Optimum Waveforms for Correlation Detection in the Sonar Environment: Noise-Limited Conditions

Abstract

Sonar systems currently in use and under development attempt to discover the presence of an underwater target by transmitting an acoustic pulse and detecting the echo with a correlation receiver. This receiver correlates its input with time and frequency translates of a stored reference waveform, usually the same as the transmitted waveform. Owing to the presence of random multipath, there is usually not a single echo, but a multiplicity of echoes with random attenuations, time delays, and frequency shifts. Under these conditions, the detection capability of the correlation receiver is shown to be dependent upon the transmitted and reference waveforms. Necessary and sufficient conditions for optimum waveforms under a maximum signal-to-noise ratio criterion with an energy constraint are derived. A technique for finding waveforms that satisfy only a necessary condition is demonstrated, but it is conjectured that it produces the optimum waveforms. Conjectured optimum waveforms are derived for selected examples, and their performance compared to that of some conventional waveforms.