Abstract
Grid mismatch is the main drawback in grid-based sparse representation. For DOA estimation, off-grid problem degrades the accuracy of angle estimation. In order to solve this problem, a dictionary learning-based off-grid DOA estimation method is proposed. Firstly, we calculate the sampling covariance matrix, then based on covariance matrix model, we formulate the DOA estimation as a sparse representation problem with Khatri-Rao product dictionary. In the proposed method, two stage iteration strategy is utilized to address the off-grid problem. In the first stage, the coarse estimation is attained by the grid-based sparse DOA estimation; in the second stage, the dictionary perturbation parameter is learned based on gradient descent method for improving the accuracy of DOA estimation. Simulation results verify the effectiveness of the proposed method.
This work was supported in part by the National Undergraduate Training Program for Innovation and Entrepreneurship under Grant 201811078117 and the Natural Science Foundation of Guangdong Province of China under Grant 2018A030310338.
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References
Malioutov D, Cetin M, Willsky AS (2005) A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans Signal Process 53:3010–3022
Yin J, Chen T (2006) Direction-of-arrival estimation using a sparse representation of array covariance vectors. IEEE Trans Signal Process 59:4489–4493
Wu X, Zhu WP, Yan J (2016) Direction-of-arrival estimation based on Toeplitz covariance matrix reconstruction. In: 2016 IEEE international conference on acoustics, speech and signal processing. IEEE Press, Shanghai, pp 3071–3075
Tan W, Feng X, Ye X et al (2018) Direction-of-arrival of strictly non-circular sources based on weighted mixed-norm minimization. EURASIP J Wirel Commun Netw 225
Bernhardt S, Boyer R, Marcos S et al (2016) Compressed sensing with basis mismatch: Performance bounds and sparse-based estimator. IEEE Trans Signal Process 64:3483–3494
Ekanadham C, Tranchina D, Simoncelli EP (2011) Recovery of sparse translation-invariant signals with continuous basis pursuit. IEEE Trans Signal Process 59:4735–4744
Yang Z, Xie L, Zhang C (2013) Off-grid direction of arrival estimation using sparse Bayesian inference. IEEE Trans Signal Process 61:38–43
Zhu H, Leus G, Giannakis GB (2011) Sparsity-cognizant total least-squares for perturbed compressive sampling. IEEE Trans Signal Process 59:2002–2016
Jagannath R, Leus G, Pribić R (2012) Grid matching for sparse signal recovery in compressive sensing. In: 2012 9th European radar conference. Amsterdam, pp 111–114
Gretsistas A, Plumbley MD (2012) An alternating descent algorithm for the off-grid DOA estimation problem with sparsity constraints. In: Proceedings of the 20th European signal processing conference. Bucharest, pp 874–878
Teke O, Gurbuz AC, Arikan O (2013) Perturbed orthogonal matching pursuit. IEEE Trans Signal Process 61:6220–6231
Camlica S, Yetik IS, Arikan O (2019) Sparsity based off-grid blind sensor calibration. Digital Signal Process 84:80–92
Wu X, Zhu WP, Yan J et al (2018) Two sparse-based methods for off-grid direction-of-arrival estimation. Signal Process 142:87–95
Zhang Z, Wu X, Li C et al (2019) An \(\ell _p\)-norm based method for off-grid DOA estimation. Circuits Syst Signal Process 38:904–917
Zamani H, Zayyani H, Marvasti F (2016) An iterative dictionary learning-based algorithm for DOA estimation. IEEE Commun Lett 20:1784–1787
Tan W, Feng X, Tan W et al (2018) An iterative adaptive dictionary learning approach for multiple snapshot DOA estimation. In: 2018 14th IEEE international conference on signal processing (ICSP). Beijing, pp 214–219
Tan W, Feng X (2019) Covariance matrix reconstruction for direction finding with nested arrays using iterative reweighted nuclear norm minimization. Int J Antenna Propag
Stoica P, Nehorai A (1989) Music, maximum likelihood, and Cramer-Rao bound. IEEE Trans Acoust Speech Signal Process 37:720–741
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Tan, W., Zheng, C., Li, J., Tan, W., Li, C. (2020). A Dictionary Learning-Based Off-Grid DOA Estimation Method Using Khatri-Rao Product. In: Liang, Q., Wang, W., Liu, X., Na, Z., Jia, M., Zhang, B. (eds) Communications, Signal Processing, and Systems. CSPS 2019. Lecture Notes in Electrical Engineering, vol 571. Springer, Singapore. https://doi.org/10.1007/978-981-13-9409-6_29
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DOI: https://doi.org/10.1007/978-981-13-9409-6_29
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