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On Gridless Sparse Methods for Multi-snapshot Direction of Arrival Estimation

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Abstract

The authors have recently proposed two kinds of gridless sparse methods for direction of arrival estimation in the presence of multiple snapshots that exploit joint sparsity among the snapshots and completely resolve grid mismatches of previous grid-based sparse methods. One is termed as gridless SPICE (GL-SPICE, GLS) that is a gridless version of the covariance-based SPICE method; the other uses deterministic atomic norm optimization which extends the recent super-resolution and continuous compressed sensing framework from the single- to multi-snapshot case. In this paper, we unify these two techniques by interpreting theoretically GLS as atomic norm methods in various scenarios and under different assumptions of noise. The new interpretations of GLS enable us to provide theoretical guarantees of GLS in the case of finite snapshots. Besides, they are applied to show that GLS is robust to source correlations though it was derived under the assumption of uncorrelated sources. Numerical results are also provided to validate our findings.

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Zai Yang

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Zai Yang & Lihua Xie

Authors
  1. Zai Yang
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  2. Lihua Xie
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Correspondence to Zai Yang.

Additional information

The research of this project was supported by the Ministry of Education, Republic of Singapore, under Grant AcRF TIER 1 RG78/15, the National Natural Science Foundation of China, under Grant 61603187, and the Natural Science Foundation of Jiangsu Province, China, under Grant BK20160845.

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Yang, Z., Xie, L. On Gridless Sparse Methods for Multi-snapshot Direction of Arrival Estimation. Circuits Syst Signal Process 36, 3370–3384 (2017). https://doi.org/10.1007/s00034-016-0462-9

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  • DOI: https://doi.org/10.1007/s00034-016-0462-9

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