Detection of a random radio pulse with unknown arrival time and central frequency when the regularity of the decision statistic is partially violated

Asymptotic expressions for the false alarm probability and signal miss probability are obtained for the problem of detecting a fluctuating radio pulse in the presence of white noise. The case is considered when the modulating function is rectangular and the spectral density of the random substructure of the radio pulse is continuous. The case of a continuous modulating function and rectangular spectral density of the random substructure is also considered. Limits of applicability of the asymptotic expressions are established with the help of statistical computer modeling.