The method of determination of the optimum frequencies for active sonar without knowledge of the absolute values of the sonar-set parameters, but only of their frequency dependence, appears to have been originated by J. W. Horton in about 1945 and is to be found in his recent text. This theory has been simplified and extended to include search rate,time-processing gain, and the ratio of echo-to-noise-plus-reverberation. The inclusion of these new factors only slightly modifies the results obtained by maximizing echo-to-noise ratio alone because of the dominant effect of the frequency dependent exponential attenuation term in the transmission loss. Because of the octave or greater width of the maxima and the lack of precision in the knowledge of the frequency dependencies, the optimum frequencies should be looked on only as broad regions. For longer-range and hence lower-frequency active sonata operating at their optimum frequencies the energy of the pulse required per unit area or volume searched increases rapidly with the design range to a high exponent for the cases considered. This corollary is probably of little practical significance since the cost of operating power is usually small compared to other costs.
The curves of optimum frequencies versus maximum range for active sonar detection under specific sets of assumptions are presented for the more recent expressions for attenuation given by Lovett [J. Acoust. Soc. Am. 58, 620–625 (1975)] for the eastern North Pacific and Thorp [J. Acoust. Soc. Am. 42, 270 (1967)] for the western North Atlantic as corrected at low frequencies by Kibblewhite et al. [J. Acoust. Soc. Am. 60, 1040–1047 (1976)].
The method of determination of the optimum frequencies for active sonar without knowledge of the absolute values of the sonar set parameters, but only of their frequency dependence, appears to have been originated by J. W. Horton in about 1945 and is to be found in his recent text [J. W. Horton, Fundamentals of Sonar (United States Naval Institute, 1957), pp. 317–324, 344–352]. This theory has been simplified and extended to include search rate and the ratio of echo to noise plus reverberation. The inclusion of search and reverberation only slightly modifies the results obtained by maximizing echo-to-noise ratio alone because of the dominating effect of the frequency dependence of the exponential attenuation term in the transmission loss. The exact frequency dependence of the attenuation is critical as a result of this dominance. The slope of the optimum frequency vs range curve on a log-log plot is the negative of the reciprocal of the frequency exponent of the attenuation.
New methods of underwater acoustic-propagation research have been developed in which noiselike or pseudorandom signals, generated by shift-register encoders, are detected by correlation techniques. The principles and problems of three classes of experiments are discussed: (1) the signal received is crosscorrelated with a time-delayed and time-compressed replica of the transmitted signal; (2) two received signals are crosscorrelated and studied as a function of hydrophone separation; (3) the received signal is correlated with that received from a later repetition of the transmitted signal. It is shown theoretically that the results of the first class of experiments are different from and unpredictable from those obtained by employing the usual filtering and detection of impulsive or single-frequency signals. The severe problem arising from multipath interference in the second class of experiments, which is different for the multipath problem in the first class of experiments, is discussed and some solutions proposed. The essential identity of the second and third classes of experiments is discussed. A companion paper discusses the instrumentation for and execution of the experiments and presents some preliminary observations.
A discussion presented of a correlation signal-processing system for studying the distortion of underwater acoustic signals, and some of the preliminary observations obtained with this equipment are given. The system uses a 100-cps-bandwidth pseudorandom signal and both 5- and 25-sec averaging times; this gives a simultaneous time resolution of 0.01 sec and frequency resolutions of 0.2 and 0.04 cps. DElay Line TIme Compressors (DELTICs) provide a high search rate in time (range). A difference-frequency correlator, employing a bank of 11 bandpass filters as averagers, provides search over ±1- and ±0.2-cps Doppler frequency shifts, respectively. The effects have been observed of clipper normalization in the presence of multipaths and the degradation of the correlation owing to reflections at high angles from a violently moving ocean surface.
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