Measurement of Time-Variant Linear Channels

The goal of channel measurement or operator identification is to obtain complete knowledge of a channel operator by observing the image of a finite number of input signals. In this paper, it is shown that the spreading support of the operator (that is, the support of the symplectic Fourier transform of the Kohn-Nirenberg symbol of the operator) has area less than one then the operator is identifiable. If the spreading support is larger than one, then the operator is not identifiable. The shape of the support region is essentially arbitrary thereby proving a conjecture of Bello. The input signal considered is a weighted delta train where the weights are the window function of a finite Gabor system whose elements satisfy a certain robust completeness property