Abstract—Cognitive radio networks require fast and reliable spectrum sensing to achieve high network utilization by secondary users. Current optimization approaches to spectrum sensing to-date have focussed on maximizing aggregate throughput while considering only a single parameter variable pertinent to sensing, notably the threshold or duration, but not both. In this work, we consider joint minimization of the average detection time for finding a spectrum hole as a function of both parameters. We show that the resulting non-convex problem is actually biconvex under practical conditions and solve for a global optimum detection time. Numerical results show that the proposed approach can considerably improve system performance in terms of the mean time to detect a spectrum hole. I
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