Detection Characteristics with Respect to the Likelihood Ratio for Incoherent Burst Echo-Signals with Known Envelopes

Characteristics of detecting incoherent burst signals with known signal-to-noise ratios for each component are evaluated with using the likelihood ratio. The data are obtained for the case when the mixture of a signal with noise is described by the Rice distribution

In the case when the number of components of a burst echo-signal is equal to or greater than three, the direct calculation of detection characteristics is complicated because of its great volume. That is why calculations were performed for pairs composing a burst signal. Here, a new likelihood ratio corresponding to the result signal was evaluated after performing calculations for each pair. As a result, detection characteristics for twenty components of a burst signal were defined.

The relation between detection characteristics and the coefficient characterizing irregularity of the signal-to-noise ratio with respect to burst signal components was determined. This coefficient is characterized by the normalized second moment of the signal-to-noise ratio in a burst signal. Moments of high orders may be neglected.

Energy losses are evaluated for the case of a fluctuating signal and when the approximation solution rule is used for detection, which takes into account for each component of a burst signal only the data about the value of stress in a mixture of a signal with noise after passing the detector and weight coefficients determined by the burst signal envelope.