Signal-design considerations for the noncoherent Gaussian channel (Corresp.)

The choice of equiprobable equipowered narrow-band waveforms of equal duration for the noncoherent communication system is considered. With the bandwidth constrained, the problem of finding optimal signal sets of given dimension is formulated as a variational one. For dimensionality , , where [ ] denotes "integer part of," and , signal inner-product matrices consisting of regular simplices placed mutually orthogonal to one another, are local extremals of the probability of error, thereby establishing a marked similarity between the coherent and noncoherent signal-design problems.