volume | PIER Journals

Abstract

In this paper, we adopt the Levenberg-Marquardt (LM) algorithm to implement the nonlinear multivariable optimization for azimuth/elevation angle-of-arrival (AOA) estimation based on the Capon beamforming algorithm. The formulation is based on the fact that the cost function of the Capon algorithm can be expressed in a least-squares form. The performance in terms of the root mean square error (RMSE) and the computational complexity is illustrated via numerical results.

1. Capon, J., "High resolution frequency-wavenumber spectrum analysis," Proceedings of the IEEE, Vol. 57, 1408-1418, 1969.
doi:10.1109/PROC.1969.7278 Google Scholar

2. Tweg, R. and B. Porat, "Numerical optimization method for array signal processing," IEEE Trans. Aerospace and Electronic Systems, Vol. 35, 549-565, 1999.
doi:10.1109/7.766937 Google Scholar

3. Selva, J., "An efficient Newton-type method for the computation of ML estimators in a uniform linear array," IEEE Trans. Signal Processing, Vol. 53, No. 6, 2036-2045, 2005.
doi:10.1109/TSP.2005.847842 Google Scholar

4. Madsen, K., H. B. Nielsen, and O. Tingleff, "Methods for Non-linear Least Squares Problem," 2nd Edition, Technical University of Denmark, 2004. Google Scholar

5. More, J., "The Levenberg-Marquardt algorithm: Implementation and theory," Lecture Notes in Mathematics, Vol. 630, 105-116, 1798. Google Scholar

6. Lee, J.-H, S.-W. Cho, and H.-S. Kim, "Newton-type method in spectrum estimation-based AOA estimation," Electronics Express, Vol. 9, No. 12, 1036-1043, 2012.
doi:10.1587/elex.9.1036 Google Scholar

7. Lee, J.-H., S.-W. Cho, and I.-S. Choi, "Simple expressions of CEP and covariance matrix for localization using LOB measurements for circular trajectory," Electronics Express, Vol. 9, No. 4, 1221-1229, 2012.
doi:10.1587/elex.9.1221 Google Scholar

8. 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. Google Scholar

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

10. Solimene, R., A. Dell'Aversano, and G. Leone, "Interferometric time reversal MUSIC for small scatterer localization," Progress In Electromagnetics Research, Vol. 131, 243-258, 2012. Google Scholar

11. Lee, J.-H., Y.-S. Jeong, S.-W. Cho, W.-Y. Yeo, and K. S. J. Pister, "Application of the newton method to improve the accuracy of TOA estimation with the beamforming algorithm and the MUSIC algorithm,", Vol. 116, 475-515, 2011. Google Scholar

12. Chen, Y. L. and J.-H. Lee, "Finite data performance analysis of LCMV antenna array beamformers with and without signal blocking," Progress In Electromagnetics Research, Vol. 130, 281-317, 2012. Google Scholar

13. Hong, T., M.-Z. Song, and Y. Liu, "RF directional modulation technique using a switched antenna array for communication and direction-finding Applications," Progress In Electromagnetics Research, Vol. 120, 195-213, 2011. Google Scholar

14. Bencheikh, M. L. and Y.Wang, "Combined ESPRIT-RootMUSIC for DOA-DOD estimation in polarimetric bistatic MIMO radar," Progress In Electromagnetics Research Letters, Vol. 22, 109-117, 2011. Google Scholar

15. Peng, H., Z. Yang, and T. Yang, "Calibration of a six-port receiver for direction finding using the artificial neural network technique," Progress In Electromagnetics Research Letters, Vol. 27, 17-24, 2011.
doi:10.2528/PIERL11081504 Google Scholar

16. Kim, Y. and H. Ling, "Direction of arrival estimation of humans with a small sensor array using an artificial neural network," Progress In Electromagnetics Research B, Vol. 27, 127-149, 2011. Google Scholar

17. Elshennawy, W. S., A. M. Attiya, E. A. H. Hashish, and I. A. Eshrah, "Direction of arrival estimation for nonuniform planar array based on piecewise interpolation method," Progress In Electromagnetics Research B, Vol. 38, 241-259, 2012. Google Scholar

