Abstract
In this paper, we consider the generalized energy detector (GED) for spectrum sensing in cognitive radios using a Bayesian approach. First, we derive the asymptotic distribution of the GED test statistics under both hypotheses using the central limit theorem. We then obtain a closed-form solution for the optimal detection threshold that minimizes the probability of overall error – defined as the linear combination of the false-alarm probability and mis-detection probability. The parameter of the GED is also chosen to minimize the probability of error. We validate our theory through Monte Carlo simulations. Additionally, we also investigate the performance degradation of GED under noise variance uncertainty.
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