A model-based estimator-correlator (EC) structure

The estimator correlator (EC) is the optimal (maximum likelihood) detector for Gaussian (or exponentially distributed) signals embedded in similarly distributed interference and is applicable to the detection of delay/Doppler spread sonar echoes. A discrete EC representation is derived by expanding continuous echo time series data with basis functions that are replications of the transmitted waveform. Scattering function (SF) models of the echo and backscattered interference spreading processes comprise prior information that is required for EC implementation. The effects of SF misinformation are illustrated by comparing the receiver operating characteristics (ROC curves) for the EC with perfect information, a mismatched EC with partial information, and the ideal but unrealizable prescient receiver. An EC implementation called hop code EC (HOPEC) is proposed that uses a frequency-shift-keyed (FSK) waveform (hop code) and is implemented with efficient FFT processing. Prior SF information is introduced via the frequency domain data covariance matrix, the elements of which are obtained as the Fourier transforms of the echo and interference scattering functions. The associated matrix Frobenius norm is shown to be a measure of the underlying scattering function variance and serves as a scalar spreading characteristic.