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The radiometer or energy detector is useful in detecting target signals about which little is known. A practical radiometer is described and analyzed for the AWGN and Rayleigh channels with and without diversity combining. The practical implications of bandwidth, the number of samples processed, and imperfect noise-power estimation are examined. The radiometer has been criticized because of its alleged sensitivity to imperfect noise-power estimates. Conditions under which the noise-power estimation error is small are discussed. It is shown that the effects of this error on the probability of detection of the target signal can be kept small.