Statistical dependence of subpulse echoes in active sonar systems using frequency diversity

Abstract

Active sonar systems using waveforms consisting of M subpulses of different frequencies are a common method for counteracting the Rayleigh fading statistics of a single pulse echo. When frequency differences between adjacent subpulses are not large in comparison with the reciprocal of target-impulse response durations, the various subpulse echoes are not statistically independent. This lack of independence reduces the 2M statistical df that are associated with statistically independent echoes. Probability density functions of squared and summed subpulse echoes plus reverberation and noise are determined as functions of target-impulse response durations and subpulse frequency spacings. Limiting cases are shown to coincide with the classical chi-square distribution results. Effects of time constants of reverberation and noise-estimation circuits on receiver operating characteristics also will be discussed.