volume | PIER Journals

Abstract

Superdirective beamforming can highly reduce the aperture size of high-frequency receive array. At the same time, the closely spaced elements of a small aperture array can make it low efficiency and sensitivity to the array uncertainty, which limit its application in practice. Using a parameter called sensitivity factor, we found that array efficiency and robustness against array error could be considered simultaneously. On that basis, we derive a novel superdirective beamforming criterion based on a constrained sensitivity factor for the HF circular receive array. New method is analytical and computationally inexpensive. Through making the directive gain with a given sensitivity factor maximum, we calculate the optimal weights of the array elements. To illustrate the proposed method can increase the acceptance of HF superdirective receive arrays in practice, several numerical results are provided.

1. Qu, Y., G. Liao, S.-Q. Zhu, et al. "Performance analysis of beamforming for MIMO radar," Progress In Electromagnetics Research, Vol. 84, 123-134, 2008.
doi:10.2528/PIER08062306 Google Scholar

2. Liang, G., W. Gong, H. Liu, and J. Yu, "Development of 61-channel digital beamforming (DBF) transmitter array for mobile satellite communication ," Progress In Electromagnetics Research, Vol. 97, No. 6, 177-195, 2009.
doi:10.2528/PIER09082303 Google Scholar

3. Zaharis, Z. D., K. A. Gotsis, and J. N. Sahalos, "Adaptive beamforming with low side lobe level using neural networks trained by mutated boolean PSO ," Progress In Electromagnetics Research, Vol. 127, 139-154, 2012.
doi:10.2528/PIER12022806 Google Scholar

4. Zaharis, Z. D., C. Skeberis, and T. D. Xenos, "Improved antenna array adaptive beamforming with low side lobe level using a novel adaptive invasive weed optimization method," Progress In Electromagnetics Research, Vol. 126, 269-283, 2012.
doi:10.2528/PIER12012408 Google Scholar

5. Jabbar, A. N., "A novel ultra-fast ultra-simple adaptive blind beamforming algorithm for smart antenna arrays," Progress In Electromagnetics Research B, Vol. 35, 329-348, 2011.
doi:10.2528/PIERB11091504 Google Scholar

6. Zaharis, Z. D., K. A. Gotsis, and J. N. Sahalos, "Comparative study of neural network training applied to adaptive beamforming of antenna arrays ," Progress In Electromagnetics Research, Vol. 126, 269-283, 2012.
doi:10.2528/PIER12012408 Google Scholar

7. Byrne, D., M. O'Halloran, E. Jones, et al. "Transmitter-grouping robust capon beamforming for breast cancer detection," Progress In Electromagnetics Research, Vol. 108, 401-416, 2010.
doi:10.2528/PIER10090205 Google Scholar

8. Lu, S., J. Sun, G. Wang, and Y.-L. Lu, "A mixing vector based an affine combination of two adaptive filters for sensor array beamforming," Progress In Electromagnetics Research, Vol. 122, 361-387, 2012.
doi:10.2528/PIER11090204 Google Scholar

9. Lin, M., K. An, J. Ouyang, Y. Huang, and M. Li, "Effect of beamforming on multi-antenna two hop asymmetric fading channels with fixed gain relays," Progress In Electromagnetics Research, Vol. 133, 367-390, 2013. Google Scholar

10. Huang, P., W. Xu, and W. Qi, "Two dimension digital beamforming preprocessing in multibeam scansar," Progress In Electromagnetics Research, Vol. 136, 495-508, 2013. Google Scholar

11. Huang, C.-C. and J.-H. Lee, "Robust adaptive beamforming using a fully data-dependent loading technique," Progress In Electromagnetics Research B, Vol. 37, 307-325, 2012.
doi:10.2528/PIERB11110406 Google Scholar

12. Lee, J.-H., G.-W. Jung, and W.-C. Tsai, "Antenna array beamforming in the presence of spatial information uncertainties," Progress In Electromagnetics Research B, Vol. 31, 139-156, 2011. Google Scholar

13. Mallipeddi, R., J. P. Lie, S. G. Razul, P. N. Suganthan, and C. M. S. See, "Robust adaptive beamforming based on covariance matrix reconstruction for look direction mismatch," Progress In Electromagnetics Research Letters, Vol. 25, 37-46, 2011. Google Scholar

14. Liu, F., J. Wang, R. Du, L. Peng, et al. "A second-order cone programming approach for robust downlink beamforming with power control in cognitive radio networks ," Progress In Electromagnetics Research M, Vol. 18, 221-231, 2011. Google Scholar

15. Zaharis, Z. D. and T. V. Yioultsis, "A novel adaptive beamforming technique applied on linear antenna arrays using adaptive mutated boolean PSO," Progress In Electromagnetics Research, Vol. 117, 165-179, 2011. Google Scholar

16. Zaharis, Z. D., "A modified Taguchi's optimization algorithm for beamforming applications," Progress In Electromagnetics Research, Vol. 127, 553-569, 2012.
doi:10.2528/PIER12040108 Google Scholar

17. Li, W.-X., Y.-P. Li, and W.-H. Yu, "On adaptive beamforming for coherent interference suppression via virtual antenna array," Progress In Electromagnetics Research, Vol. 125, 165-184, 2012.
doi:10.2528/PIER12010802 Google Scholar

18. Mallipeddi, R., J. P. Lie, P. N. Suganthan, et al. "A differential evolution approach for robust adaptive beamforming based on joint estimation of look direction and array geometry," Progress In Electromagnetics Research, Vol. 119, 381-394, 2011.
doi:10.2528/PIER11052205 Google Scholar

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

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

21. Uzsoky, M. and L. Solymar, "Theory of superdirective linear arrays," Acta Physica, Ac. Hung., Vol. 6, No. 2, 185-205, 1956.
doi:10.1007/BF03157322 Google Scholar

22. Ma, Y. L., Y. X. Yang, Z. Y. He, et al. "Theoretical and practical solutions for high-order superdirectivity of circular sensor arrays," IEEE Trans. on Industrial Electronics, Vol. 60, No. 2, 203-209, 2013.
doi:10.1109/TIE.2012.2185020 Google Scholar

23. Shamoninaa, E., K. H. Ringhoferb, and L. Solymara, "Configurations optimizing the directivity of planar arrays," International Journal of Electronics and Communications, Vol. 56, No. 2, 115-119, 2002.
doi:10.1078/1434-8411-54100080 Google Scholar

24. Newman, E., J. Richmond, and C. Walter, "Superdirective receiving arrays," IEEE Trans. on Antennas and Propagation, Vol. 26, No. 5, 629-635, 1978.
doi:10.1109/TAP.1978.1141928 Google Scholar

25. Gilbert, E. N. and S. P. Morgan, "Optimum design of directive antenna arrays subject to random variations," Bell Syst. Tech. Journal, Vol. 34, 637-671, 1955. Google Scholar

26. 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 Google Scholar

27. Cheng, D. K. and F. I. Tseng, "Gain optimization for arbitrary antenna arrays," IEEE Trans. on Antennas and Propagation, Vol. 15, No. 3, 973-974, 1965.
doi:10.1109/TAP.1965.1138542 Google Scholar

28. Cox, H., "Robust adaptive beamforming," IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. 35, No. 10, 1365-1376, 1987.
doi:10.1109/TASSP.1987.1165054 Google Scholar

Dr. Qing-Chen Zhou

Prof. Huotao Gao

Dr. Huajun Zhang

Dr. Fan Wang