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In this paper, we propose a class of spectrum-sensing schemes for cognitive radio with receive diversity. By employing the generalized likelihood ratio test (GLRT) in the detectors on the antenna branches and exploiting a nonlinear diversity-combining strategy, the proposed scheme exhibits better performance than conventional schemes in various fading and noise environments. Exact expressions of the detection and false-alarm probabilities of the proposed scheme are derived in nonfading and Nakagami fading channels with Gaussian noise. Through computer simulations, it is confirmed that the proposed scheme provides a significant performance gain over conventional schemes in impulsive noise environments.