methods in the case of unknown primary transmitter polarization and/or presence of noise power uncertainty.