18. Zhou, Q.-C., H. Gao, F. Wang, and J. Shi, "Modified DOA estimation methods with unknown source number based on projection pretransformation," Progress In Electromagnetics Research B, Vol. 38, 387-403, 2012. Google Scholar

19. Zaharis, Z. D., C. Skeberis, and T. D. Xenos, "Improved antenna array adaptive beamforming with low side lobe level using a novel adaptive invasive weed optimization method," Progress In Electromagnetics Research, Vol. 124, 137-150, 2012.
doi:10.2528/PIER11120202 Google Scholar

20. Li, W.-X., Y.-P. Li, and W.-H. Yu, "On adaptive beamforming for coherent interference suppression via virtual antenna array," Progress In Electromagnetics Research, Vol. 125, 125-184, 2012. Google Scholar

21. Zaharis, Z. D., K. A. Gotsis, and J. N. Sahalos, "Comparative study of neural network training applied to adaptive beamforming of antenna arrays," Progress In Electromagnetics Research, Vol. 126, 269-283, 2012.
doi:10.2528/PIER12012408 Google Scholar

22. Liu, X., T. Jiang, L. Yang, and H.-B. Zhu, "Constrained trilinear decomposition with application to array signal processing," Progress In Electromagnetics Research, Vol. 128, 195-214, 2012. Google Scholar

23. Mallipeddi, R., J. P. Lie, P. N. Suganthan, S. G. Razul, and C. M. S. See, "A differential evolution approach for robust adaptive beamforming based on joint estimation of look direction and Array Geometry," Progress In Electromagnetics Research, Vol. 119, 381-394, 2011.
doi:10.2528/PIER11052205 Google Scholar

24. Eom, S. Y., Y.-B. Jung, S. A. Ganin, and A. V. Shishlov, "A cylindrical shaped-reflector antenna with a linear feed array for shaping complex beam patterns ," Progress In Electromagnetics Research, Vol. 119, 477-495, 2011.
doi:10.2528/PIER11062912 Google Scholar

25. Zaharis, Z. D. and T. V. Yioultsis, "A novel adaptive beamforming technique applied on linear antenna arrays using adaptive mutated boolean PSO," Progress In Electromagnetics Research, Vol. 117, 165-179, 2011. Google Scholar

26. Li, W.-T., Y.-Q. Hei, and X.-W. Shi, "Pattern synthesis of conformal arrays by a modified particle swarm optimization," Progress In Electromagnetics Research, Vol. 117, 237-252, 2011. Google Scholar

27. Wang, W.-B., Q. Feng, and D. Liu, "Application of chaotic particle swarm optimization algorithm to pattern synthesis of antenna arrays," Progress In Electromagnetics Research, Vol. 115, 173-189, 2011. Google Scholar

28. Li, R., L. Xu, X.-W. Shi, N. Zhang, and Z.-Q. Lv, "Improved differential evolution strategy for antenna array pattern synthesis problems," Progress In Electromagnetics Research, Vol. 113, 429-441, 2011. Google Scholar

29. Zaharis, Z. D., K. A. Gotsis, and J. N. Sahalos, "Adaptive beamforming with low side lobe level using neural networks trained by mutated boolean PSO," Progress In Electromagnetics Research, Vol. 127, 139-154, 2012.
doi:10.2528/PIER12022806 Google Scholar

30. Zaharis, Z. D., "A modified Taguchi's optimization algorithm for beamforming applications," Progress In Electromagnetics Research, Vol. 127, 553-569, 2012.
doi:10.2528/PIER12040108 Google Scholar

31. Wu, X. P., J.-M. Shi, Z. S. Chen, and B. Xu, "A new plasma antenna of beam-forming," Progress In Electromagnetics Research, Vol. 126, 539-553, 2012.
doi:10.2528/PIER12021906 Google Scholar

32. Jeong, S.-H., H.-Y. Yu, J.-E. Lee, J.-N. Oh, and K.-H. Lee, "A multi-beam and multi-range radar with FMCW and digital beam forming for automotive applications," Progress In Electromagnetics Research, Vol. 124, 285-299, 2012.
doi:10.2528/PIER11110805 Google Scholar

