Abstract
Two-dimensional (2D) direction-of-arrival (DOA) estimation with arbitrary planar sparse array has attracted more interest in massive multiple-input multiple-output application. The research on this issue recently has been advanced with the development of atomic norm technique, which provides super resolution methods for DOA estimation, when the number of snapshots is limited. In this paper, we study the problem of 2D DOA estimation from the sparse array with the sensors randomly selected from uniform rectangular array. In order to identify all azimuth and elevation angles of the incident sources jointly, the 2D atomic norm approach is proposed, which can be solved by semidefinite programming. However, the computational cost of 2D atomic norm is high. To address this issue, our work further reduces the computational complexity of the problem significantly by utilizing the atomic norm approximation method based on the concept of multiple measurement vectors. The numerical examples are provided to demonstrate the practical ability of the proposed method to reduce computational complexity and retain the estimation performance as compared to the competitors.
Acknowledgements
This work is supported in part by National Natural Science Foundation of China under grant 61871400 and 61571463; the Natural Science Foundation of Jiangsu Province under grant BK20171401.
References
[1] R. Rajamäki and V. Koivunen, “Sparse active rectangular array with few closely spaced elements,” IEEE. Signal Process. Lett., vol. 25, no. 12, pp. 1820–1824, Dec. 2018.10.1109/LSP.2018.2876066Search in Google Scholar
[2] R. J. Kozick and S. A. Kassam, “Synthetic aperture pulse-echo imaging with rectangular boundary arrays,” IEEE. Trans. Image Process., vol. 2, no. 1, pp. 68–79, Jan. 1993.10.1109/83.210867Search in Google Scholar PubMed
[3] R. T. Hoctor and S. A. Kassam, “Array redundancy for active line arrays,” IEEE. Trans. Image Process., vol. 5, no. 7, pp. 1179–1183, Jul. 1996.10.1109/83.502396Search in Google Scholar PubMed
[4] P. Stoica and R. L. Moses, Spectral Analysis of Signals. Upper Saddle River, NJ, USA: Prentice Hall, 2005, pp. 263–285.10.1007/978-3-031-02525-9Search in Google Scholar
[5] R. Schmidt, A Signal Subspace Approach to Multiple Emitter Location Spectral Estimation. Palo Alto, CA, USA: Ph.D. dissertation, Dept. Elect. Eng., Stanford Univ., 1981.Search in Google Scholar
[6] R. Roy and T. Kailath, “ESPRIT-estimation of signal parameters via rotational invariance techniques,” IEEE. Trans. Acoust. Speech Signal Process., vol. 37, no. 7, pp. 984–995, Jul. 1989.10.1109/29.32276Search in Google Scholar
[7] T. Wang, B. AI, R. HE, and Z. Zhong, “Two-dimensional direction-of-arrival estimation for massive MIMO systems,” IEEE. Access, vol. 3, pp. 2122–2128, Nov. 2015.10.1109/ACCESS.2015.2496944Search in Google Scholar
[8] D. L. Donoho, “Compressed sensing,” IEEE. Trans. Inf. Theory, vol. 52, no. 4, pp. 1289–1306, Apr. 2006.10.1109/TIT.2006.871582Search in Google Scholar
[9] D. Malioutov, M. Cetin, and A. Willsky, “A sparse signal reconstruction perspective for source localization with sensor arrays,” IEEE. Trans. Signal Process., vol. 53, no. 8, pp. 3010–3022, Aug. 2005.10.1109/TSP.2005.850882Search in Google Scholar
[10] F. Shen, Y. Liu, G. Zhao, X. Chen, and X. Li, “Sparsity-Based Off-Grid DOA Estimation With Uniform Rectangular Arrays,” IEEE. Sens. J., vol. 18, no. 8, pp. 3384–3390, Apr. 2018.10.1109/JSEN.2018.2800906Search in Google Scholar
[11] Z. Tan, P. Yang, and A. Nehorai, “Joint sparse recovery method for compressed sensing with structured dictionary mismatch,” IEEE. Trans. Signal Process., vol. 62, no. 19, pp. 4997–5008, Oct. 2014.10.1109/TSP.2014.2343940Search in Google Scholar
