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Scattering functions from several experiments demonstrate that acoustic underwater channels are doubly spread. Receivers used on these channels to date have difficulty with large Doppler spreads. A receiver to perform coherent communication over Doppler spread channels is presented in this first paper of two. The receiver contains a channel tracker and a linear decoder. The tracker operates by means of a modified recursive least squares algorithm which makes use of frequency-domain filters called Doppler lines. The decoder makes use of the channel tracker coefficients in order to perform minimum mean square error decoding. This first paper treats theoretical aspects whereas the second part presents implementation issues and results.