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Achieving reliable underwater communication in shallow water is a difficult task because of the random time-varying nature of multipath propagation. When the product of Doppler-related signal bandwidth spread and multipath-related time spread of the channel is larger than one, some types of adaptive signal processing may not work very well. In this paper, various methods of coherent space-time processing are compared for a condition of a marginally overspread channel operating at 50 kHz. Various combinations of suboptimal spatially adaptive and time adaptive methods are considered. The coherent path beamformer (CPB) and recursive least squares (RLS) adaptive beamformer, both in combination with RLS time filtering, are analyzed. Also considered in the analysis is the combined RLS space-time optimal adaptive processor. Many experiments using broad-band phase-shift-keyed transmissions in shallow water have been conducted to provide data for testing these various processing methods. Because of the rapid time variation of the multipath, the product of bandwidth spread and time spread at this test site approached unity. In this environment, a suboptimal approach consisting of the adaptive beamformer followed by RLS equalization reduced reverberation and transmission errors.