Blind Two-Dimensional Super-Resolution and Its Performance GuaranteeDownload PDFOpen Website

Published: 01 Jan 2022, Last Modified: 16 May 2023IEEE Trans. Signal Process. 2022Readers: Everyone
Abstract: We study the problem of identifying the parameters of a linear system from its response to multiple <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unknown</i> waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the unknown waveforms. Such kind of problem is severely ill-posed and does not yield a unique solution without introducing further constraints. To fully characterize the system, we assume that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain properties. Then, we develop a blind two-dimensional (2D) super-resolution framework that applies to a large number of applications. In this framework, we show that under a minimum separation between the time-frequency shifts, all the unknowns that characterize the system can be recovered precisely and with high probability provided that a lower bound on the number of the observed samples is satisfied. The proposed framework is based on a 2D atomic norm minimization problem, which is shown to be reformulated and solved via semidefinite programming. Simulation results that confirm the theoretical findings of the paper are provided.
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