33. Lu, S., J. Sun, G. Wang, and Y.-L. Lu, "A mixing vector based an affine combination of two adaptive filters for sensor array beamforming," Progress In Electromagnetics Research, Vol. 122, 361-387, 2012.
doi:10.2528/PIER11090204 Google Scholar

34. Mallipeddi, R., J. P. Lie, S. G. Razul, P. N. Suganthan, and C. M. S. See, "Robust adaptive beamforming based on covariance matrix reconstruction for Look direction mismatch," Progress In Electromagnetics Research Letters, Vol. 25, 37-46, 2011. Google Scholar

35. Lee, J.-H., G.-W. Jung, and W.-C. Tsai, "Antenna array beamforming in the presence of spatial information uncertainties," Progress In Electromagnetics Research B, Vol. 31, 139-156, 2011. Google Scholar

36. Lee, J.-H., "Robust antenna array beamforming under cycle frequency mismatch," Progress In Electromagnetics Research B, Vol. 35, 307-328, 2011.
doi:10.2528/PIERB11082207 Google Scholar

37. Jabbar, A. N., "A novel ultra-fast ultra-simple adaptive blind beamforming algorithm for smart antenna arrays," Progress In Electromagnetics Research B, Vol. 35, 329-348, 2011.
doi:10.2528/PIERB11091504 Google Scholar

38. Huang, C.-C. and J.-H. Lee, "Robust adaptive beamforming using a fully data-dependent loading technique," Progress In Electromagnetics Research B, Vol. 37, 307-325, 2012.
doi:10.2528/PIERB11110406 Google Scholar

39. Cho, S.-W. and J.-H. Lee, "Effect of threshold value on the performance of natural frequency-based radar target recognition," Progress In Electromagnetics Research, Vol. 135, 527-562, 2013. Google Scholar

40. Lee, J.-H., S.-W. Cho, S.-H. Park, and K.-T. Kim, "Performance analysis of radar target recognition using natural frequency: Frequency domain approach," Progress In Electromagnetics Research, Vol. 132, 315-345, 2012. Google Scholar

41. Lee, J.-H. and S.-H. Jeong, "Performance of natural frequency-based target detection in frequency domain," Journal of Electromagnetic Waves and Applications, Vol. 26, No. 17-18, 2426-2437, 2012.
doi:10.1080/09205071.2012.735789 Google Scholar

42. Lee, J.-H. and H.-T. Kim, "Comments on extraction of the natural frequencies of a radar target from a measured response using E-pulse techniques," IEEE Transactions Antennas and Propagation, Vol. 53, No. 11, 3853-3855, Nov. 2005. Google Scholar

43. Lee, J.-H. and H.-T. Kim, "Radar target recognition based on late time representation: Closed form expression for criterion," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 9, 2455-2462, 2006.
doi:10.1109/TAP.2006.880665 Google Scholar

44. Li, J. and P. Stoica, Robust Adaptive Beamforming, Wiley-Interscience, 2006.

45. Li, J., P. Stoica, and Z. Wang, "On robust Capon beamforming and diagonal loading," IEEE Transactions on Signal Processing, Vol. 51, No. 7, 1702-1715, 2003.
doi:10.1109/TSP.2003.812831 Google Scholar

46. Li, J., P. Stoica, and Z. Wang, "Doubly constrained robust Capon beamformer," IEEE Transactions on Signal Processing, Vol. 52, 2407-2423, 2004.
doi:10.1109/TSP.2004.831998 Google Scholar

47. Du, L., J. Li, and P. Stoica, "Fully automatic computation of diagonal loading levels for robust adaptive beamforming," IEEE Transactions on Aerospace and Electronics Systems, Vol. 46, 449-458, 2010.
doi:10.1109/TAES.2010.5417174 Google Scholar

48. Elnashar, A., S. Elnoubi, and H. El-Mikati, "Further study on robust adaptive beamforming with optimum diagonal loading," IEEE Transactions on Antennas and Propagation, Vol. 54, 3647-3658, 2006.
doi:10.1109/TAP.2006.886473 Google Scholar

Dr. Sung-Woo Cho

Professor Joon-Ho Lee