Correlation Detection of Boundaries in Sonar Applications with Repeated Codes

In many sonar applications, there is a need to detect boundaries, such as sea bottom, sea surface, or ice sheets. The maximum operating range for those applications can be limited by the minimum required signal-to-noise ratio (SNR) at which the detection algorithms can operate with high enough fidelity. We propose two bottom detection methods that compute the covariance and correlation coefficient at a time lag, and compare the performance of these detectors with that of power detection. We derive a closed-form solution for the joint characteristic function of the real and imaginary parts of the detector signal and numerically invert it to obtain the probability density function of the amplitude under the null and alternative hypotheses. The detection probability is then computed over a range of operating conditions, including code length, number of samples, and SNR. It is shown that the performance of the three detectors is substantially similar for a wide range of conditions. However, the correlation-coefficient detector has an important advantage over the other two detectors in that it can operate on amplitude-limited signals, for which the amplitude information has been suppressed. The correlation-coefficient detector is implemented on a commercially available Doppler velocity log and tested in the field. Measured performance is shown to agree reasonably well with the theoretical predictions.