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The design of signals for digital communication over fast-fading Gaussian channels is considered; the emphasis is on nonorthogonal signaling schemes. A discrete channel model is used. Necessary and sufficient conditions on the transmitted signals are found that make the Bayes receiver independent of the channel parameters. By using a geometric interpretation of the resultant receiver a heuristic design criterion is developed. Then union bounds for particular nonorthogonal signaling schemes are evaluated. Nonorthogonal schemes based on modulation similar to differential-phase-shift-keyed (DPSK) modulation are found to use substantially less bandwidth than equivalent schemes based on generalized frequency-shift-keyed modulation.