volume | PIER Journals

Abstract

In order to improve the angle measurement precision with a low computational complexity, a 2-D direction of arrival (DOA) estimation algorithm UCA-TF-MI-ESPRIT is proposed in this paper. This algorithm is based on the mode space algorithm and the time-frequency (TF) multiple invariance rotational invariance technique (MI-ESPRIT). Firstly, a uniform circular array (UCA) is equivalent to a virtual uniform linear array (ULA) by utilizing mode-space algorithm. Then, the smoothed pseudo Wigner-Ville distribution (SPWVD) of the ULA output is calculated. The spatial time-frequency matrix can be obtained through the average of multiple time-frequency points in the time-frequency plane, and the signal subspace can also be obtained through using eigen decomposition. Then a simple and effective subarray dividing approach is proposed, and the multiple rotational invariant equation of the array is obtained by using the Bessel function. Finally, the closed-form solution is obtained using multi-least-squares (MLS) criterion so that the 2-D DOA estimation of LFM signals in UCA is completed. The simulation results verify the effectiveness of the algorithm proposed by this paper.

1. Du, W., D. L. Su, S. G. Xie, and H. T. Hui, "A fast calculation method for the receiving mutual impedances of uniform circular arrays," IEEE Antennas and Wireless Propagation Letters, Vol. 11, No. 2, 893-896, Aug. 2012.
doi:10.1109/LAWP.2012.2211329

2. Liao, B., K. M. Tsui, and S. C. Chan, "Frequency invariant uniform concentric circular arrays with directional elements," IEEE Transactions on Aerospace and Electronics Systems, Vol. 49, No. 2, 871-884, Apr. 2013.
doi:10.1109/TAES.2013.6494386

3. Jackson, B. R., S. Rajan, B. J. Liao, and S. C.Wang, "Direction of arrival estimation using directive antennas in uniform circular arrays," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 2, 736-747, Feb. 2015.
doi:10.1109/TAP.2014.2384044

4. Pan, Y. J., X. F. Zhang, S. Y. Xie, J. J. Huang, and N. C. Yuan, "An ultra-fast DOA estimator with circular array interferometer using lookup table," Radioengineering, Vol. 24, No. 3, 850-856, Sep. 2015.
doi:10.13164/re.2015.0850

5. Wang, M., X. C. Ma, S. F. Yan, and C. P. Hao, "An autocalibration algorithm for uniform circular array with unknown mutual coupling," IEEE Antennas and Wireless Propagation Letters, Vol. 15, 12-15, Apr. 2015.

6. Schmidt, R. O., "Multiple emitter location and signal parameter estimation," IEEE Transactions on Antennas and Propagation, Vol. 34, No. 3, 276-280, Mar. 1986.
doi:10.1109/TAP.1986.1143830

7. Roy, R. and T. Kailath, "ESPRIT - A subspace rotation approach to estimation of parameters of cisoids in noise," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 34, No. 5, 1340-1342, Oct. 1986.
doi:10.1109/TASSP.1986.1164935

8. Roy, R. and T. Kailath, "ESPRIT-estimation of signal parameters via rotational invariance techniques," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 37, No. 7, 984-995, Jul. 1989.
doi:10.1109/29.32276

9. Wang, Y. L., H. Chen, Y. N. Peng, and Q. Wan, Spatial Spectrum Estimation, 340-346, Tsinghua University Press, Beijing, China, 2004.

10. Griffiths, H. D. and R. Eiges, "Sectoral phase modes from circular antenna arrays," Electronics Letters, Vol. 28, No. 17, 1581-1582, Aug. 1992.
doi:10.1049/el:19921006

11. Zoltowski, M. D. and C. P. Mathews, "Closed-form 2D angle estimation with uniform circular arrays via phase mode excitation and ESPRIT," The 27th Asilomar Conference on Signals, Systems and Computers, 169-173, Los Alamitos, USA, 1993.

