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Electronics and Telecommunications Research Institute (한국전자통신연구원)
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Blind signal separation for coprime planar arrays: An improved coupled trilinear decomposition method

  • Zhongyuan Que (College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics) ;
  • Xiaofei Zhang (College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics) ;
  • Benzhou Jin (College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics)
  • Received : 2021.11.16
  • Accepted : 2022.06.13
  • Published : 2023.02.20
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Abstract

In this study, the problem of blind signal separation for coprime planar arrays is investigated. For coprime planar arrays comprising two uniform rectangular subarrays, we link the signal separation to the tensor-based model called coupled canonical polyadic decomposition (CPD) and propose an improved coupled trilinear decomposition approach. The output data of coprime planar arrays are modeled as a coupled tensor set that can be further interpreted as a coupled CPD model, allowing a signal separation to be achieved using coupled trilinear alternating least squares (TALS). Furthermore, in the procedure of the coupled TALS, a Vandermonde structure enforcing approach is explicitly applied, which is shown to ensure fast convergence. The results of Monto Carlo simulations show that our proposed algorithm has the same separation accuracy as the basic coupled TALS but with a faster convergence speed.

Keywords

Acknowledgement

This work was supported by National Natural Science Foundation of China (Grants 61971217, 61971218, and 61631020), National Natural Science Foundation of Jiangsu (Grant BK20200444), the fund of Sonar Technology Key Laboratory (Research on the theory and algorithm of signal processing for two-dimensional underwater acoustics coprime array) and the fund of Sonar Technology Key Laboratory (Range estimate and location technology of passive target via multiple array combination), and Jiangsu Key Research and Development Project (Grant BE2020101).

