A Theory of Active Sonar Detection

The results of a theory of echo detection developed for radar are extended to sonar for the case of narrow-banid transmitted signals. The exposition specifically omits discussion of the decision problem and the statistical nature of the whole process of detection. The theory assumes that the received signal is processed by cross correlation with a normalized replica of the expected signal. The problem of echo to noise is analyzed by sampling theory leading, in the case of Gaussian noise, to the energy principle which states that in all cases the output echo-to-noise ratio is the ratio of the input signal energy to the input noise power spectrum density. The threshold effect in detection is briefly discussed in conjunction with the problem of noise ambiguities. The problem of echo to reverberation (clutter) is treated by the use of the time and frequency shift correlation function leading to the ambiguity diagrams for various waveforms. The calculation of the relative reverberation power for short and long pulses of single frequency, FM and pseudorandom or noise-like waveforms for certain special cases is presented to illustrate the application of these principles. The paper concludes with a discussion of some limitations to the theory in terms of its narrow-band approximation, the instability of platforms and medium, and combined space-time ambiguities.