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Statistical Distribution of Difference of the Maximum-Likelihood Angle-of-Arrival Spectra

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Abstract

We consider the performance analysis of the maximum-likelihood (ML) angle-of-arrival (AOA) estimation algorithm in this paper. Based on the observation that the ML AOA spectrum is noncentral chi-square distributed with known degree of freedom and known noncentrality, we propose how to numerically evaluate the probability density function of the difference between two ML spectra associated with two different directions. By judiciously choosing the two different angles, we can analytically determine the probability that the ML spectrum at the nearest grid is greater than the ML spectrum at the second nearest grid by arbitrary value. Numerical examples are used to validate the derived expressions.

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References

  1. M.L. Bencheikh, Y. Wang, Combined ESPRIT-RootMUSIC for DOA-DOD estimation in polarimetric bistatic MIMO radar. Prog. Electromagn. Res. Lett. 22, 109–117 (2011)

    Article  Google Scholar 

  2. D. Byrne, M. O’Halloran, M. Glavin, E. Jones, Data independent radar beamforming algorithms for breast cancer detection. Prog. Electromagn. Res. 107, 331–348 (2010)

    Article  Google Scholar 

  3. S.-W. Cho, J.-H. Lee, Efficient implementation of the Capon beamforming using the Levenberg–Marquardt scheme for two dimensional AOA estimation. Prog. Electromagn. Res. 137, 19–34 (2013)

    Article  Google Scholar 

  4. A. Ferrol, P. Larzabal, M. Viberg, On the asymptotic performance analysis of subspace DOA estimation in the presence of modeling errors: case of MUSIC. IEEE Trans. Signal Process. 54(3), 907–920 (2006)

    Article  Google Scholar 

  5. X. Gu, Y. Zhang, Resolution threshold analysis of MUSIC algorithm in radar range imaging. Prog. Electromagn. Res. B 31, 297–321 (2011)

    Article  Google Scholar 

  6. R.A. Horn, C.R. Johnson, Matrix analysis (Cambridge Univ. Press, Cambridge, 1986)

    Google Scholar 

  7. H. Krim, P. Forster, J.G. Proakis, Operator approach to performance analysis of root-MUSIC and root-min-norm. IEEE Trans. Signal Process. 40(7), 1687–1696 (1992)

    Article  MATH  Google Scholar 

  8. J.-H. Lee, S.-W. Cho, I.-S. Choi, Newton-type method in spectrum estimaion-based AOA estimation. IEICE Electron. Exp. 9(14) (2012)

  9. J.-H. Lee, Y.-S. Jeong, S.-W. Cho, W.-Y. Yeo, K.S.J. Pister, Application of the Newton method to improve the accuracy of TOA estimation with the beamforming algorithm and the MUSIC algorithm. Prog. Electromagn. Res. 116, 475–515 (2011)

    Article  Google Scholar 

  10. J.-H. Lee, S.-W. Cho, S.-H. Jeong, Application of the Levenberg–Marquardt scheme to the MUSIC algorithm for AOA estimation. Int. J. Antennas and Propag. 402842, 1–8 (2013)

    Google Scholar 

  11. J.-H. Lee, S.-W. Cho, H.-J. Moon, Application of the alternating projection strategy to the Capon beamforming and the MUSIC algorithm for azimuth/elevation AOA estimation. J. Electromagn. Waves Appl. 27(12), 1439–1454 (2013)

    Article  Google Scholar 

  12. J.-H. Lee, S.-W. Cho, Performance improvement of the AOA estimation algorithm using the Newton iteration. Appl. Comput. Electromagn. Soc. J. 28(3), 249–272 (2013)

    Google Scholar 

  13. J. Liang, D. Liu, Two L-shaped array-based 2-D DOAs estimation in the presence of mutual coupling. Prog. Electromagn. Res. 112, 273–298 (2011)

    Article  Google Scholar 

  14. Y. Li, H. Ling, Improved current decomposition in helical antennas using the ESPRIT algorithm. Prog. Electromagn. Res. 106, 279–293 (2010)

    Article  Google Scholar 

  15. J.E. Mooney, Z. Ding, L.S. Riggs, Performance analysis of a GLRT automated target discrimination scheme. IEEE Trans. Antennas Propag. 49(12), 1827–1835 (2001)

    Article  Google Scholar 

  16. S.U. Pillai, B.H. Kwon, Performance analysis of MUSIC-type high resolution estimators for direction finding in correlated and coherent scenes. IEEE Trans. Acoust. Speech Signal Process. 37(8), 1176–1189 (1989)

    Article  Google Scholar 

  17. B.D. Rao, K.V.S. Hari, Performance analysis of root-MUSIC. IEEE Trans. Acoust. Speech Signal Process. 37(8), 1939–1949 (1989)

    Article  Google Scholar 

  18. P. Stoica, A. Nehorai, MUSIC, maximum likelihood, and Cramer–Rao bound. IEEE Trans. Acoust. Speech Signal Process. 37(5), 720–741 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  19. P. Stoica, A. Nehorai, MUSIC, maximum likelihood, and Cramer–Rao bound: further results and comparisons. IEEE Trans. Acoust. Speech Signal Process. 38(12), 2140–2150 (1990)

    Article  Google Scholar 

  20. A.L. Swindlehurst, T. Kailath, A performance analysis of subspace-based methods in the presence of model errors. I. The MUSIC algorithm. IEEE Trans. Signal Process. 40(7), 1758–1774 (1992)

    Article  MATH  Google Scholar 

  21. P. Yang, F. Yang, Z.-P. Nie, DOA estimation with sub-array divided technique and interporlated ESPRIT algorithm on a cylindrical conformal array antenna. Prog. Electromagn. Res. 103, 201–216 (2010)

    Article  Google Scholar 

  22. Q.T. Zhang, Probability of resolution of the MUSIC algorithm. IEEE Trans. Signal Process. 43(4), 978–987 (1995)

    Article  Google Scholar 

  23. W. Zhang, A. Hoorfar, L. Li, Through-the-wall target localization with time reversal MUSIC method. Prog. Electromagn. Res. 106, 75–89 (2010)

    Article  Google Scholar 

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Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2A10012245).

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Authors and Affiliations

  1. Department of Information and Communication Engineering, Sejong University, Seoul, Korea

    Joon-Ho Lee, So-Hee Jeong & Eun-Kyung Lee

  2. LIG Nex1 Co., Ltd., 333, Pangyo-ro, Bundang-gu, Seongnam-City, Gyeonggi-do, 463-400, Korea

    Sung-Woo Cho

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  1. Joon-Ho Lee
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  2. Sung-Woo Cho
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  4. Eun-Kyung Lee
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Correspondence to Joon-Ho Lee.

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Lee, JH., Cho, SW., Jeong, SH. et al. Statistical Distribution of Difference of the Maximum-Likelihood Angle-of-Arrival Spectra. Circuits Syst Signal Process 35, 1705–1727 (2016). https://doi.org/10.1007/s00034-015-0141-2

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