Abstract: The performance of the traditional spectrum sensing methods based on the second order statistics (noise environment is assumed to be a Gaussian distribution) may degrade severely due to the heavy tail characteristics of the probability density function (PDF) of the non-Gaussian noise in the actual environment. To this end, we propose a novel fractional lower order moments based detector, which does not require any a priori knowledge about the primary user (PU), channels and noise. The non-Gaussian environment is modeled by the Gaussian mixture distribution. For both non-fading and Nakagami fading communication channels between the transmitter of the PU and the multiple antennas of the second user (SU), its detection performance in terms of the probabilities of detection and false alarm are derived by using the central limit theorem and the generalized binomial theorem. Analytical and computer simulation results show that the fractional lower order moments based detector can significantly enhance the spectrum sensing performance over the conventional energy detection with non-fading as well as fading channels in the non-Gaussian noise environments, and the multi-antenna diversity scheme exhibits better detection performance and higher utilization of spectrum resources.