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2013-07-12
Direction Finding for Bistatic MIMO Radar Using EM Maximum Likelihood Algorithm
By
Progress In Electromagnetics Research, Vol. 141, 99-116, 2013
Abstract
In this paper, we investigate an expectation-maximization (EM) maximum likelihood (ML) algorithm of direction finding (DF) for bistatic multiple-input multiple-output (MIMO) radar, where it is shown that the DF problem can be described as a special case of ML estimation with incomplete data. First, we introduce the signal and the noise models, and derive the ML estimations of the direction parameters. Considering the computational complexity, we make use of the EM algorithm to compute the ML algorithm, referred to EM ML algorithm, which can be applied to the arbitrary antenna geometry and realize the auto-pairing between direction-of-departures (DODs) and direction-of-arrivals (DOAs). Then the initialization is considered. In addition, both the convergence and the Cramer-Rao bound (CRB) analysis are derived. Finally, simulation results demonstrate the potential and asymptotic efficiency of this approach for MIMO radar systems.
Citation
Hao Wen Chen Degui Yang Hong-Qiang Wang Xiang Li Zhaowen Zhuang , "Direction Finding for Bistatic MIMO Radar Using EM Maximum Likelihood Algorithm," Progress In Electromagnetics Research, Vol. 141, 99-116, 2013.
doi:10.2528/PIER13050102
http://www.jpier.org/PIER/pier.php?paper=13050102
References

1. Li, J. and P. Stoica, "MIMO radar with colocated antennas: Review of some recent work," IEEE Signal Process. Mag., Vol. 24, No. 5, 106-114, Sep. 2007.
doi:10.1109/MSP.2007.904812

2. Haimovich, A. M., R. S. Blum, and L. Cimini, "MIMO radar with widely separated antennas," IEEE Signal Process. Mag., Vol. 25, No. 1, 116-129, Jan. 2008.
doi:10.1109/MSP.2008.4408448

3. Li, J. and P. Stoica, MIMO Radar Signal Processing, Wiley, New York, 2008.
doi:10.1002/9780470391488

4. Bencheikh, M. L., Y. D. Wang, and H. Y. He, "Polynomial root finding technique for joint DOA DOD estimation in bistatic MIMO radar," Signal Processing, Vol. 90, No. 9, 2723-2730, Sep. 2010.
doi:10.1016/j.sigpro.2010.03.023

5. Chen, J. L., H. Gu, and W. M. Su, "A new method for joint DOD and DOA estimation in bistatic MIMO radar," Signal Processing, Vol. 90, No. 2, 714-718, Feb. 2010.
doi:10.1016/j.sigpro.2009.08.003

6. Liu, X. L. and G. S. Liao, "Direction finding and mutual coupling estimation for bistatic MIMO radar," Signal Processing, Vol. 92, No. 2, 517-522, Feb. 2012.
doi:10.1016/j.sigpro.2011.08.017

7. Xie, R., Z. Liu, and J. X. Wu, "Direction finding with automatic pairing for bistatic MIMO radar," Signal Processing, Vol. 92, No. 1, 198-203, Jan. 2012.
doi:10.1016/j.sigpro.2011.07.004

8. Zheng, Z., J. Zhang, and J. Y. Zhang, "Joint DOD and DOA estimation of bistatic MIMO radar in the presence of unknown mutual coupling," Signal Processing, Vol. 92, No. 12, 3039-3048, 2012.
doi:10.1016/j.sigpro.2012.06.013

9. Lv, H., D. Z. Feng, H. W. Liu, J. He, and C. Xiang, "Tri-iterative least-square method for bearing estimation in MIMO radar," Signal Processing, Vol. 89, No. 12, 2686-2691, Dec. 2009.
doi:10.1016/j.sigpro.2009.05.011

10. Li, C. C., G. S. Liao, S. Q. Zhu, and S. Y. Wu, "An ESPRIT-like algorithm for coherent DOA estimation based on data matrix decomposition in MIMO radar," Signal Processing, Vol. 91, No. 8, 1803-1811, Aug. 2011.
doi:10.1016/j.sigpro.2011.02.004

11. Xie, R., Z. Liu, and Z. J. Zhang, "DOA estimation for monostatic MIMO radar using polynomial rooting," Signal Processing, Vol. 90, No. 12, 3284-3288, Dec. 2010.
doi:10.1016/j.sigpro.2010.05.008

12. Si, W., L. Wan, L. Liu, and Z. Tian, "Fast estimation of frequency and 2-D DOAs for cylindrical conformal array antenna using state-space and propagator method," Progress In Electromagnetics Research, Vol. 137, 51-71, 2013.

13. Cheng, S.-C. and K.-C. Lee, "Reducing the array size for DOA estimation by an antenna model switch technique," Progress In Electromagnetics Research, Vol. 131, 117-134, 2012.

14. Lie, J. P., B. P. Ng, and C. M. S. See, "Multiple UWB emitters DOA estimation employing time hopping spread spectrum," Progress In Electromagnetics Research, Vol. 78, 83-101, 2008.
doi:10.2528/PIER07091303

15. Mukhopadhyay, M., B. K. Sarkar, and A. Chakraborty, "Augmentation of anti-jam GPS system using smart antenna with a simple DOA estimation algorithm," Progress In Electromagnetics Research, Vol. 67, 231-249, 2007.
doi:10.2528/PIER06090504

16. Yang, P., F. Yang, and Z.-P. Nie, "DOA estimation with sub-array divided technique and interporlated ESPRIT algorithm on a cylindrical conformal array antenna," Progress In Electromagnetics Research, Vol. 103, 201-216, 2010.
doi:10.2528/PIER10011904

17. Liang, J. and D. Liu, "Two L-shaped array-based 2-D DOAs estimation in the presence of mutual coupling," Progress In Electromagnetics Research, Vol. 112, 273-298, 2011.

