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Joint Estimation of Mutual Coupling, Element Factor, and Phase Center in Antenna Arrays

Abstract

A novel method is proposed for estimation of the mutual coupling matrix of an antenna array. The method extends previous work by incorporating an unknown phase center and the element factor (antenna radiation pattern) in the model, and treating them as nuisance parameters during the estimation of coupling. To facilitate this, a parametrization of the element factor based on a truncated Fourier series is proposed. The performance of the proposed estimator is illustrated and compared to other methods using data from simulations and measurements, respectively. The Cramér-Rao bound (CRB) for the estimation problem is derived and used to analyze how the required amount of measurement data increases when introducing additional degrees of freedom in the element factor model. We find that the penalty in SNR is 2.5 dB when introducing a model with two degrees of freedom relative to having zero degrees of freedom. Finally, the tradeoff between the number of degrees of freedom and the accuracy of the estimate is studied. A linear array is treated in more detail and the analysis provides a specific design tradeoff.

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References

  1. Tse D, Viswanath P: Fundamentals of Wireless Communication. Cambridge University Press, Cambridge, UK; 2005.

    Book  MATH  Google Scholar 

  2. Swindlehurst A, Kailath T: A performance analysis of subspace-based methods in the presence of model errors—part I: the MUSIC algorithm. IEEE Transactions on Signal Processing 1992,40(7):1758-1774. 10.1109/78.143447

    Article  MATH  Google Scholar 

  3. Jansson M, Swindlehurst A, Ottersten B: Weighted subspace fitting for general array error models. IEEE Transactions on Signal Processing 1998,46(9):2484-2498. 10.1109/78.709536

    Article  Google Scholar 

  4. Friedlander B, Weiss AJ: Effects of model errors on waveform estimation using the MUSIC algorithm. IEEE Transactions on Signal Processing 1994,42(1):147-155. 10.1109/78.258129

    Article  Google Scholar 

  5. Steyskal H, Herd JS: Mutual coupling compensation in small array antennas. IEEE Transactions on Antennas and Propagation 1990,38(12):1971-1975. 10.1109/8.60990

    Article  Google Scholar 

  6. Yang J, Swindlehurst AL: The effects of array calibration errors on DF-based signal copy performance. IEEE Transactions on Signal Processing 1995,43(11):2724-2732. 10.1109/78.482121

    Article  Google Scholar 

  7. Balanis CA: Antenna Theory: Analysis and Design. John Wiley & Sons, New York, NY, USA; 1997.

    Google Scholar 

  8. Svantesson T: The effects of mutual coupling using a linear array of thin dipoles of finite length. Proceedings of the 9th IEEE SP Workshop on Statistical Signal and Array Processing (SSAP '98), September 1998, Portland, Ore, USA 232-235.

    Chapter  Google Scholar 

  9. Dandekar KR, Ling H, Xu G: Effect of mutual coupling on direction finding in smart antenna applications. Electronics Letters 2000,36(22):1889-1891. 10.1049/el:20001309

    Article  Google Scholar 

  10. Friedlander B, Weiss A: Direction finding in the presence of mutual coupling. IEEE Transactions on Antennas and Propagation 1991,39(3):273-284. 10.1109/8.76322

    Article  Google Scholar 

  11. Su T, Dandekar K, Ling H: Simulation of mutual coupling effect in circular arrays for direction-finding applications. Microwave and Optical Technology Letters 2000,26(5):331-336. 10.1002/1098-2760(20000905)26:5<331::AID-MOP17>3.0.CO;2-M

    Article  Google Scholar 

  12. Lindmark B, Lundgren S, Sanford J, Beckman C: Dual-polarized array for signal-processing applications in wireless communications. IEEE Transactions on Antennas and Propagation 1998,46(6):758-763. 10.1109/8.686759

    Article  Google Scholar 

  13. Mowlér M, Lindmark B: Estimation of coupling, element factor, and phase center of antenna arrays. Proceedings of IEEE Antennas and Propagation Society International Symposium, July 2005, Washington, DC, USA 4B: 6-9.

    Article  Google Scholar 

  14. Lindmark B: Comparison of mutual coupling compensation to dummy columns in adaptive antenna systems. IEEE Transactions on Antennas and Propagation 2005,53(4):1332-1336.

    Article  Google Scholar 

  15. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Upper Saddle River, NJ, USA; 1993.

    MATH  Google Scholar 

  16. Van Trees HL: Detection, Estimation, and Modulation Theory. Wiley-Interscience, New York, NY, USA; 2007.

    MATH  Google Scholar 

  17. Gorman J, Hero A: Lower bounds for parametric estimation with constraints. IEEE Transactions on Information Theory 1990,36(6):1285-1301. 10.1109/18.59929

    MathSciNet  Article  MATH  Google Scholar 

  18. Stoica P, Ng BC: On the Crameér-Rao bound under parametric constraints. IEEE Signal Processing Letters 1998,5(7):177-179. 10.1109/97.700921

    Article  Google Scholar 

  19. Mowlér M, Larsson EG, Lindmark B, Ottersten B: Methods and bounds for antenna array coupling matrix estimation. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '07), April 2007, Honolulu, Hawaii, USA 2: 881-884.

    Google Scholar 

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Correspondence to Marc Mowlér.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mowlér, M., Lindmark, B., Larsson, E.G. et al. Joint Estimation of Mutual Coupling, Element Factor, and Phase Center in Antenna Arrays. J Wireless Com Network 2007, 030684 (2007). https://doi.org/10.1155/2007/30684

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  • DOI: https://doi.org/10.1155/2007/30684

Keywords

  • Fourier Series
  • Factor Model
  • Estimation Problem
  • Specific Design
  • Linear Array