A universal identifier for communication channels

Abstract

Pseudo-differential operators, viewed as superpositions of time-frequency shifts, are natural models for communication channels. Channel identification is thus to find a proper input signal that induces an injective map on certain spaces of pseudodifferential operators. It is known that this is possible for channels with finite energy and spreading support area less than 1 (resp. 1/2) if the location and shape of the support area is known (resp. unknown) and the identifier depends on the spreading support. We will construct a universal input signal, which is independent of the spreading support, that identifies all such spaces of channels. The novelty of this result lies in the universality of this identifier. KeywordsPseudo-differential operators • Channel identification • Time-frequency analysis • Gabor analysis Mathematics Subject Classification 47G30 • 42B35 • 42C35 Major parts of this research was supported by the Deutsche Forschungsgemeinschaft (DFG) project 111001434 when the author resided in Germany.