Estimation of coherent detection performance for spread scattering in reverberation-noise mixtures

Narrow-band matched filter processing gain is estimated for medium- and high-frequency active sonars for which the random backscattering processes are assumed to be wide sense stationary in time frequency and uncorrelated in delay-Doppler wide sense stationary and uncorrelated scattering [WSSUS conditions]. Echo and reverberation processes that are WSSUS are described by two-dimensional scattering functions defined in the delay-Doppler plane. The average receiver responses are estimated from the convolution of the appropriate scattering function with the waveform ambiguity function. Estimates of matched filter processing gain are derived for continuous wave (CW) linear frequency modulation (LFM), and discrete frequency shift keyed (FSK) (hop code) waveforms reflected from point and uniform delay spread scatterers masked by reverberation. These bound matched filter performance for a particular waveform and interference distribution since most delay spread scattering falls somewhere between these extremes. The scattering and ambiguity functions are modeled by bounded constant amplitude functions in delay-Doppler that permit the convolutions to be approximated by overlapping area calculations. The results are presented in tabular form as simple formulas that are functions of the reverberation, noise, and waveform parameters. The estimates are shown to be consistent with processing gain measurements made from multiple realizations of synthesized and in-water data.