12. Swindlehurst, A. L., B. Ottersten, R. Roy, and T. Kailath, "Multiple invariance ESPRIT," IEEE Transactions on Signal Processing, Vol. 40, No. 4, 867-881, Apr. 1992.
doi:10.1109/78.127959

13. Xu, Y. G. and Z. W. Liu, "Closed-form multiple invariance ESPRIT," Multidim Syst. Sign Process, Vol. 18, 47-54, Feb. 2007.
doi:10.1007/s11045-006-0010-z

14. Zhang, X. F., X. Gao, and D. Z. Xu, "Multi-invariance ESPRIT based blind DOA estimation for MC-CDMA with an antenna array," IEEE Transactions on Vehicular Technology, Vol. 58, No. 8, 4686-4690, Oct. 2009.
doi:10.1109/TVT.2009.2020596

15. Tang, X. H. and Q. L. Li, Time Frequency Analysis and Wavelet Transform, 82-118, Science Press, Beijing, China, 2016.

16. Amin, M. G., "Spatial time frequency distributions for direction finding and blind source separation," The International Society for Optical Engineering (Proc. SPIE), Vol. 3723, 62-70, Orlando, USA, 1999.

17. Belouchrani, A. and M. G. Amin, "Blind source separation based on time-frequency signal representations," IEEE Transactions on Signal Processing, Vol. 46, No. 11, 2888-2897, Nov. 1998.
doi:10.1109/78.726803

18. Belouchrani, A. and M. G. Amin, "Time frequency MUSIC," IEEE Signal Processing Letters, Vol. 6, No. 5, 109-110, May 1999.
doi:10.1109/97.755429

19. Gershman, A. B. and M. G. Amin, "Wideband direction-of-arrival estimation of multiple chirp signals using spatial time-frequency distributions," IEEE Signal Processing Letters, Vol. 7, No. 6, 152-155, Jun. 2000.
doi:10.1109/97.844636

20. Zhang, Y. M., W. F. Mu, and M. G. Amin, "Subspace analysis of spatial time-frequency distribution matrices," IEEE Transactions on Signal Processing, Vol. 49, No. 4, 747-759, Apr. 2001.
doi:10.1109/78.912919

21. Nguyen, L. T., B. Adel, A. M. Karim, and B. Boualem, "Separating more sources than sensors using time-frequency distributions," EURASIP Journal on Applied Signal Processing, Vol. 17, 2828-2847, Jul. 2005.

22. Abdeldjalil, A. E. B., L. T. Nguyen, A. M. Karim, B. Adel, and G. Yves, "Underdetermined blind separation of nondisjoint sources in the time-frequency domain," IEEE Transactions on Signal Processing, Vol. 55, No. 3, 897-907, Mar. 2007.
doi:10.1109/TSP.2006.888877

23. Zhang, Y. M. and M. G. Amin, "Blind separation of nonstationary sources based on spatial time-frequency distributions," EURASIP Journal on Applied Signal Processing, Vol. 2006, 1-13, Aug. 2006.

24. Zhang, Y. M., M. G. Amin, and B. Himed, "Joint DOD/DOA estimation in MIMO radar exploiting time-frequency signal representations," EURASIP Journal on Advances in Signal Processing, Vol. 102, 1-10, May 2012.
doi:10.1186/1687-6180-2012-1

25. Mohamed, K., B. Adel, and A. M. Karim, "Performance analysis for time-frequency MUSIC algorithm in presence of both additive noise and array calibration errors," EURASIP Journal on Advances in Signal Processing, Vol. 94, 1-11, Apr. 2012.

26. Lin, J. C., X. C. Ma, S. F. Yan, and C. P. Hao, "Time-frequency multi-invariance ESPRIT algorithm for DOA estimation," IEEE Antennas and Wireless Propagation Letters, Vol. 15, 770-773, Aug. 2015.

27. Lin, M. and L. Yang, "Blind calibration and DOA estimation with uniform circular arrays in the presence of mutual coupling," IEEE Antennas and Wireless Propagation Letters, Vol. 5, No. 1, 315-318, Jul. 2006.

28. Wu, Y. T. and H. C. So, "Simple and accurate two-dimensional angle estimation for a single source with uniform circular array," IEEE Antennas and Wireless Propagation Letters, Vol. 7, No. 1, 78-80, Apr. 2008.

29. Liao, B., Y. T. Wu, and S. C. Chan, "A generalized algorithm for fast two-dimensional angle estimation of a single source with uniform circular arrays," IEEE Antennas and Wireless Propagation Letters, Vol. 11, No. 1, 984-986, Aug. 2012.
doi:10.1109/LAWP.2012.2213792

Dr. Kaibo Cui

Dr. Weiwei Wu

Dr. Jingjian Huang

Dr. Xi Chen

Dr. Nai-Chang Yuan