volume | PIER Journals

Abstract

The performance of traditional beamformers tends to degrade due to inaccurate estimation of covariance matrix and imprecise knowledge of array steering vector. The inaccurate estimation of covariance matrix can be attributed to limited data samples and the presence of desired signal in the training data. The mismatch between the actual and presumed steering vectors can be due to the error in the position (geometry) and/or in the look direction estimate. In this paper, we propose a differential evolution (DE) based robust adaptive beamforming that is able to achieve near optimal performance even in the presence of geometry error. Initially, we estimate an optimal steering vector by maximizing and minimizing the signal power in and out of the desired signal's angular range, respectively. Then, we estimate the look direction and reconstruct the covariance matrix. Based on the obtained steering vector, estimate for look direction and reconstructed covariance matrix, near optimal output SINR, can be obtained with the increase in the input SNR without observing any saturation even in the presence of geometry error. Numerical simulations are presented to demonstrate the efficacy of the proposed algorithm.

1. 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, 177-195, 2009.
doi:10.2528/PIER09082303 Google Scholar

2. Qu, Y., G. Liao, S.-Q. Zhu, X.-Y. Liu, and H. Jiang, "Performance analysis of beamforming for MIMO radar," Progress In Electromagnetics Research, Vol. 84, 123-134, 2008.
doi:10.2528/PIER08062306 Google Scholar

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

4. Yang, P., F. Yang, Z.-P. Nie, B. Li, and X. Tang, "Robust adaptive beamformer using interpolation technique for conformal antenna array," Progress In Electromagnetics Research B, Vol. 23, 215-228, 2010.
doi:10.2528/PIERB10061504 Google Scholar

5. 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

6. Liu, F., J. Wang, R. Du, L. Peng, and P. Chen, "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

7. Reed, I. S., J. D. Mallett, and L. E. Nrennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. on Aerosp. Electron. Syst., Vol. 10, 853-863, Nov. 1974.
doi:10.1109/TAES.1974.307893 Google Scholar

8. 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 Google Scholar

9. Gu, Y.-J., Z.-G. Shi, K. S. Chen, and Y. Li, "Robust adaptive beamforming for a class of Gaussian steering vector mismatch," Progress In Electromagnetics Research, Vol. 81, 315-328, 2008.
doi:10.2528/PIER08010202 Google Scholar

10. Umrani, A. W., Y. Guan, and F. A. Umrani, "Effect of steering error vector and angular power distributions on beamforming and transmit diversity systems in correlated fading channel," Progress In Electromagnetics Research, Vol. 105, 383-402, 2010.
doi:10.2528/PIER10042902 Google Scholar

11. Huang, C.-C. and J.-H. Lee, "Adaptive array beamforming using signal cyclostationarity and finite data," Progress In Electromagnetics Research C, Vol. 21, 217-228, 2011. Google Scholar

12. Wang, W., R.Wu, and J. Liang, "A novel diagonal loading method for robust adaptive beamforming," Progress In Electromagnetics Research C, Vol. 18, 245-255, 2011. Google Scholar

13. Li, J. and P. Stoica, Robust Adaptive Beamforming , John Wiley & Sons, Inc. Hoboken, New Jersey, 2004.

14. Gershman, A. B., "Robust adaptive beamforming in sensor arrays," Int. J. Electron. Commun., Vol. 53, 305-314, Dec. 1999. Google Scholar

15. Jacobs, J. P. and J. P. de Villiers, "Gaussian-process-regression-based design of ultrawide-band and dual-band CPW-FED slot antennas ," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 13, 1763-1772, 2010. Google Scholar

16. Pu, T.-L., K.-M. Huang, B. Wang, and Y. Yang, "Application of micro-genetic algorithm to the design of matched high gain patch antenna with zero-refractive-index metamaterial lens," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 8-9, 1207-1217, 2010.
doi:10.1163/156939310791586025 Google Scholar

17. Zhang, Y.-J., S.-X. Gong, X. Wang, and W. T. Wang, "A hybrid genetic-algorithm space-mapping method for the optimization of aperture-coupled asymmetrical U-shaped slot antennas ," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 16, 2139-2153, 2010.
doi:10.1163/156939310793699118 Google Scholar

18. Mirzavand, R., B. Honarbakhsh, A. Abdipour, and A. Tavakoli, "Matamaterial-based phase shifters for ultra wide-band application," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 11-12, 1489-1496, 2009.
doi:10.1163/156939309789476446 Google Scholar

19. Yan, Y.-L., F. Guang, S.-X. Gong, X. Chen, and Z.-Y. Zhang, "Wideband YAGI-UDA antenna design using adaptive differential evolution algorithm," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 17-18, 2523-2536, 2010.
doi:10.1163/156939310793675709 Google Scholar

20. Li, J.-Y. and J. L. Guo, "Optimization technique using differential evolution for YAGI-UDA antennas," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 4, 449-461, 2009.
doi:10.1163/156939309787612356 Google Scholar

