### Abstract

Previous research has identified several exact methods for the evaluation of the probability of detection for energy detectors operating on Nakagami-$$m$$ faded channels. However, these methods rely on discrete summations of complicated functions, and so can take a prohibitively long time to evaluate. In this paper, three approximations for the probability of detection in Nakagami-$$m$$ faded channels, having distinct regions of applicability, are derived. All have closed forms, and enable the fast and accurate computation of key performance metrics.

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