On the Signal Selection Problem for Phase Coherent and Incoherent Communication Channels

Citation

Farber, Steven Mark (1968) On the Signal Selection Problem for Phase Coherent and Incoherent Communication Channels. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2JDG-ST74. https://resolver.caltech.edu/CaltechTHESIS:11052012-151028981

Abstract

Landau and Slepian [10] have recently obtained a lower bound for the probability of error for any equienergy signal set in the infinite band Gaussian, additive noise channel. They further claim that the regular simplex signal set achieves equality in their lower bound and thereby proves the optimality of this set.

In the following paper it is proven that the simplex signals achieve equality in the lower bound of Landau and Slepian only when the dimension n is less than or equal to three. There is also shown to be an equivalence between certain optimal signal sets for the phase coherent channel described by Landau and Slepian and certain optimal signal sets for the incoherent case which have been recently discovered by Schaffner and Krieger [11] and [12].

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