21. Xie, L., Y.-C. Jiao, Y.-Q. Wei, and G. Zhao, "A compact band-notched UWB antenna optimized by a novel self-adaptive differential evolution algorithm," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 17-18, 2353-2361, 2010.
doi:10.1163/156939310793675817 Google Scholar

22. Li, J.-Y., "A bi-swarm optimizing strategy and its application of antenna design ," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 14-15, 1877-1886, 2009.
doi:10.1163/156939309789932449 Google Scholar

23. Li, Y., Y.-J. Gu, Z.-G. Shi, and K. S. Chen, "Robust adaptive beamforming based on particle filter with noise unknown," Progress In Electromagnetics Research, Vol. 90, 151-169, 2009.
doi:10.2528/PIER09010302 Google Scholar

24. Castaldi, G., V. Galdi, and G. Gerini, "Evaluation of a neural-network-based adaptive beamforming scheme with magnitude-only constraints," Progress In Electromagnetics Research B, Vol. 11, 1-14, 2009.
doi:10.2528/PIERB08092303 Google Scholar

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

26. Palanisamy, P. and N. Rao, "Direction of arrival estimation based on fourth-order cumulant using propagator method," Progress In Electromagnetics Research B, Vol. 18, 83-99, 2009.
doi:10.2528/PIERB09081806 Google Scholar

27. Zhang, X., A. Gao, G. Feng, and D. Xu, "Blind joint DOA and DOD estimation and identifiability results for MIMO radar with di®erent transmit/receive array manifolds ," Progress In Electromagnetics Research B, Vol. 18, 101-119, 2009.
doi:10.2528/PIERB09050603 Google Scholar

28. Yang, P., F. Yang, and Z.-P Nie, "DOA estimation with sub-array divided technique and interpolated esprit algorithm on a cylindrical conformal array antenna," Progress In Electromagnetics Research, Vol. 103, 201-216, 2010.
doi:10.2528/PIER10011904 Google Scholar

29. Mallipeddi, R., J. P. Lie, P. N. Suganthan, S. G. Razul, and C. M. S. See, "Near optimal robust adaptive beamforming approach based on evolutionary algorithm," Progress In Electromagnetics Research B, Vol. 29, 157-174, 2011.
doi:10.2528/PIERB10110810 Google Scholar

30. Mallipeddi, R., J. P. Lie, P. N. Suganthan, S. G. Razul, 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

31. Selén, Y., R. Abrahamsson, and P. Stoica, "Automatic robust adaptive beamforming via ridge regression," Signal Processing, Vol. 88, No. 1, 33-49, 2008.
doi:10.1016/j.sigpro.2007.07.003 Google Scholar

32. Storn, R., K. V. Price, and J. Lampinen, "Differential Evolution --- A Practical Approach to Global Optimization," Berlin, 2005. Google Scholar

33. Das, S. and P. N. Suganthan, "Differential evolution: A survey of the state-of-the-art," IEEE Trans. on Evolutionary Computation, Vol. 15, No. 1, 4-31, Feb. 2011.
doi:10.1109/TEVC.2010.2059031 Google Scholar

34. Qin, A. K., V. L. Huang, and P. N. Suganthan, "Differential evolution algorithm with strategy adaptation for global numerical optimization," IEEE Trans. on Evolutionary Computation, Vol. 13, 398-417, Apr. 2009.
doi:10.1109/TEVC.2008.927706 Google Scholar

35. Mallipeddi, R. and P. N. Suganthan, "Ensemble of constraint handling techniques," IEEE Trans. on Evolutionary Computation, Vol. 14, No. 5, 561-579, Aug. 2010.
doi:10.1109/TEVC.2009.2033582 Google Scholar

36. Mallipeddi, R., P. N. Suganthan, Q. K. Pan, and M. F. Tasgetiren, "Differential evolution algorithm with ensemble of parameters and mutation strategies," Applied Soft Computing, Vol. 11, No. 2, 1679-1696, 2010.
doi:10.1016/j.asoc.2010.04.024 Google Scholar

37. Lie, J. P., X. Li, W. Ser, C. M. S. See, L. Lei, "Adaptive uncertainty based iterative robust capon beamformer," Proc. IEEE Int. Acoustics Speech and Signal Processing (ICASSP) Conf. , 2526-2529, 2010. Google Scholar

38. Yu, Z. L., Z. Gu, J. Zhou, Y. Li, S. Wee, and M. H. Er, "A robust adaptive beamformer based on worst-case semi-definite programming ," IEEE Trans. on Signal Processing, Vol. 58, No. 11, 5914-5919, 2010.
doi:10.1109/TSP.2010.2058107 Google Scholar

39. Mouhamadou, M., P. Vaudon, and M. Rammal, "Smart antenna array patterns synthesis: Null steering and multi-user beamforming by phase control," Progress In Electromagnetics Research, Vol. 60, 95-106, 2006.
doi:10.2528/PIER05112801 Google Scholar

Dr. Rammohan Mallipeddi

Dr. Joni Lie

Dr. P. N. Suganthan

Dr. Sirajudeen Gulam Razul

Dr. Chong Meng S. See