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An Improved PARAFAC Estimator for 2D-DOA Estimation Using EMVS Array

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Abstract

The topic of direction-of-arrival (DOA) estimation has attracted extensive attention in wireless communications, radars, sonars, etc. Compared to the traditional scalar sensor, electromagnetic vector sensor (EMVS) is attractive since it provides two-dimensional (2D) DOA estimation and additional polarization information of the incoming signals. However, existing algorithms are only suitable for Gaussian white noise scenario. In this paper, we investigate into DOA estimation using EMVS array with spatially colored noise, and a parallel factor (PARAFAC) estimator is proposed. Unlike the conventional direct PARAFAC algorithm, the covariance tensor-based PARAFAC model is considered. For fast PARAFAC decomposition purpose, the fourth-order covariance PARAFAC tensor is rearranged into a third-order PARAFAC tensor, so that the existing COMFAC algorithm is available and thus the factor matrices are estimated. Thereafter, the elevation angle estimation is accomplished via least squares (LS) technique, and the azimuth angles are estimated via vector cross-product. Besides, the polarization status of the source signal can be estimated via LS approach, which may be helpful to identify weak signals. Our estimator is flexible since it can be easily extended to nonuniform array and spatially colored noise scenario. Moreover, it offers better estimation performance than the traditional PARAFAC algorithm in the presence of colored noise. Detailed analyses concerning identifiability, complexity as well as Cramér–Rao bound (CRB) are provided. To show the effectiveness of the proposed estimator, numerical simulations have been designed.

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References

  1. H. Abeida, J. Delmas, Gaussian cramer-rao bound for direction estimation of noncircular signals in unknown noise fields. IEEE Trans. Signal Process. 53(12), 4610–4618 (2005). https://doi.org/10.1109/TSP.2005.859226

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Ahmed, Z. Xiaofei, Z. Wang, DOA estimation for coprime EMVS arrays via minimum distance criterion based on PARAFAC analysis. IET Radar Sonar Nav. 13(1), 65–73 (2019). https://doi.org/10.1049/iet-rsn.2018.5155

    Article  Google Scholar 

  3. I. Bekkerman, J. Tabrikian, Target detection and localization using MIMO radars and sonars. IEEE Trans. Signal Process. 54(10), 3873–3883 (2006). https://doi.org/10.1109/TSP.2006.879267

    Article  MATH  Google Scholar 

  4. Bro. R, Sidiropoulos. N, Giannakis. G (1999) A fast least squares algorithm for separating trilinear mixtures. In: Proc. Int. Workshop on Independ. Compon. Anal. Blind Signal Separation (ICA 99), pp. 289–294. Aussois, France

  5. C.E. Chen, F. Lorenzelli, R.E. Hudson, K. Yao, Stochastic maximum-likelihood DOA estimation in the presence of unknown nonuniform noise. IEEE Trans. Signal Process. 56(7), 3038–3044 (2008). https://doi.org/10.1109/TSP.2008.917364

    Article  MathSciNet  MATH  Google Scholar 

  6. H. Chen, C. Hou, Q. Wang, L. Huang, W. Yan, Cumulants-based toeplitz matrices reconstruction method for 2-D coherent DOA estimation. IEEE Sens. J. 14(8), 2824–2832 (2014). https://doi.org/10.1109/JSEN.2014.2316798

    Article  Google Scholar 

  7. Q. Cheng, Y. Hua, Further study of the pencil-MUSIC algorithm. IEEE Trans. Aero. Elec. Sys. 32(1), 284–299 (1996). https://doi.org/10.1109/7.481269

    Article  Google Scholar 

  8. S. Chintagunta, P. Palanisamy, 2D-DOD and 2D-DOA estimation using the electromagnetic vector sensors. Signal Process. 147, 163–172 (2018). https://doi.org/10.1016/j.sigpro.2018.01.025

    Article  MATH  Google Scholar 

  9. Fernandez del Rio. JE, Catedra-Perez. (1997) MF The matrix pencil method for two-dimensional direction of arrival estimation employing an L-shaped array. IEEE Trans. Antenna. Propag. 45(11), 1693–1694. https://doi.org/10.1109/8.650082

  10. R. Goossens, H. Rogier, A hybrid UCA-RARE/Root-MUSIC approach for 2-D direction of arrival estimation in uniform circular arrays in the presence of mutual coupling. IEEE Trans. Antenna. Propag. 55(3), 841–849 (2007). https://doi.org/10.1109/TAP.2007.891848

    Article  Google Scholar 

  11. M. Haardt, F. Roemer, G. Del Galdo, Higher-order SVD-based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems. IEEE Trans. Signal Process. 56(7), 3198–3213 (2008). https://doi.org/10.1109/TSP.2008.917929

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Han, A. Nehorai, Nested vector-sensor array processing via tensor modeling. IEEE Trans. Signal Process. 62(10), 2542–2553 (2014). https://doi.org/10.1109/TSP.2014.2314437

