volume | PIER Journals

Abstract

The existing robust narrowband beamformers based on probability-constrained optimization have an excellent performance as compared to several state-of-the-art robust beamforming algorithms. However, they always assume that the steering vector errors are small enough. Without this assumption, we extend the probability-constrained approach to a wideband beamformer. In addition, a novel robust wideband beamformer with frequency invariance constraints is proposed by introducing the response variation (RV) element. Our problems can be reformulated in a convex form as the iterative second order cone programming (SOCP) problem and solved effectively using well-established interior point method. Compared with existing robust wideband beamformers, a more efficient control over the beamformer's response against the steering vector errors is achieved with an improved output signal-to-interference-plus-noise ratio (SINR).

1. Liu, W. and S. Weiss, Wideband Beamforming: Concepts and Techniques, John Wiley & Sons, 2010.
doi:10.1002/9780470661178

2. Yang, K., Z. Zhao, and Q. H. Liu, "Robust adaptive beamforming against array calibration errors," Progress In Electromagnetics Research, Vol. 140, 341-351, 2013.
doi:10.2528/PIER13042203 Google Scholar

3. 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

4. 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

5. Vook, E. W. and R. T. Compton, Jr., "Bandwidth performance of linear adaptive arrays with tapped delay-line processing," IEEE Trans. Aerosp. Electron. Syst., Vol. 28, No. 3, 901-908, Jul. 1992.
doi:10.1109/7.256314 Google Scholar

6. Lin, N., W. Liu, and R. J. Langley, "Performance analysis of an adaptive broadband beamformer based on a two-element linear arraywith sensor delay-line processing," Signal Processing , Vol. 90, 269-281, Jan. 2010.
doi:10.1016/j.sigpro.2009.06.016 Google Scholar

7. Frost, III, O. L., "An algorithm for linearly constrained adaptive array processing," Proc. IEEE, Vol. 60, No. 8, 926-935, Aug. 1972.
doi:10.1109/PROC.1972.8817 Google Scholar

8. Van Veen, B. D. and K. M. Buckley, "Beamforming: A versatile approach to spatial ﬁltering," IEEE Acoust., Speech, Signal Processing Mag., Vol. 5, No. 2, 4-24, Apr. 1988. Google Scholar

9. Brandstein, M. S. and D. Ward, Microphone Arrays: Signal Processing Techniques and Applications, Springer, 2001.

10. Li, J. and P. Stoica, Robust Adaptive Beamforming, Wiley, 2005.
doi:10.1002/0471733482

11. Carlson, B. D., "Covariance matrix estimation errors and diagonal loading in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., Vol. 24, 397-401, Jul. 1988.
doi:10.1109/7.7181 Google Scholar

12. Er, M. H. and A. Cantoni, "Derivative constraints for broadband element space antenna array processors," IEEE Trans. Antennas Propag., Vol. 31, No. 6, 1378-1393, Dec. 1983. Google Scholar

13. Rubsamen, M. and A. B. Gershman, "Robust presteered broadband beamforming based on worst-case performance optimization," Proc. IEEE Workshop on Sensor Array and Multichannel Signal Processing, 340-344, Darmstadt, Germany, Jul. 2008. Google Scholar

14. El-Keyi, A., T. Kirubarajan, and A. B. Gershman, "Wideband robust beamforming based on worst-case performance optimization," Proc. IEEE Workshop on Statistical Signal Processing, 265-270, Bordeaux, Jul. 2005. Google Scholar

15. Zhao, Y., W. Liu, and R. J. Langley, "Adaptive wideband beamforming with frequency invariance constraints," IEEE Trans. Antennas Propag., Vol. 59, No. 4, 1175-1184, Apr. 2011.
doi:10.1109/TAP.2011.2110630 Google Scholar

16. Duan, H., B. P. Ng, C. M. See, and J. Fang, "Applications of the SRV constraint in broadband pattern synthesis," Signal Processing, Vol. 88, 1035-1045, Apr. 2008.
doi:10.1016/j.sigpro.2007.11.001 Google Scholar

17. Vorobyov, S. A., Y. Rong, and A. B. Gershman, "Robust adaptive beamforming using probability-constrained optimization," Proc. IEEE Stat. Signal Process. Workshop, 934-939, Bordeaux, France, Jul. 2005. Google Scholar

18. Vorobyov, S. A., Y. Rong, 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, 5719-5725, Nov. 2008.
doi:10.1109/TSP.2008.929866 Google Scholar

19. Wang, W., C. Liu, and Y. Zhao, "A novel probability-constrained approach to robust wideband beamforming with sensor delay lines," IET International Radar Conference 2013, Xi'an, Shanxi, Apr. 2013. Google Scholar

20. 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, 425-459, Feb. 2005.
doi:10.1109/TSP.2004.840777 Google Scholar

Dr. Chengcheng Liu

Dr. Yaqi Liu

Dr. Yongjun Zhao

Dr. Dexiu Hu