Asymptotic error exponents in energy-detector and estimator-correlator signal detection

Abstract

The performance in signal detection is evaluated by the error (false-alarm and missed-detection) probabilities.However,calculating these probabilities is a difficult taskin practice. This paper studies the asymptotic behavior of the energy-detector and th eestimator-correlator by mean soft he Stein’s lemma.The Stein’s lemma is an information-theory result that provides the best achievable error exponent in the error probabilities when the number of observations goes to infinity.The derived closed form expressions explain how detection performance is driven by the detector parameters and the second-order statistics of the problem.More specifically, it is shown that the error exponents depend on the signal-to-noise ratio (SNR) and the observation size.The prime focus is to establish a link between the required observation size for a fixed error probability as a function of the SNR.Numerical results show the tightness of the lemma.