volume | PIER Journals

Abstract

Adaptive beamforming, which uses a weight vector to maximize the signal-to-interference-plus-noise ratio (SINR), is often sensitive to estimation error and uncertainty in the parameters, such as direction of arrival (DOA), steering vector and covariance matrix. Robust beamforming attempts to mitigate this sensitivity and diagonal loading in sample covariance matrix can improve the robustness. In this paper, beamformer based on particle filter (PF) is proposed to improve the robustness by optimizing the diagonal loading factor in sample covariance matrix. In the proposed approach, the level of diagonal loading is regarded as a group of particles and optimized using PF. In order to compute the post probability of particles beyond the knowledge of noise, a simplified cost function is derived first. Then, a statistical approach is developed to decide the level of diagonal loading. Finally, simulations with several frequently encountered types of estimation error are conducted. Results show better performance of the proposed beamformer as compared with other typical beamformers using diagonal loading. In particular, the prominent advantage of the proposed approach is that it can perform well even noise and error in the steering vector are unknown.

1. Dessouky, M., H. Sharshar, and Y. Albagory, "Improving the cellular coverage from a high altitude platform by novel tapered beamforming technique," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1721-1731, 2007. Google Scholar

2. Dessouky, M., H. Sharshar, and Y. Albagory, "A novel tapered beamforming window for uniform concentric circular arrays," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2077-2089, 2006.
doi:10.1163/156939306779322701 Google Scholar

3. Abdelaziz, A. A., "Improving the performance of an antenna array by using radar absorbing cover," Progress In Electromagnetics Research Letters, Vol. 1, 129-138, 2008.
doi:10.2528/PIERL07112503 Google Scholar

4. Capineri, L., "Estimation of relative permittivity of shallow soils by using the ground penetrating radar response from different buried targets," Progress In Electromagnetics Research Letters, Vol. 2, 63-71, 2008.
doi:10.2528/PIERL07122803 Google Scholar

5. Landesa, L., et al. "Bias of the maximum likelihood DOA estimation from inaccurate knowledge of the antenna array response," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 9, 1205-1217, 2007. Google Scholar

6. Bell, K. L. and Y. Ephraim, "A bayesian approach to robust adaptive beamforming," IEEE Transactions on Signal Processing, Vol. 48, No. 2, 386-398, Feb. 2000.
doi:10.1109/78.823966 Google Scholar

7. Gu, Y. J., Z. Shi, Y. Li, and K. S. Chen, "Robust adaptive beamforming for steering vector uncertainties based on equivalent DOAs method," Progress In Electromagnetics Research, PIER 79, 277-290, 2008. Google Scholar

8. Gu, Y. J., Z. Shi, Y. Li, and K. S. Chen, "Robust adaptive beamforming for a class of Gaussian steering vector mismatch," Progress In Electromagnetics Research, PIER 81, 315-328, 2008. Google Scholar

9. Li, Y. and K. S. Chen, "Robust beamforming based on extended bayesian filter," Journal of Microwaves, Vol. 6, 21-26, 2008(in Chinese). Google Scholar

10. Capon, J., "High resolution frequency-wavenumber spectrum analysis," Proceedings of the IEEE, Vol. 57, 1408-1418, Seattle, 1969. Google Scholar

11. Riley, J. D., "Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix," Mathematical Tables and Other Aids to Computation, Vol. 9, 96-101, Jul. 1955. Google Scholar

12. Tikhonov, A. N., Methods for the Solution of Ill-posed Problems, Nauka, Moscow, 1974.

13. Carlson, B. D., "Covariance matrix estimation errors and diagonal loading in adaptive arrays," IEEE Transactions on Aerospace and Electronic Systems, Vol. 24, No. 4, 397-401, Jul. 1988.
doi:10.1109/7.7181 Google Scholar

14. Cheremisin, O. P., "Efficiency of adaptive algorithms with regularized sample covariance matrix," Radio Engineering and Electronic Physics, Vol. 27, No. 10, 69-77, 1981. Google Scholar

15. Kim, Y. L., "Optimal loading factor for minimal sample support space-time adaptive radar," Proceedings of IEEE international Conference on Acoustics, Speech and Signal Processing, 2505-2508, 1998. Google Scholar

16. Boris, N. O., "Optimization of loading factor preventing target cancallation," Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, 2008. Google Scholar

17. Tian, Z., K. L. Bell, and H. Van, "A recursive least squares implementation for LCMP beamforming under quadratic constraint," IEEE Transactions on Signal Processing, Vol. 49, No. 6, 1138-1145, Jun. 2001.
doi:10.1109/78.923296 Google Scholar

18. Vorobyov, S. A., A. B. Gershman, and Z. Q. Luo, "Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem," IEEE Transactions on Signal Processing, Vol. 51, 313-324, 2003.
doi:10.1109/TSP.2002.806865 Google Scholar

19. Reed, I. S. and J. D. Mallat, "Rapid convergence rate in adaptive arrays," IEEE Transactions on Aerospace and Electronic Systems, Vol. 10, 853-863, Nov. 1974.
doi:10.1109/TAES.1974.307893 Google Scholar

20. Ristic, B., S. Arulampalam, and N. Gordon, Beyond the Kalman Filter: Particle Filter for Tracking Applications, Artech House, Boston, London, 2004.

21. Shi, Z., S. Hong, and K. S. Chen, "Experimental study on tracking the state of analog Chua's circuit with particle filter for chaos synchronization," Physics Letters A, Vol. 372, 5575-5580, 2008.
doi:10.1016/j.physleta.2008.06.082 Google Scholar

22. Monzingo, R. A. and T. W. Miller, Introduction to Adaptive Array, Wiley, New York, 1980.

23. Jeong, Y. S. and J. H. Lee, "Estimation of time delay using conventional beamforming-based algorithm for UWB systems," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2413-2420, 2007.
doi:10.1163/156939307783134281 Google Scholar

24. Karlsson, R., F. Gustafsson, and T. Karlsson, "Particle filtering and Cramer-Rao lower bound for underwater navigation," Proc. IEEE Conf. Acoustics, Speech and Signal Processing, Hong Kong, Apr. 2003. Google Scholar

25. Miodrag, B., M. Petar, and H. Sangjin, "Resampling algorithms for particle filters: A computational complexity perspective," EURASIP Journal on Applied Signal Processing, Vol. 2004, No. 15, 2267-2277, 2004.
doi:10.1155/S1110865704405149 Google Scholar

Dr. Yu Li

Dr. Yujie Gu

Professor Zhi-Guo Shi

Dr. Kang Chen