Density criteria for the identification of linear time-varying systems

Authors

Céline Aubel and Helmut Bölcskei

Reference

Proc. of IEEE International Symposium on Information Theory (ISIT), Hong Kong, China, pp. 2568-2572, June 2015.

Abstract

This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that stable identifiability is possible if the upper uniform Beurling density of the delay-Doppler support set is strictly smaller than 1/2 and stable identifiability is impossible for densities strictly larger than 1/2. The proof of this density theorem reveals an interesting relation between LTV system identification and interpolation in the Bargmann-Fock space. Finally, we introduce a subspace method for solving the system identification problem at hand.

Keywords

System identification, Beurling density, short-time Fourier transform, frame theory

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