    Article  MathSciNet  MATH  Google Scholar 

  13. J. He, L. Li, T. Shu (2021) Direction finding of mixed fully and partially polarized sources using linear cold arrays. Signal Process. 178. https://doi.org/10.1016/j.sigpro.2020.107815

  14. J. He, L. Li, T. Shu (2021) Sparse nested arrays with spatially spread orthogonal dipoles: High accuracy passive direction finding with less mutual coupling. IEEE Trans. Aero. Elec. Sys https://doi.org/10.1109/TAES.2021.3054056

  15. J. He, Z. Liu, Computationally efficient 2D direction finding and polarization estimation with arbitrarily spaced electromagnetic vector sensors at unknown locations using the propagator method. Digital Signal Proc. 19(3), 491–503 (2009). https://doi.org/10.1016/j.dsp.2008.01.002

    Article  Google Scholar 

  16. J. He, Z. Zhang, C. Gu, T. Shu, W. Yu, Cumulant-based 2-d direction estimation using an acoustic vector sensor array. IEEE Trans. Aero. Elec. Sys. 56(2), 956–971 (2020). https://doi.org/10.1109/TAES.2019.2921194

    Article  Google Scholar 

  17. H. Huang, J. Yang, Y. Song, H. Huang, G. Gui, Deep learning for super-resolution channel estimation and DOA estimation based massive MIMO system. IEEE Trans. Veh. Tech. 67(9), 8549–8560 (2018)

    Article  Google Scholar 

  18. J. Li, Direction and polarization estimation using arrays with small loops and short dipoles. IEEE Trans. Antennas Propag. 41(3), 379–387 (1993). https://doi.org/10.1109/8.233120

    Article  Google Scholar 

  19. B. Liao, Fast angle estimation for MIMO radar with nonorthogonal waveforms. IEEE Trans. Aero. Elec. Sys. 54(4), 2091–2096 (2018). https://doi.org/10.1109/TAES.2018.2847958

    Article  Google Scholar 

  20. T. Liu, F. Wen, L. Zhang, K. Wang (2019) Off-grid doa estimation for colocated MIMO radar via reduced-complexity sparse Bayesian learning. IEEE Access 7 . https://doi.org/10.1109/ACCESS.2019.293053

  21. S. Miron, N. Le Bihan, J. Mars, (2005) Vector-sensor MUSIC for polarized seismic sources localization. EURASIP J. Adv. Signal Process. 48(8). https://doi.org/10.1155/ASP.2005.74

  22. A. Nehorai, E. Paldi, Vector-sensor array processing for electromagnetic source localization. IEEE Trans. Signal Process. 42(2), 376–398 (1994). https://doi.org/10.1109/78.275610

    Article  Google Scholar 

  23. W. Rao, D. Li, J.Q. Zhang, A tensor-based approach to L-shaped arrays processing with enhanced degrees of freedom. IEEE Signal Process. Lett. 25(2), 234–238 (2018). https://doi.org/10.1109/lsp.2017.2783370

    Article  Google Scholar 

  24. R. Roy, T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7), 984–995 (1989). https://doi.org/10.1109/29.32276

    Article  MATH  Google Scholar 

  25. J. Shi, F. Wen, T. Liu, Nested MIMO radar: coarrays, tensor modeling and angle estimation. IEEE Trans. Aero. Elec. Sys. 57(1), 573–585 (2021). https://doi.org/10.1109/TAES.2020.3034012

    Article  Google Scholar 

  26. N.D. Sidiropoulos, L. De Lathauwer, X. Fu, K. Huang, E.E. Papalexakis, C. Faloutsos, Tensor decomposition for signal processing and machine learning. IEEE Trans. Signal Process. 65(13), 3551–3582 (2017). https://doi.org/10.1109/TSP.2017.2690524

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Steinwandt, F. Roemer, M. Haardt, G. Del Galdo, Deterministic cramer-rao bound for strictly non-circular sources and analytical analysis of the achievable gains. IEEE Trans. Signal Process. 64(17), 4417–4431 (2016). https://doi.org/10.1109/TSP.2016.2566603

    Article  MathSciNet  MATH  Google Scholar 

  28. P. Stoica, A. Nehorai, Performance study of conditional and unconditional direction-of-arrival estimation. IEEE Trans. Acous. Speech Signal Process. 38(10), 1783–1795 (1990). https://doi.org/10.1109/29.60109

    Article  MATH  Google Scholar 

  29. X. Wang, M. Huang, L. Wan (2020) Joint 2D-DOD and 2D-DOA estimation for coprime EMVS-MIMO radar. Circ. Syst. Signal Process. https://doi.org/10.1007/s00034-020-01605-5

  30. Y. Wang, W. Wu, X. Zhang, W. Zheng, Transformed nested array designed for DOA estimation of non-circular signals: Reduced sum-difference co-array redundancy perspective. IEEE Commun. Lett. 24(6), 1262–1265 (2020). https://doi.org/10.1109/LCOMM.2020.2977293

    Article  Google Scholar 

  31. F. Wen, J. Shi (2020) Fast direction finding for bistatic EMVS-MIMO radar without pairing. Signal Process. 173. https://doi.org/10.1016/j.sigpro.2020.107512

