In this work, the agility of detection algorithms in cognitive radio is studied. A sequential change detection framework is developed to investigate the delay of detection algorithms. Three scenarios with different information about primary users' parameters available at cognitive users are considered. Optimal detection schemes that minimize the detection delay under certain false alarm constraints are developed. Minimal detection delay is characterized as a function of the false alarm probability and the Kullback-Leibler distance between signal plus noise and noise only models.
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