Comparison of the deskewed short-time correlator and the maximum likelihood correlator

Abstract

Cross correlation of broad-band Doppler-scaled signals in noise is degraded by the Doppler-induced loss of signal coherence. The maximum likelihood correlator (MLC) compensates for Doppler scaling by time companding one of the two input waveforms, providing optimal differential time delay and relative time companding estimates. The price paid in using the MLC is significant implementation complexity. This paper compares a more efficient suboptimal technique, the deskewed short-time correlator (DSTC), with the MLC. Expressions for the output SNR of the MLC and DSTC are derived, as are expressions for DSTC accuracy of estimating differential time delay and relative time companding. Numerical evaluation of these expressions for low-pass white signal and noise shows that DSTC output SNR is only fractional dB below optimum, and estimation accuracy approaches the appropriate Cramer-Rao lower bounds. Comparison of implementation complexity indicates that the DSTC requires similar storage while reducing the number of computations by more than an order of magnitude. The deskewed short-time correlator is thus shown to provide implementational simplicity and near-optimal performance.