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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.

Matched filter (MF) detection in spread environmentsis often seriously degraded by the mismatch between the waveform replica and the composite signal formed by the spreading environment. Typically the spreading is caused by multiple delayed reflections due to scatter extent or multipath especially in shallow water sonar applications. It is possible to recover some detector performance by incoherent summation of weighted MF realizations in a process called incoherent recombining (IR). Several IR strategies for Gaussian data that assume varying amounts of prior scattering function (SF) information are examined, their receiver operating characteristics (ROCs) computed, and compared with those of the unrealizable "prescient" receiver (PR). They include optimally weighted and unweighted versions of the maximum likelihood estimator-correlator (EC), and variations of the "at-least-one" (ALO) detector that examines sequences of MF realizations declaring a detection if at least one threshold is crossed. As might be expected, performance improves with the accuracy of the prior information incorporated in the detector formulation. He has conducted research on active sonar echolocation for 31 years with emphasis in detection and estimation, high resolution sonar imaging, scattering functions, waveform design, and wideband (wavelet) processing of sonar signals. His most recent work has been on techniques for echo detection and classification of sonar echos in spread channels based upon their space-time correlative properties. Dr. Ricker has issued over 275 reports and published extensively in IEEE Transactions, JASA, and JUA on various aspects of signal processing and echo location. He holds two patents in the signal processing area. Anthony J. Cutezo received the B.S.E.E. degree from the Pennsylvania State University (PSU), University Park, in 1975 and the M.S.E.E. degree from PSU in 1990.He has been with the Applied Research Laboratory at PSU since 1985 and is currently an Associate Research Engineer engaged in signal processing research. His interests include statistical detection and parameter estimation.

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