18. Lizzi, L., F. Viani, M. Benedetti, P. Rocca, and A. Massa, "The M-DSO-ESPRIT method for maximum likelihood DOA estimation," Progress In Electromagnetics Research, Vol. 80, 477-497, 2008.
doi:10.2528/PIER07121106

19. Agatonovic, M., Z. Stankovic, I. Milovanovic, N. Doncov, L. Sit, T. Zwick, and B. Milovanovic, "Efficient neural network approach for 2D DOA estimation based on antenna array measurements," Progress In Electromagnetics Research, Vol. 137, 741-758, 2013.

20. Bekkerman, I. and J. Tabrikian, "Target detection and localization using MIMO radars and sonars," IEEE Trans. on Signal Process., Vol. 54, No. 10, 3873-3883, Oct. 2006.
doi:10.1109/TSP.2006.879267

21. Li, J., X. Xu, and P. Stoica, "Range compression and waveform optimization for MIMO radar: A Cramer-Rao bound based study," IEEE Trans. on Signal Process., Vol. 56, No. 1, 218-232, Jan. 2008.
doi:10.1109/TSP.2007.901653

22. Dempster, A. P., N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Roy. Statist. Soc. Ser. B, Vol. 39, No. 1, 1-38, Jan. 1977.

23. Chung, P. J. and J. F. Bohme, "Comparative convergence analysis of EM and SAGE algorithms in DOA estimation," IEEE Trans. on Signal Process., Vol. 49, No. 12, 2940-2949, Dec. 2001.
doi:10.1109/78.969503

24. McLachlan, G. and T. Krishnan, The EM Algorithm and Extensions, John Wiley & Sons, New York, 1996.

25. Feder, M. and E. Weinstein, "Parameter estimation of superim-posed signals using the EM algorithm," IEEE Trans. on Acoust., Speech, Signal Process., Vol. 36, No. 4, 477-489, Apr. 1988.
doi:10.1109/29.1552

26. Li, J., B. Halder, P. Stoica, and M. Viberg, "Computationally efficient angle estimation for signals with known waveforms," IEEE Trans. on Signal Process., Vol. 43, No. 9, 2154-2163, Sep. 1995.
doi:10.1109/78.414778

27. Wu, C. F. J., "On the convergence properties of the EM algorithm," Ann. Statist., Vol. 11, No. 1, 95-103, Mar. 1983.
doi:10.1214/aos/1176346060

28. Hero, A. O. and J. A. Fessler, "Convergence in norm for alternating expectation-maximization (EM) type algorithms," Statistica Sinica, Vol. 5, No. 1, 41-54, Jan. 1995.

29. Hochwald, B. and A. Nehorai, "Concentrated Cramer-Rao bound expressions," IEEE Trans. on Acoustics, Speech, and Signal Process., Vol. 40, No. 2, 363-371, Feb. 1994.

30. Yan, H. D., J. Li, and G. S. Liao, "Multitarget identification and localization using bistatic MIMO radar systems," EURASIP J. Adv. Signal Process., Vol. 40, No. 1, 1-8, Jan. 2008.

31. Weiss, A. J., A. S. Willisky, and B. C. Levy, "Maximum likelihood array processing for estimation of superimposed signals," Proc. IEEE, Vol. 76, No. 2, 202-205, Feb. 1988.
doi:10.1109/5.4396

32. Ziskind, I. and M. Wax, "Maximum likelihood localization of multiple suorces by alternating projection," IEEE Trans. on Acoust., Speech, Signal Process., Vol. 36, No. 10, 1553-1560, Oct. 1988.
doi:10.1109/29.7543

33. Feder, M. and E. Weistein, "Parameter estimation of superim-posed signals using the EM algorithm," IEEE Trans. on Acoust., Speech, Signal Process., Vol. 36, No. 4, 477-489, Apr. 1988.
doi:10.1109/29.1552

34. Oh, S. K. and C. K. Un, "Simple computational methods of the AP algorithm for maximum likelihood localization of multiple radiating sources," IEEE Trans. on Signal Process., Vol. 40, No. 11, 2848-2854, Nov. 1992.
doi:10.1109/78.165678

35. Miller, M. I. and D. R. Fuhrmann, "Maximum-likelihood narrow-band direction finding and the EM algorithm," IEEE Trans. on Acoust., Speech, Signal Process., Vol. 38, No. 9, 1560-1577, Sep. 1990.
doi:10.1109/29.60075

36. Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, Vol. 220, No. 4598, 671-680, May 1983.
doi:10.1126/science.220.4598.671

37. Chen, H. W., W. Zhou, J. Yang, Y. X. Peng, and X. Li, "Manifold studies on fundamental limits of direction finding MIMO radar systems," IET Radar Sonar and Navigation, Vol. 6, No. 8, 708-718, Dec. 2012.
doi:10.1049/iet-rsn.2011.0342