Skip to main content


  • Research Article
  • Open Access

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

  • 1Email author,
  • 1,
  • 1, 2 and
  • 1
EURASIP Journal on Wireless Communications and Networking20072007:030684

  • Received: 17 November 2006
  • Accepted: 1 August 2007
  • Published:


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.


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


Authors’ Affiliations

ACCESS Linnaeus Center, School of Electrical Engineering, Royal Institute of Technology (KTH), Stockholm, 100 44, Sweden
Department of Electrical Engineering (ISY), Linköping University, Linköping, 58183, Sweden


  1. Tse D, Viswanath P: Fundamentals of Wireless Communication. Cambridge University Press, Cambridge, UK; 2005.View ArticleMATHGoogle 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. 10.1109/78.143447View ArticleMATHGoogle 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. 10.1109/78.709536View ArticleGoogle 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. 10.1109/78.258129View ArticleGoogle Scholar
  5. Steyskal H, Herd JS: Mutual coupling compensation in small array antennas. IEEE Transactions on Antennas and Propagation 1990,38(12):1971-1975. 10.1109/8.60990View ArticleGoogle 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. 10.1109/78.482121View ArticleGoogle 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.View ArticleGoogle 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:20001309View ArticleGoogle 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. 10.1109/8.76322View ArticleGoogle 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-MView ArticleGoogle 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. 10.1109/8.686759View ArticleGoogle 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.View ArticleGoogle 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.View ArticleGoogle Scholar
  15. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Upper Saddle River, NJ, USA; 1993.MATHGoogle Scholar
  16. Van Trees HL: Detection, Estimation, and Modulation Theory. Wiley-Interscience, New York, NY, USA; 2007.MATHGoogle Scholar
  17. Gorman J, Hero A: Lower bounds for parametric estimation with constraints. IEEE Transactions on Information Theory 1990,36(6):1285-1301. 10.1109/18.59929MathSciNetView ArticleMATHGoogle Scholar
  18. Stoica P, Ng BC: On the Crameér-Rao bound under parametric constraints. IEEE Signal Processing Letters 1998,5(7):177-179. 10.1109/97.700921View ArticleGoogle 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


© Marc Mowlér et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.