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Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors

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Abstract

Compared to the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE employing fourth-order cumulants (referred to as FOC-RARE) is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling errors than that of the SOS-RARE from the resolution point of view.

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References

  1. SEE C M S. Sensor array calibration in the presence of mutual coupling and unknown sensor gains and phases [J]. Electronics Letters, 1994, 30(5): 373–374.

    Article  Google Scholar 

  2. SEE C M S, POTH B K. Parametric sensor array calibration using measured steering vectors of uncertain locations [J]. IEEE Transactions on Signal Processing, 1999, 47(4): 1133–1137.

    Article  Google Scholar 

  3. CHENG Q, HUA Y B, STOICA P. Asymptotic performance of optimal gain-and-phase estimators of sensor arrays [J]. IEEE Transactions on Signal Processing, 2000, 48(12): 3587–3590.

    Article  MATH  Google Scholar 

  4. WANG D, WU Y. Array errors active calibration algorithm and its improvement [J]. Science China Information Sciences, 2010, 53(5): 1016–1033. (in Chinese)

    Article  MathSciNet  Google Scholar 

  5. FRIEDLANDER B, WEISS A J. Direction finding in the presence of mutual coupling [J]. IEEE Transactions on Antennas and Propagation, 1991, 39(3): 273–284.

    Article  Google Scholar 

  6. SELLONE F, SERRA A. A novel mutual coupling compensation algorithm for uniform and linear arrays [J]. IEEE Transactions on Signal Processing, 2007, 55(2): 560–573.

    Article  MathSciNet  Google Scholar 

  7. WIJNHOLDS S J, VEEN A J. Multisource self-calibration for sensor arrays [J]. IEEE Transactions on Signal Processing, 2009, 57(9): 3512–3522.

    Article  MathSciNet  Google Scholar 

  8. YE Z F, DAI J S, XU X, WU X P. DOA estimation for uniform linear array with mutual coupling [J]. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(1): 280–288.

    Article  Google Scholar 

  9. WANG B H, WANG Y L, CHEN H. Robust DOA estimation and array calibration in the presence of mutual coupling for uniform linear array [J]. Science in China Ser.F: Information Sciences, 2004, 47(3): 348–361. (in Chinese)

    Article  Google Scholar 

  10. QI C, WANG Y, ZHANG Y, CHEN H. DOA estimation and self-calibration algorithm for uniform circular array [J]. Electronics Letters, 2005, 41(20): 1092–1094.

    Article  Google Scholar 

  11. GOOSSENS R, ROGIER H. A hybrid UCA-RARE/Root-MUSIC approach for 2-D direction of arrival estimation in uniform circular arrays in the presence of mutual coupling [J]. IEEE Transactions on Antennas and Propagation, 2007, 55(3): 841–849.

    Article  Google Scholar 

  12. LIU C, YE Z F, ZHANG Y F. Autocalibration algorithm for mutual coupling of planar array [J]. Signal Processing, 2010, 90(3): 784–794.

    Article  MathSciNet  MATH  Google Scholar 

  13. HU X Q, CHEN H, WANG Y L, CHEN J W. A self-calibration algorithm for cross array in the presence of mutual coupling [J]. Science China Information Sciences, 2011, 54(4): 836–848. (in Chinese)

    Article  MathSciNet  Google Scholar 

  14. LIANG J L, ZENG X J, WANG W Y, CHEN H Y. L-shaped array-based elevation and azimuth direction finding in the presence of mutual coupling [J]. Signal Processing, 2011, 91(5): 1319–1328.

    Article  MATH  Google Scholar 

  15. WANG B H, WANG Y L, CHEN H, GUO Y. Array calibration of angularly dependent gain and phase uncertainties with carry-on instrumental sensors [J]. Science in China Ser.F: Information Sciences, 2004, 47(6): 777–792. (in Chinese)

    Article  Google Scholar 

  16. PESAVENTO M, GERSHMAN A B, WONG K M. Direction finding in partly calibrated sensor arrays composed of multiple subarrays [J]. IEEE Transactions on Signal Processing, 2002, 50(9): 2103–2115.

    Article  Google Scholar 

  17. SEE C M S, GERSHMAN A B. Direction-of-arrival estimation in partly calibrated subarray-based sensor arrays [J]. IEEE Transactions on Signal Processing, 2004, 52(2): 329–338.

    Article  MathSciNet  Google Scholar 

  18. WANG D, WU Y. Effects of finite samples on the resolution performance of the rank reduction estimator [J]. Science China Information Sciences, 2013, 56(1): 1–14.

    Google Scholar 

  19. XIANG L, YE Z, XU X, CHANG C, XU W, HUANG Y S. Direction of arrival estimation for uniform circular array based on fourth-order cumulants in the presence of unknown mutual coupling [J]. IET Microwaves, Antennas and Propagation, 2008, 2(3): 281–287.

    Article  Google Scholar 

  20. LI X B, SHI Y W, ZHANG H. RARE-Cumulant algorithm for direction of arrival estimation and array calibration [C]// Proceedings of International Conference on Advanced Infocomm Technology. Shengzhen: IEEE Press, 2008: 29–31.

