Optimization of a Crosscorrelator for the Case of a Linear Delay
Winslow R. Remley · The Journal of the Acoustical Society of America · 1962
An omnidirectional noise source can be detected and its asymptotic bearing determined by crosscorrelating the outputs of spatially separated sensors and detecting the peaks in the correlation curves. In general, however, if the geometry is time-varying, the statistical relationships of the signals are not stationary, and the correlation between the received signals can be seriously degraded. This problem may be obviated by employing a short integration time in the conventional correlation operation and by assuming the delay is a constant during this time interval. However, the output noise of the correlator is inversely proportional to the integration time and, consequently, to maximize the output signal-to-noise ratio, one must compromise between signal correlation and noise suppression. In this report, the output threshold signal-to-noise ratio of a crosscorrelation detector is calculated for a general signal spectrum and integration time under the assumption of a constant delay rate but of otherwise ideal conditions. It is shown that the delay-rate degradation of the output signal is equivalent to introducing a factor which is obtained by smoothing the autocorrelation function of the input signals. Subsequently, low-pass, rectangular-signal spectra are assumed, and the output signal-to-noise ratio of the crosscorrelator is numerically evaluated for various delay rates and time-bandwidth products. For zero delay rate, the output signal-to-noise is a linear function of the time-bandwidth product, but, for nonzero delay rates, optimum points exist.