Effect of Pulse Duration on Echo Matched-Filter Statistics in a Shallow-Water Channel

Active sonar echo statistics (i.e., the probability density function of the match-filtered echo) are an important part of performance prediction. System design parameters such as pulse amplitude, duration and bandwidth are usually only assumed to alter the signal-to-noise-power ratio (SNR) at the detector and not the echo statistical model or its parameters. While this may be an accurate assumption for low bandwidth waveforms in a static propagation channel, it is not necessarily so when the echo is resolved or the channel is time varying. Echoes from a moored, vertical air hose were obtained during the 2013 Target and Reverberation Experiment (TREX-2013) and used to evaluate the impact of pulse duration on echo statistics. Using the scintillation index (SI) to represent the statistical character of the air-hose echo measurements, increasing pulse duration was seen to make the echoes more deterministic (i.e., to decrease SI). Assuming a time-varying Rician channel, a model was developed relating the pulse duration, channel correlation time, and ratio of coherent to incoherent power in the channel to the echo SI. Comparison with the TREX-13 air-hose measurements showed a good or excellent fit to five of the six 1-h measurement periods analyzed. Increasing pulse duration beyond the channel correlation time essentially increases the ratio of coherent to incoherent power in the echo, which improves detection performance when SNR is fixed (e.g., in a reverberation-limited scenario). If a single channel instantiation already produces a nearly deterministic echo, the performance improvement is minimal. However, when the channel is weakly Rician (e.g., a shallow-water channel at large ranges relative to water depth), the improvement can be significant.