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In cognitive radio (CR) networks, secure spectrum sensing is a very important issue. The primary user emulation attack (PUEA), a special attack of the spectrum sensing technology in CR Networks, reduces the spectrum utilization obviously. And our analysis reveals the undetected PUEA can prevent unlicensed users from accessing the space licensed spectrum effectively. In this paper, we propose the maximum-minimum eigenvalue detection-based method to mitigate the effect of the undetected PUEA in CR networks with correlated signals and spatially-correlated shadow fading. In our proposed method, the spatial correlation characteristic is used to select users attending the cooperation of the spectrum sensing. Simulation results show that our proposed method can effectively mitigate the effect of the PUEA.