In spectrum sensing, if the primary user (PU) signal and the channel noise both follow Gaussian distribution and neither of their probability distribution functions (PDFs) are known, the traditional approaches based on entropy or Likelihood Ratio Test (LRT) etc., become infeasible. To address this problem, we propose a spectrum sensing method that exploits the similarity of PDFs of two time-adjacent detected data sets with cross entropy, while accounting for achieving the detection performance of LRT which is Neyman-Pearson optimal in detecting the primary user. We show that the detection performance of the proposed method asymptotically approximates that of LRT in detecting the PU. The simulation results confirm our analysis.