The impact of signal overcontainment on cross-correlation detection performance

Cross-correlation algorithms can be used to detect a signal that is common to both channels. The current understanding of the detection performance of cross-correlation algorithms is based on the assumption that the processing and signal bandwidths are equal. Under these conditions, it is well known that the signal-to-noise ratio required to achieve a desired performance decreases as the integration time increases. However, in practice, it is usually necessary to use a processing bandwidth that is larger than the signal bandwidth (called signal overcontainment). The detection performance of cross-correlation algorithms is quantified for the signal overcontainment case. It is shown that the signal-to-noise ratio can be decreased by increasing the signal overcontainment for small signal "time-bandwidth" products.