Signal Design for Low-Error Probability in Fading Dispersive Channels

The signal design problem for FSK communication via fading dispersive channels is considered. The channel is modeled as a linear filter whose time-varying impulse response is a sample function from a zero-mean Gaussian random field of arbitrary WSSUS type. The additive noise component in the received waveforms is supposed to be a zero-mean white Gaussian random process, and maximum likelihood demodulation is assumed. The signal design procedure here adopted consists of minimizing a known upper bound on the error probability, whereas the previous similar design method by Daly intended maximizing an upper bound on the detection probability for radar-astronomy targets. Though with slightly different optimal numerical values, here, as in Daly's problem, the signal design depends on a single parameter which is a simple functional of the channel timefrequency covariance function and of the signal envelope ambiguity function. A detailed example shows how the results of this concise paper can be used to optimize signal parameters and to predict the performance loss due to nonoptimal signal envelopes.