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Multidimensional Systems and Signal Processing

, Volume 30, Issue 1, pp 239–256 | Cite as

Two-dimensional DOA estimation for generalized coprime planar arrays: a fast-convergence trilinear decomposition approach

  • Xiaofei Zhang
  • Wang ZhengEmail author
  • Weiyang Chen
  • Zhan Shi
Article
  • 137 Downloads

Abstract

In this paper, we investigate the problem of two-dimensional (2D) direction of arrival (DOA) estimation of multiple signals for generalized coprime planar arrays consisting of two rectangular uniform planar subarrays. We propose a fast-convergence trilinear decomposition approach, which uses propagator method (PM) as the initialization of the angle estimation to speed the convergence of trilinear decomposition. The received signal of each subarray can be fitted into a trilinear model or parallel factor (PARAFAC) model so that the trilinear alternating least square algorithm can be used to estimate the angle information. Meanwhile, the necessary initialization of DOA estimates can be achieved via PM, which endows the proposed approach a fast convergence and subsequently results in a low complexity. Specifically, we eliminate the ambiguous estimates by utilizing the coprime property and the true DOA estimates can be achieved by selecting the nearest ones of all DOA estimates. The proposed approach can obtain the same estimation performance as the conventional PARAFAC algorithm, but with a low computational cost. Numerical simulation results are provided to validate the effectiveness and superiority of the proposed algorithm.

Keywords

Trilinear decomposition Parallel factor Generalized coprime planar array Two-dimensional direction of arrival Propagator method Fast convergence 

Notes

Acknowledgements

This work is supported by China NSF Grants (61371169, 61601167), Jiangsu NSF (BK20161489), the open research fund of State Key Laboratory of Millimeter Waves, Southeast University (No. K201826), and the Fundamental Research Funds for the Central Universities (No. NE2017103).

