Adaptive pulse optimization for improved sonar range accuracy

Using the theory of optimal receivers, the range accuracy of echolocating systems can be expressed as a function of pulse bandwidth and SNR through the well-known Woodward equation. That equation, however, was developed in the limit of very high SNRs and assumes that the correct peak of the cross-correlation function is known a priori. We show that for increasing levels of noise, the accuracy of the cross-correlation receiver undergoes a sharp transition from the Woodward equation for a coherent receiver to a modified Woodward equation for a semicoherent receiver. Since this transition appears at different SNRs for pulses with different center frequencies and bandwidths, it is possible to choose the optimal pulse for any given SNR. We show that the adaptive method we propose outperforms the classical cross-correlation receiver for low SNRs. The same ideas can be applied to the case of a fixed broadband signal, by performing the cross correlation at the receiver end separately in a set of frequency bands with the appropriate center frequencies and bandwidths.