[12] V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky, “The convex geometry of linear inverse problems,” Found. Comput. Math., vol. 12, no. 6, pp. 805–849, Dec. 2012.10.1007/s10208-012-9135-7Search in Google Scholar
[13] B. N. Bhaskar, G. Tang, and B. Recht, “Atomic norm denoising with applications to line spectral estimation,” IEEE. Trans. Signal Process., vol. 61, no. 23, pp. 5987–5999, Dec. 2013.10.1109/Allerton.2011.6120177Search in Google Scholar
[14] G. Tang, B. N. Bhaskar, P. Shah, and B. Recht, “Compressed sensing off the grid,” IEEE. Trans. Inf. Theory, vol. 59, no. 11, pp. 7465–7490, Nov. 2013.10.1109/TIT.2013.2277451Search in Google Scholar
[15] Z. Yang and L. Xie, “Exact joint sparse frequency recovery via optimization methods,” IEEE. Trans. Signal Process., vol. 64, no. 19, pp. 5145–5157, Oct. 2016.10.1109/TSP.2016.2576422Search in Google Scholar
[16] Y. Li and Y. Chi, “Off-the-grid line spectrum denoising and estimation with multiple measurement vectors,” IEEE. Trans. Signal Process., vol. 64, no. 5, pp. 1257–1269, Mar. 2016.10.1109/TSP.2015.2496294Search in Google Scholar
[17] M. Al-Sadoon, N. Ali, Y. Dama, A. Zuid, S. Jones, R. Abd-Alhameed, and J. Noras, “A new low complexity angle of arrival algorithm for 1D and 2D direction estimation in MIMO smart antenna systems,” sensors, vol. 17, pp. 2631–2650, Nov. 2017.10.3390/s17112631Search in Google Scholar PubMed PubMed Central
[18] S. Cai, X. Shi, and H. Zhu, “Direction-of-arrival estimation and tracking based on a sequential implementation of C-SPICE with an off-grid model,” sensors, vol. 17, pp. 2718–2729, Nov. 2017.10.3390/s17122718Search in Google Scholar PubMed PubMed Central
[19] J. Liu, W. Zhou, and F. Juwono, “Joint smoothed l0-norm DOA estimation algorithm for multiple measurement vectors in MIMO radar,” sensors, vol. 17, pp. 1068–1083, May. 2017.10.3390/s17051068Search in Google Scholar PubMed PubMed Central
[20] Y. Chi and Y. Chen, “Compressive two dimensional harmonic retrieval via atomic norm minimization,” IEEE. Trans. Signal Process., vol. 63, no. 4, pp. 1030–1042, Feb. 2015.10.1109/TSP.2014.2386283Search in Google Scholar
[21] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge university press: Cambridge, UK, 2004, pp. 168–169.10.1017/CBO9780511804441Search in Google Scholar
[22] Z. Tian, Z. Zhang, and Y. Wang, “Low-complexity optimization for two-dimensional direction-of-arrival estimation via decoupled atomic norm minimization,” in 2017 IEEE Int. Conf. on Acoust., Speech and Signal Processing (ICASSP), Mar. 2017, pp. 3071–3075.10.1109/ICASSP.2017.7952721Search in Google Scholar
[23] Y. Hua, “Estimating two-dimensional frequencies by matrix enhancement and matrix pencil,” IEEE. Trans. Signal Process., vol. 40, no. 9, pp. 2267–2280, Sep. 1992.10.1109/ICASSP.1991.150104Search in Google Scholar
[24] M. Grant, S. Boyd, and Y. Ye, “CVX: Matlab software for disciplined convex programming,” 2008.Search in Google Scholar
[25] Y. Chen and Y. Chi, “Robust spectral compressed sensing via structured matrix completion,” IEEE. Trans. Inf. Theory, vol. 60, no. 10, pp. 6576–6601, Oct. 2014.10.1109/TIT.2014.2343623Search in Google Scholar
[26] J. Shi, G. Hu, X. Zhang, and S. Jin, “Smoothing matrix set-based MIMO radar coherent source localisation,” Int. J. Electron., vol. 105, no. 8, pp. 1345–1357, Feb. 2018.10.1080/00207217.2018.1440433Search in Google Scholar
[27] J. Shi, G. Hu, X. Zhang, F. Sun, and H. Zhou, “Sparsity-based 2-D DOA estimation for co-prime array: from sum-difference co-array viewpoint,” IEEE. Trans. Signal Process., vol. 60, no. 10, pp. 6576–6601, Oct. 2014.Search in Google Scholar
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