References

  1. Boudaher, E., Ahmad, F., Amin, M., & Hoorfar, A. (2015). DOA estimation with co-prime arrays in the presence of mutual coupling. In Proceeding European signal processing conference (pp. 2830–2834), Nice, France.Google Scholar
  2. Bro, R. (1997). PARAFAC: Tutorial and application. Chemometrics Intell. Lab. Syst., 38, 149–171.Google Scholar
  3. Cai, J. J., Li, P., & Zhao, G. Q. (2013). Two-dimensional DOA estimation with reduced-dimension MUSIC. Journal of Xi’an Electronic and Science University, 40(3), 81–86.Google Scholar
  4. Cao, R., Zhang, X., & Wang, C. (2015). Reduced-dimensional PARAFAC-based algorithm for joint angle and Doppler frequency estimation in monostatic MIMO radar. Wireless Personal Communications, 80(3), 1231–1249.Google Scholar
  5. Chen, W. Y., & Zhang, X. F. (2014). Improved spectrum searching generalized-ESPRIT algorithm for joint DOD and DOA estimation radar with non-uniform linear arrays. Journal of Circuits System & Computers, 23(8), 229–236.Google Scholar
  6. Chen, Y. M., Lee, J. H., & Yeh, C. C. (1993). Two-dimensional angle-of-arrival estimation for uniform planar arrays with sensor position errors. IEE Proceedings F Radar & Signal Processing, 140(1), 37–42.Google Scholar
  7. Cheng, Y., Yu, R., Gu, H., & Su, W. (2013). Multi-SVD based subspace estimation to improve angle estimation accuracy in bistatic MIMO radar. Signal Processing, 93(7), 2003–2009.Google Scholar
  8. Haardt, M., Roemer, F., & Galdo, G. D. (2008). Higher-order SVD-based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems. IEEE Transactions on Signal Processing, 56(7), 3198–3213.MathSciNetzbMATHGoogle Scholar
  9. Harshman, R. A. (1970). Foundation of the PARAFAC procedure: Model and conditions for an ‘explanatory’ multi-mode factor analysis. UCLA Working Papers in Phonetics, 16, 1–84.Google Scholar
  10. Harshman, R. A. (1972). Determination and proof of minimum uniqueness conditions for PARAFAC. UCLA Working Papers in Phonetics, 22, 111–117.Google Scholar
  11. Kolda, T. G., & Bader, B. W. (2009). Tensor decompositions and applications. Siam Review, 51(3), 455–500.MathSciNetzbMATHGoogle Scholar
  12. Krim, H., & Viberg, M. (1996). Two decades of array signal processing research: The parametric approach. IEEE Signal Processing Magazine, 13(4), 67–94.Google Scholar
  13. Kruskal, J. B. (1977). Three-way arrays: Rank and uniqueness of trilinear decompositions. Linear Algebra and Applications, 18, 95–138.zbMATHGoogle Scholar
  14. Li, J. F., & Zhang, X. F. (2013). Closed-form blind 2D-DOD and 2D-DOA estimation for MIMO radar with arbitrary arrays. Wireless Personal Communications, 69(1), 175–186.Google Scholar
  15. Li, J. F., Zhang, X. F., & Chen, H. (2012). Improved two-dimensional DOA estimation algorithm for two-parallel uniform linear arrays using propagator method. Signal Processing, 92(12), 3032–3038.Google Scholar
  16. Liu, C. L., & Vaidyanathan, P. P. (2016). Super nested arrays: Linear sparse arrays with reduced mutual coupling—Part I: Fundamentals. IEEE Transactions on Signal Processing, 64(16), 1–1.MathSciNetGoogle Scholar
  17. Liu, K., So, H. C., Costa, J. P. C. L. D., & Huang, L. (2013). Core consistency diagnostic aided by reconstruction error for accurate enumeration of the number of components in PARAFAC models. IEEE international conference on acoustics, speech and signal processing (pp. 6635–6639).Google Scholar
  18. Liu, S., Yang, L. S., Wu, D. C., & Huang, J. H. (2014). Two-dimensional DOA estimation using a co-prime symmetric cross array. Progress in Electromagnetics Research C, 54, 67–74.Google Scholar
  19. Mathews, C. P., & Zoltowski, M. D. (1994). Eigen-structure techniques for 2-D angle estimation with uniform circular array. IEEE Transactions on Signal Processing, 42(9), 2395–2407.Google Scholar
  20. Pal, P., & Vaidyanathan, P. P. (2011a). Coprime sampling and the MUSIC algorithm. In Proceeding of the digital signal processing workshop and IEEE signal processing education workshop (vol. 47, pp. 289–294).Google Scholar
  21. Pal, P., & Vaidyanathan, P. P. (2011b). Theory of sparse coprime sensing in multiple dimensions. IEEE Transactions on Signal Processing, 59(8), 3592–3608.MathSciNetzbMATHGoogle Scholar
  22. Pal, P., & Vaidyanathan, P. P. (2011c). Sparse sensing with coprime samplers and arrays. IEEE Transactions on Signal Processing, 59(2), 573–586.MathSciNetzbMATHGoogle Scholar
  23. Sidiropoulos, N. D., Bro, R., & Giannakis, G. B. (2000). Parallel factor analysis in sensor array processing. IEEE Transactions on Signal Processing, 48(8), 2377–2388.Google Scholar
  24. Sidiropoulos, N. D., Giannakis, G. B., & Bro, R. (2000). Parallel factor analysis in sensor array processing. IEEE Transactions on Signal Processing, 48(8), 2377–2388.Google Scholar
  25. Stoica, P., & Nehorai, A. (1989). MUSIC, maximum likelihood, and Cramer–Rao bound. IEEE Transactions on Acoustics Speech & Signal Processing, 37(5), 720–741.MathSciNetzbMATHGoogle Scholar
  26. Vu, D. T., Renaux, A., Boyer, R., & Marcos, S. (2011). A Cramér-Rao bounds based analysis of 3D antenna array geometries made from ULA branches. Multidimensional Systems & Signal Processing, 24(1), 1–35.zbMATHGoogle Scholar
  27. Wen, F., Xiong, X., Su, J., & Zhang, Z. (2017a). Angle estimation for bistatic MIMO radar in the presence of spatial colored noise. Signal Processing, 134(C), 261–267.Google Scholar
  28. Wen, F., Xiong, X., & Zhang, Z. (2017b). Angle and mutual coupling estimation in bistatic MIMO radar based on PARAFAC decomposition. Digital Signal Processing, 65, 1–10.MathSciNetGoogle Scholar
  29. Wen, F., Zhang, Z., Zhang, G., Zhang, Y., Wang, X. H., & Zhang, X. Y. (2017c). A tensor-based covariance differencing method for direction estimation in bistatic MIMO radar with unknown spatial colored noise. IEEE Access, 5, 18451–18458.  https://doi.org/10.1109/ACCESS.2017.2749404.Google Scholar
  30. Weng, Z., & Djurić, P. M. (2014). A search-free DOA estimation algorithm for coprime arrays. Digital Signal Processing, 24(1), 27–33.Google Scholar
  31. Wu, Q., Sun, F., Lan, P., & Ding, G. (2016). Two-dimensional direction-of-arrival estimation for co-prime planar arrays: A partial spectral search approach. IEEE Sensors Journal, 16(14), 5660–5670.Google Scholar
  32. Xin, J., Zheng, N., & Sano, A. (2007). Simple and efficient nonparametric method for estimating the number of signals without eigen-decomposition. IEEE Transactions on Signal Processing, 55(4), 1405–1420.MathSciNetzbMATHGoogle Scholar
  33. Zhang, X. F., Cao, R. Z., & Zhou, M. (2013). Noncircular-PARAFAC for 2D-DOA estimation of noncircular signals in arbitrarily spaced acoustic vector-sensor array subjected to unknown locations. EURASIP Journal on Advances in Signal Processing, 2013(1), 1–10.Google Scholar
  34. Zhang, X. F., Wang, F., & Xu, D. Z. (2010). Theory and application of array signal processing. Beijing: National Defence Industry Press.Google Scholar
  35. Zhang, X., Xu, Z., Xu, L., & Xu, D. (2011). Trilinear decomposition-based transmit angle and receive angle estimation for multiple-input multiple-output radar. IET Radar Sonar Navigation, 5(6), 626–631.Google Scholar
  36. Zheng, W., Zhang, X. F., & Zhai, H. (2017). Generalized coprime planar array geometry for two-dimensional DOA estimation. IEEE Communications Letters, 21(5), 1075–1078.Google Scholar
  37. Zhou, C., Shi, Z., Gu, Y., & Shen, X. (2013). DECOM: DOA estimation with combined MUSIC for coprime arrays. In Proceeding IEEE international conference on wireless communications and signal processing (pp. 1–5).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Electronic and Information EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

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