The performance in signal detection is evaluated by the error (false-alarm and missed-detection) probabilities. However, calculating these probabilities is a difficult task in practice. This paper studies the asymptotic behavior of the energy-detector and the estimator-correlator by means of the 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.

Peer Reviewed