  32. F. Wen, J. Shi, Z. Zhang, Joint 2D-DOD, 2D-DOA, and polarization angles estimation for bistatic EMVS-MIMO radar via PARAFAC analysis. IEEE Trans. Veh. Technol. 69(2), 1626–1638 (2020). https://doi.org/10.1109/TVT.2019.2957511

    Article  Google Scholar 

  33. F. Wen, J. Shi, Z. Zhang (2021) Closed-form estimation algorithm for EMVS-MIMO radar with arbitrary sensor geometry. Signal Process. 186. https://doi.org/10.1016/j.sigpro.2021.108117

  34. F. Wen, X. Xiong, J. Su, Z. Zhang, Angle estimation for bistatic MIMO radar in the presence of spatial colored noise. Signal Process. 134, 261–267 (2017). https://doi.org/10.1016/j.sigpro.2016.12.017

    Article  Google Scholar 

  35. F. Wen, Z. Zhang, G. Zhang, Y. Zhang, X. Wang, X. Zhangc, A tensor-based covariance differencing method for direction estimation in bistatic MIMO radar with unknown spatial colored noise. IEEE Access 5, 18451–18458 (2017). https://doi.org/10.1109/ACCESS.2017.2749404

    Article  Google Scholar 

  36. K.T. Wong, X. Yuan (2011)“vector cross-product direction-finding” with an electromagnetic vector-sensor of six orthogonally oriented but spatially noncollocating dipoles/loops. IEEE Trans. Signal Process. 59(1), 160–171. https://doi.org/10.1109/TSP.2010.2084085

  37. K.T. Wong, M.D. Zoltowski, Uni-vector-sensor ESPRIT for multisource azimuth, elevation, and polarization estimation. IEEE Trans. Antennas Propag. 45(10), 1467–1474 (1997). https://doi.org/10.1109/8.633852

    Article  Google Scholar 

  38. K.T. Wong, M.D. Zoltowski, Closed-form direction finding and polarization estimation with arbitrarily spaced electromagnetic vector-sensors at unknown locations. IEEE Trans. Antennas Propag. 48(5), 671–681 (2000). https://doi.org/10.1109/8.855485

    Article  Google Scholar 

  39. K.T. Wong, M.D. Zoltowski, Self-initiating music-based direction finding and polarization estimation in spatio-polarizational beamspace. IEEE Trans. Antennas Propag. 48(8), 1235–1245 (2000). https://doi.org/10.1109/8.884492

    Article  Google Scholar 

  40. X. Yang, Z. Zheng, B. Hu, Off-grid DOA estimation of incoherently distributed non-circular sources via generalised approximate message passing. Electron. Lett. 52(4), 262–264 (2016). https://doi.org/10.1049/el.2015.1973

    Article  Google Scholar 

  41. Yilmazer. N, Jinhwan Koh, Sarkar. TK (2006) Utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival. IEEE Trans. Antenna. Propag. 54(1), 175–181. https://doi.org/10.1109/TAP.2005.861567

  42. N. Yuen, B. Friedlander, DOA estimation in multipath: an approach using fourth-order cumulants. IEEE Trans. Signal Processing 45(5), 1253–1263 (1997). https://doi.org/10.1109/78.575698

    Article  Google Scholar 

  43. X. Zhang, Z. Xu, L. Xu, D. Xu, Trilinear decomposition-based transmit angle and receive angle estimation for multiple-input multiple-output radar. IET Radar Sonar Nav. 5(6), 626–631 (2011). https://doi.org/10.1049/iet-rsn.2010.0265

    Article  Google Scholar 

  44. Z.D. Zheng, Y. ZJ, Fast method for multi-target localisation in bistatic MIMO radar. Electron. Lett. 47(2), 138–139 (2011). https://doi.org/10.1049/el.2010.2577

    Article  Google Scholar 

  45. M.D. Zoltowski, M. Haardt, C.P. Mathews, Closed-form 2-D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT. IEEE Trans. Signal Process. 44(2), 316–328 (1996). https://doi.org/10.1109/78.485927

    Article  Google Scholar 

  46. M.D. Zoltowski, K.T. Wong, ESPRIT-based 2-D direction finding with a sparse uniform array of electromagnetic vector sensors. IEEE Trans. Signal Process. 48(8), 2195–2204 (2000). https://doi.org/10.1109/78.852000

    Article  Google Scholar 

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Authors and Affiliations

  1. Electronic and Information School, Yangtze University, Jingzhou, 434200, China

    Chengyu Wang, Lin Ai & Fangqing Wen

  2. College of Electronic Countermeasure, National University of Defense Technology, Hefei, 230037, China

    Junpeng Shi

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  1. Chengyu Wang
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Wang, C., Ai, L., Wen, F. et al. An Improved PARAFAC Estimator for 2D-DOA Estimation Using EMVS Array. Circuits Syst Signal Process 41, 147–165 (2022). https://doi.org/10.1007/s00034-021-01748-z

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