    Google Scholar 

  21. YE Z F, DAI J S. DOA estimation for nonuniform circular array with mutual coupling based on fourth order cumulants [J]. Journal of University of Science and Technology of China, 2008, 38(7): 770–775. (in Chinese)

    Google Scholar 

  22. LIU F, LV J Q. Signal direction of arrival estimation based high-order cumulants and a partially calibrated array [C]// Proceedings of International Conference on Communications, Circuits and Systems. Guilin: IEEE Press, 2006: 293–297.

    Google Scholar 

  23. WANG D, WU Y. Cumulants-based instrumental sensors method for self-calibration of sensor position errors [J]. Systems Engineering and Electronics, 2010, 32(7): 143–150. (in Chinese)

    Google Scholar 

  24. WU B, CHEN H, LI J D. Direction of arrival (DOA) estimation under non-toeplitz mutual coupling matrix of ULA [J]. Radar Science and Technology, 2009, 7(5): 358–364. (in Chinese)

    MathSciNet  Google Scholar 

  25. SHERIF A E, ALEX B G, KON M W. Rank reduction direction-of-arrival estimators with an improved robustness against subarray orientation errors [J]. IEEE Transactions on Signal Processing, 2006, 54(5): 1951–1955.

    Article  Google Scholar 

  26. WANG D, WU Y. Performance analysis of rank reduction estimator in the presence of unexpected modeling errors [J]. Journal on Communications, 2011, 32(8): 81–90. (in Chinese)

    Google Scholar 

  27. WANG D, WU Y. Statistical characteristics and resolution probability of rank reduction spatial spectrum in the presence of unexpected model errors [J]. Journal of Applied Sciences, 2011, 29(2): 176–186. (in Chinese)

    Google Scholar 

  28. LUO Na, QIAN Feng, ZHAO Liang, ZHONG Wei-min. Gaussian process assisted coevolutionary estimation of distribution algorithm for computationally expensive problems [J]. Journal of Central South University, 2012, 19(2): 443–452. (in Chinese)

    Article  Google Scholar 

  29. FERRÉOL A, LARZABAL P, VIBERG M. On the asymptotic performance analysis of subspace DOA estimation in the presence of modeling errors: Case of MUSIC [J]. IEEE Transactions on Signal Processing, 2006, 54(3): 907–920.

    Article  Google Scholar 

  30. FERRÉOL A, LARZABAL P, VIBERG M. On the resolution probability of MUSIC in presence of modeling errors [J]. IEEE Transactions on Signal Processing, 2008, 56(5): 1945–1953.

    Article  MathSciNet  Google Scholar 

  31. PORAT B, FRIEDLANDER B. Direction finding algorithms based on high-order statistics [J]. IEEE Transactions on Signal Processing, 1991, 39(9): 2016–2023.

    Article  MATH  Google Scholar 

  32. HARRY B, MICHAEL S W. Statistical characterization of the MUSIC null spectrum [J]. IEEE Transactions on Signal Processing, 1991, 39(6): 1333–1347.

    Article  Google Scholar 

  33. ZHANG Q T. Probability of resolution of the MUSIC algorithm [J]. IEEE Transactions on Signal Processing, 1995, 43(4): 978–987.

    Article  Google Scholar 

  34. SHARMAN K C, DURRANI T S. Resolving power of signal subspace methods for finite data length [C]// Proceedings of International Conference on Acoustics, Speech and Signal Processing, Florida: IEEE Press, 1985, 10: 1501–1504.

    Google Scholar 

  35. FERRÉOL A, LARZABAL P, VIBERG M. Statistical analysis of the MUSIC algorithm in the presence of modeling errors, taking into account the resolution probability [J]. IEEE Transactions on Signal Processing, 2010, 58(8): 4156–4166.

    Article  MathSciNet  Google Scholar 

  36. LIAO G S, BAO Z, WANG B. Robustness analysis of 4-order cumulants-based MUSIC algorithm in presence of sensor errors [J]. Journal on Communications, 1997, 18(8): 33–38. (in Chinese)

    Google Scholar 

  37. JANSSEN J, STOICA P. On the expectation of the product of four matrix-valued Gaussian random variables [J]. IEEE Transactions on Automatic Control, 1988, 33(9): 867–870.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Information System Engineering, PLA Information Engineering University, Zhengzhou, 450002, China

    Ding Wang  (王鼎) & Ying Wu  (吴瑛)

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  1. Ding Wang  (王鼎)
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  2. Ying Wu  (吴瑛)
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Correspondence to Ding Wang  (王鼎).

Additional information

Foundation item: Project(61201381) supported by the National Nature Science Foundation of China; Project(YP12JJ202057) supported by the Future Development Foundation of Zhengzhou Information Science and Technology College, China

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Wang, D., Wu, Y. Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors. J. Cent. South Univ. 20, 3116–3130 (2013). https://doi.org/10.1007/s11771-013-1835-x

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  • DOI: https://doi.org/10.1007/s11771-013-1835-x

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