volume | PIER Journals

Abstract

Based on gain optimization methods, superdirective beamformers can achieve high beam directivity with small aperture array. However, the extreme sensitivity to array uncertainty is a main obstacle to engineering application. In this work, a robust gain optimization algorithm under uncertainty set constraint is proposed. Considering steering vector mismatch is the result of combined effect of various array errors, and it is a measurable indicator especially in receiving system. We apply its uncertainty as a constraint on gain optimization method, which is more intuitive in physical sense. Different from existing solutions, it makes a better tradeoff among directive gain, robustness and radiation efficiency. Experimental analysis verifies its good performance in engineering.

1. Shashikant, M. S. and J. K. Butler, "Constrained optimization of the performance indices of arbitrary array antennas," IEEE Transactions on Antennas and Propagation, Vol. 19, No. 4, 493-497, 1971.
doi:10.1109/TAP.1971.1139955

2. Schelkunoff, S. A., "A mathematical theory of linear arrays," Bell System Technical Journal, Vol. 22, No. 1, 80-107, 1943.
doi:10.1002/j.1538-7305.1943.tb01306.x

3. Yaru, N., "A note on super-gain antenna arrays," Proceedings of the IRE, Vol. 39, No. 9, 1080-1085, 1951.
doi:10.1109/JRPROC.1951.273753

4. Cheng, D., F. Tseng, and J. K. Butler, "Gain optimization for arbitrary array," IEEE Transactions on Antennas and Propagation, Vol. 13, No. 6, 973-974, 1965.
doi:10.1109/TAP.1965.1138542

5. Chryssomallis, M. and J. N. Sahalos, "A synoptic study of different superdirective endfire array concepts," Archiv fr Elektrotechnik, Vol. 76, No. 6, 469-476, 1993.
doi:10.1007/BF01576027

6. Lo, Y. T., S. W. Lee, and Q. H. Lee, "Optimization of directivity and signal-to-noise ratio of an arbitrary antenna array," Proceedings of the IEEE, Vol. 54, No. 8, 1033-1045, 1966.
doi:10.1109/PROC.1966.4988

7. Ma, Y. L., Y. X. Yang, Z. Y. He, et al. "Theoretical and practical solutions for high-order superdirectivity of circular sensor arrays," IEEE Transactions on Industrial Electronics, Vol. 60, No. 1, 203-209, 2013.
doi:10.1109/TIE.2012.2185020

8. Newman, E. H., J. H. Richmond, and C. H. Walter, "Superdirective receiving arrays," IEEE Transactions on Antennas and Propagation, Vol. 26, No. 5, 629-639, 1978.
doi:10.1109/TAP.1978.1141928

9. Barrick, D. E. and P. M. Lilleboe, "Circular superdirective receive antenna arrays,", Patent No. US 6,844,849 B1, Jan. 18, 2005.

10. Uzsoky, M. and L. Solymar, "Theory of super-directive linear arrays," Acta Physica Academiae Scientiarum Hungaricae, Vol. 6, No. 2, 185-205, 1956.
doi:10.1007/BF03157322

11. Doclo, S. and M. Moonen, "Superdirective beamforming robust against microphone mismatch," IEEE Transactions on Audio Speech and Language Processing, Vol. 15, No. 2, 617-631, 2007.
doi:10.1109/TASL.2006.881676

12. Zhou, Q. C., H. Gao, H. Zhang, and F. Wang, "Robust superdirective beamforming for HF circular receive antenna arrays," Progress In Electromagnetics Research, Vol. 136, 665-679, 2013.
doi:10.2528/PIER12122301

13. Zhou, Q. C., H. Gao, H. Zhang, and L. Zhou, "Superdirective beamforming with interferences and noise suppression via second-order cone programming," Progress In Electromagnetics Research C, Vol. 43, 255-269, 2013.

14. Trucco, A. and M. Crocco, "Design of an optimum superdirective beamformer through generalized directivity maximization," IEEE Transactions on Signal Processing, Vol. 62, No. 23, 6118-6129, 2014.
doi:10.1109/TSP.2014.2360819

15. Zhang, H. J., H. Gao, Q. C. Zhou, et al. "A novel digital beamformer applied in vehicle mounted hf receiving device," IEICE Electronics Express, Vol. 11, No. 2, 1-8, 2014.
doi:10.1587/elex.11.20130919

16. Zhou, Q. C., H. Gao, H. J. Zhang, et al. "Pattern synthesis method applied in designing HF superdirective receive arrays," IEICE Electronics Express, Vol. 10, No. 21, 1-7, 2014.

