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A unified theory from which the design of a large class of coherent digital communication systems can be optimally carried out is presented. In the design of digital communication systems, the error rate is the criterion which is invariably emphasized. In many digital systems, however, there is relative motion between transmitter and receiver which must be estimated by making use of Doppler frequency information. A new analysis of a general class of coherent digital systems is herein developed, in which the tradeoffs that exist between Doppler measurement capability and bit demodulation error rate are quantitatively presented. The theoretically unrecoverable power loss which exists when employing frequency division multiplexing subcarriers as compared to time division multiplexing is described. The results point out that there is significant parametric dependence of the optimal choice of system parameters on the carrier loop signal-to-noise ratio and the data rate.