Efficient Super-Resolution Two-Dimensional Harmonic Retrieval with Multiple Measurement Vectors

Journal article (2022)

Authors

Yu Zhang Nanjing University of Aeronautics and Astronautics
Yue Wang George Mason University
Zhi Tian George Mason University
G.J.T. Leus Signal Processing Systems - EEMCS
Gong Zhang Nanjing University of Aeronautics and Astronautics
Research Group
Signal Processing Systems (EEMCS) (TU Delft)
Copyright: © 2022 Yu Zhang, Yue Wang, Zhi Tian, G.J.T. Leus, Gong Zhang
DOI
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https://doi.org/10.1109/TSP.2022.3150964
Minimization Super-resolution Computational complexity Signal resolution Harmonic analysis 2D harmonic retrieval Atomic measurements Covariance matrices D-ANM MMV RR transformation Superresolution
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Published Date

2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Microelectronics

Research Group

Signal Processing Systems

Abstract

This paper develops an efficient solution for super-resolution two-dimensional (2D) harmonic retrieval from multiple measurement vectors (MMV). Given the sample covariance matrix constructed from the MMV, a gridless compressed sensing approach is proposed based on the atomic norm minimization (ANM). In the approach, our key step is to perform a redundancy reduction (RR) transformation that effectively reduces the large problem size at hand, without loss of useful frequency information. For uncorrelated sources, the transformed 2D covariance matrices in the RR domain retain a salient structure, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. Accordingly, the decoupled ANM (D-ANM) framework can be applied for super-resolution 2D frequency estimation. Moreover, the resulting RR-enabled D-ANM technique, termed RR-D-ANM, further allows an efficient relaxation under certain conditions, which leads to low computational complexity of the same order as the 1D case. Simulation results verify the advantages of our solutions over benchmark methods, in terms of higher computational efficiency and detectability for 2D harmonic retrieval.