17. Zhang, H. J., H. Gao, L. Zhou, et al. "HF superdirective smart antenna system for interference suppression," IEICE Electronics Express, Vol. 12, No. 3, 1-7, 2015.
doi:10.1587/elex.12.20141165

18. Besson, O., A. A. Monakov, and C. Chalus, "Signal waveform estimation in the presence of uncertainties about the steering vector," IEEE Transactions on Signal Processing, Vol. 52, No. 9, 1-7, 2004.
doi:10.1109/TSP.2004.831917

19. Gu, Y. J., Z.-G. Shi, K. S. Chen, and Y. Li, "Robust adaptive beamforming for steering vector uncertainties based on equivalent DOAs method," Progress In Electromagnetics Research, Vol. 79, 277-290, 2008.
doi:10.2528/PIER07102202

20. Vorobyov, S. A., "Principles of minimum variance robust adaptive beamforming design," Signal Processing, Vol. 93, 3264-3277, 2012.

21. Vorobyov, S. A., A. B. Gershman, Z. Q, and Luo, "Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem," IEEE Transactions on Signal Processing, Vol. 51, No. 2, 313-324, 2003.
doi:10.1109/TSP.2002.806865

22. 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

23. Li, J., P. Stoica, and Z.Wang, "Doubly constrained robust capon beamformer," IEEE Transactions on Signal Processing, Vol. 52, No. 9, 2407-2423, 2004.
doi:10.1109/TSP.2004.831998

24. Lorenz, R. G. and S. P. Boyd, "Robust minimum variance beamforming," IEEE Transactions on Signal Processing, Vol. 53, No. 5, 1684-1696, 2005.
doi:10.1109/TSP.2005.845436

25. Besson, O. and F. Vincent, "Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors," IEEE Transactions on Signal Processing, Vol. 53, No. 2, 452-459, 2005.
doi:10.1109/TSP.2004.840777

26. Vorobyov, S. A., H. H Chen, and A. B. Gershman, "On the relationship between robust minimum variance beamformers with probabilistic and worst-case distortionless response constraints," IEEE Transactions on Signal Processing, Vol. 56, No. 11, 5719-5724, 2008.
doi:10.1109/TSP.2008.929866

27. Gershman, A. B., N. D. Sidiropoulos, S. ShahbazPanahi, et al. "Convex optimization-based beamforming," IEEE Signal Processing Magazine, Vol. 27, No. 3, 62-75, 2010.
doi:10.1109/MSP.2010.936015

28. Lei, L., J. P. Lie, A. B. Gershman, et al. "Robst adaptive beamforming and steering vector estimation in partly calibrated sensor arrays a structured uncertainty approach," IEEE International Conference on Acoustics Speech and Signal Processing, Vol. 56, No. 11, 2534-2537, 2010.

29. Khabbazibasmenj, A., S. A. Vorobyov, and A. Hassanien, "Robust adaptive beamforming based on steering vector estimation with as little as possible prior information," IEEE Transactions on Signal Processing, Vol. 60, No. 6, 2974-2987, 2012.
doi:10.1109/TSP.2012.2189389

30. Capon, J., "High-resolution frequency-wavenumber spectrum analysis," Proceedings of the IEEE, Vol. 57, No. 8, 1408-1418, 1969.
doi:10.1109/PROC.1969.7278

31. Tylavsky, D. J. and G. R. L. Sohie, "Generalization of the matrix inversion lemma," Proceedings of the IEEE, Vol. 74, No. 7, 1050-1052, 1986.
doi:10.1109/PROC.1986.13587

32. Gao, H., H. Ke, Z. Yang, et al. "The relationship between mutual coefficient errors and the amplitude and phase errors of channels," Journal of Wuhan University, Vol. 48, No. 1, 121-124, 2002.

33. Qi, C., Z. Chen, Y. Zhang, et al. "DOA estimation and self-calibration algorithm for multiple subarrays in the presence of mutual coupling," IEE Processing-Radar Sonar and Navigation, Vol. 153, No. 4, 333-337, 2006.
doi:10.1049/ip-rsn:20045128

34. Wang, D., "Improved active calibration algorithms in the presence of channel gain/phase uncertainties and sensor mutual coupling effects," Circuits Systems and Signal Processing, Vol. 34, No. 6, 1825-1868, 2015.
doi:10.1007/s00034-014-9926-y

Dr. Huajun Zhang

Prof. Huotao Gao

Dr. Lin Zhou

Dr. Huanhuan Shang

Dr. Huaqiao Zhao