Cognitive radio is regarded as a core technology to support wireless information systems. Spectrum sensing is one of the key steps to achieve cognitive radio technology. To address this problem in the presence of Alpha stable noise in wireless communication systems, we propose a nonparametric autocorrelation method, which takes advantages of the characteristics of signal autocorrelation and noise nonstationarity. The autocorrelated signal is distinguished from Alpha stable noise. As a result, the proposed method is immune from noise uncertainty. Simulation results show the validity of the proposed method under Alpha stable noise, for example, impulsive noise in wireless information systems.