Passive detection of Gaussian signals with narrow‐band and broad‐band components

The performance of the optimum passive detector for Gaussian signals is studied for TW (observation interval—signal spectral bandwidth) products of the order of unity. Detection and false‐alarm probabilities are evaluated for carrier‐symmetric bandpass signals. Conditions are then obtained under which it is preferable to use either the narrow‐band or the broad‐band component of the received signal. Though in most situations the results advocate processing the higher‐energy component, there are situations of practical importance where the lower‐energy component may be preferred.