References

  1. C. Jutten and P. Comon, Chapter 1-Introduction, Handbook of Blind Source Separation, P. Comon and C. Jutten, (eds.), Academic Press, Oxford, 2010, pp. 1-22. 
  2. J. Li, P. Stoica, and Z. Wang, On robust Capon beamforming and diagonal loading, (IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings, Hong Kong, China), Apr. 2003. https://doi.org/10.1109/ICASSP.2003.1199947 
  3. X. Zhang and D. Xu, Angle estimation in bistatic MIMO radar using improved reduced dimension Capon algorithm, J. Syst. Eng. Electron. 24 (2013), no. 1, 84-89.  https://doi.org/10.1109/JSEE.2013.00011
  4. R. Schmidt, Multiple emitter location and signal parameter estimation, IEEE Trans. Antennas Propag. 34 (1986), no. 3, 276-280.  https://doi.org/10.1109/TAP.1986.1143830
  5. X. Zhang, L. Xu, L. Xu, and D. Xu, Direction of Departure (DOD) and Direction of Arrival (DOA) estimation in MIMO radar with reduced-dimension MUSIC, IEEE Commun. Lett. 14 (2010), no. 12, 1161-1163.  https://doi.org/10.1109/LCOMM.2010.102610.101581
  6. R. Roy and T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques, IEEE Trans. Acoust. Speech Signal Process. 37 (1989), no. 7, 984-995.  https://doi.org/10.1109/29.32276
  7. A. Hyvarinen and E. Oja, A fast fixed-point algorithm for independent component analysis, Neural Comput. 9 (1997), no. 7, 1483-1492.  https://doi.org/10.1162/neco.1997.9.7.1483
  8. A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, and E. Moulines, A blind source separation technique using secondorder statistics, IEEE Trans. Signal Proc. 45 (1997), no. 2, 434-444.  https://doi.org/10.1109/78.554307
  9. J. F. Cardoso and A. Souloumiac, Blind beamforming for nonGaussian signals, IEE Proc. F. (Radar Signal Process.) 140 (1993), no. 6, 362-370.  https://doi.org/10.1049/ip-f-2.1993.0054
  10. P. Ioannides and C. A. Balanis, Uniform circular and rectangular arrays for adaptive beamforming applications, IEEE Antennas Wirel. Propag. Lett. 4 (2005), 351-354.  https://doi.org/10.1109/LAWP.2005.857039
  11. B. Liao and S.-C. Chan, Adaptive beamforming for uniform linear arrays with unknown mutual coupling, IEEE Antennas Wirel. Propag. Lett. 11 (2012), 464-467.  https://doi.org/10.1109/LAWP.2012.2196017
  12. Y. Zhou, Z. Fei, S. Yang, J. Kuang, S. Chen, and L. Hanzo, Joint angle estimation and signal reconstruction for coherently distributed sources in massive MIMO systems based on 2-D unitary ESPRIT, IEEE Access 5 (2017), 9632-9646.  https://doi.org/10.1109/ACCESS.2017.2707557
  13. P. P. Vaidyanathan and P. Pal, Theory of sparse coprime sensing in multiple dimensions, IEEE Trans. Signal Process. 59 (2011), no. 8, 3592-3608.  https://doi.org/10.1109/TSP.2011.2135348
  14. P. P. Vaidyanathan and P. Pal, Sparse sensing with co-prime samplers and arrays, IEEE Trans. Signal Process. 59 (2011), no. 2, 573-586.  https://doi.org/10.1109/TSP.2010.2089682
  15. C. Zhou, Z. Shi, Y. Gu, and X. Shen, DECOM: DOA estimation with combined MUSIC for coprime array, (International Conference on Wireless Communications and Signal Processing, Hangzhou, China), Oct. 2013. https://doi.org/10.1109/WCSP. 2013.6677080 
  16. Z. Weng and P. M. Djuric, A search-free DOA estimation algorithm for coprime arrays, Digital Signal Process. 24 (2014), 27-33.  https://doi.org/10.1016/j.dsp.2013.10.005
  17. Q. Wu, F. Sun, P. Lan, G. Ding, and X. Zhang, Twodimensional direction-of-arrival estimation for co-prime planar arrays: A partial spectral search approach, IEEE Sensors J. 16 (2016), no. 14, 5660-5670.  https://doi.org/10.1109/JSEN.2016.2567422
  18. W. Zheng, X. Zhang, and H. Zhai, Generalized coprime planar array geometry for 2-D DOA estimation, IEEE Commun. Lett. 21 (2017), no. 5, 1075-1078.  https://doi.org/10.1109/LCOMM.2017.2664809
  19. Y. Gu, C. Zhou, N. A. Goodman, W.-Z. Song, and Z. Shi, Coprime array adaptive beamforming based on compressive sensing virtual array signal, (IEEE International Conference on Acoustics, Speech and Signal Processing, Shanghai, China), Mar. 2016. https://doi.org/10.1109/ICASSP.2016.7472224 
  20. C. Zhou, Y. Gu, S. He, and Z. Shi, A robust and efficient algorithm for coprime array adaptive beamforming, IEEE Trans. Veh. Technol. 67 (2018), no. 2, 1099-1112.  https://doi.org/10.1109/TVT.2017.2704610
  21. J. Li and M. Zhou, Improved trilinear decomposition-based method for angle estimation in multiple-input multiple-output radar, IET Radar Sonar Navigation 7 (2013), no. 9, 1019-1026. _eprint: https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-rsn.2012.0345 
  22. N. D. Sidiropoulos, R. Bro, and G. B. Giannakis, Parallel factor analysis in sensor array processing, IEEE Trans. Signal Process. 48 (2000), no. 8, 2377-2388.  https://doi.org/10.1109/78.852018
  23. N. D. Sidiropoulos, G. B. Giannakis, and R. Bro, Blind PARAFAC receivers for DS-CDMA systems, IEEE Trans. Signal Process. 48 (2000), no. 3, 810-823.  https://doi.org/10.1109/78.824675
  24. L. Xu, F. Wen, and X. Zhang, A novel unitary PARAFAC algorithm for joint DOA and frequency estimation, IEEE Commun. Lett. 23 (2019), no. 4, 660-663.  https://doi.org/10.1109/LCOMM.2019.2896593
  25. X. Zhang, Z. Xu, L. Xu, and D. Xu, Trilinear decompositionbased transmit angle and receive angle estimation for multipleinput multiple-output radar, IET Radar, Sonar Navig. 5 (2011), no. 6, 626-631.  https://doi.org/10.1049/iet-rsn.2010.0265
  26. X. Zhang, W. Zheng, W. Chen, and Z. Shi, Two-dimensional DOA estimation for generalized coprime planar arrays: a fastconvergence trilinear decomposition approach, Multidim. Syst. Sign. Process. 30 (2019), no. 1, 239-256.  https://doi.org/10.1007/s11045-018-0553-9
  27. M. Sorensen, I. Domanov, and L. De Lathauwer, Coupled canonical polyadic decompositions and multiple shift invariance in array processing, IEEE Trans. Signal Process. 66 (2018), no. 14, 3665-3680. https://ieeexplore.ieee.org/document/8357500/  https://doi.org/10.1109/TSP.2018.2835423
  28. M. Sorensen and L. D. De Lathauwer, Coupled canonical polyadic decompositions and (coupled) decompositions in multilinear rank-$(L_r,n,L_r,n,1)$ terms-Part I: Uniqueness, SIAM J. Matrix Anal. Appl. 36 (2015), no. 2, 496-522. https://doi.org/10.1137/140956853 
  29. M. Sorensen, I. Domanov, and L. De Lathauwer, Coupled canonical polyadic decompositions and (coupled) decompositions in multilinear rank- $(L_{r,n},L_{r,n},1)$ terms-Part II: Algorithms, SIAM J. Matrix Anal. Appl. 36 (2015), no. 3, 1015-1045.  https://doi.org/10.1137/140956865
  30. Yih-Min Chen, Ju-Hong Lee, and Chien-Chung Yeh, Twodimensional angle-of-arrival estimation for uniform planar arrays with sensor position errors, IEE Proc. F Radar Signal Process. UK 140 (1993), no. 1, 37. 
  31. N. Vervliet, O. Debals, and L. De Lathauwer, Tensorlab 3.0 - Numerical optimization strategies for large-scale constrained and coupled matrix/tensor factorization, (50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA), Nov. 2016. https://doi.org/10.1109/ACSSC.2016.7869679