A linearly constrained minimum variance (LCMV) antenna array beamformer using finite data samples suffers from slow convergence when the received array data contain the desired signal. It has been reported that signal blocking techniques speed up the convergence rate and increase the robustness of LCMV antenna array beamformers. However, the reason of this improvement has not been explored in the literature. Moreover, the existing formulas for the output signal-to-interference-plus-noise ratio (SINR) are too rough to realize the influence of signal blocking techniques on the performance. In this paper, we show that the correlation due to finite samples causes the redundant component (termed as the cross weight) embedded in the weight vector of a LCMV beamformer even if the signal sources and noise are independent. The cross power results from the cross weight degrades the performance when the sample size is small. In contrast, the cross weight and cross power can be fully eliminated when a signal blocking technique is used. The theoretical results presented in this paper provide a comprehensive description on the effectiveness and the price of using signal blocking for antenna array beamforming. Simulation results are also given for confirming the validity of the theoretical results.
2. Chang, L. and C.-C. Yeh, "Performance of DMI and eigenspace-based beamformers," IEEE Trans. Antennas Propag., Vol. 40, No. 11, 1336-1347, Nov. 1992.
3. Reed, I. S., J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., Vol. 10, No. 6, 853-863, Nov. 1974.
4. Widrow, B., K. M. Duvall, R. P. Gooch, and W. C. Newman, "Signal cancellation phenomena in adaptive antennas: Causes and cures ," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 469-478, May 1982.
5. Haimovich, A. M. and Y. Bar-Ness, "An eigenanalysis interference canceler," IEEE Trans. Signal Process., Vol. 39, No. 1, 76-84, Jan. 1991.
6. Choi, Y.-H., "Performance improvement of adaptive arrays with signal blocking," IEICE Trans. Comm., Vol. E86-B, No. 8, 2553-2557, Aug. 2003.
7. Choi, Y.-H., "Signal-blocking-based adaptive beamformer with simple direction error correction," Electron. Lett., Vol. 40, No. 8, 463-464, Apr. 2004.
8. Lee, J.-H. and C.-C. Lee, "Analysis of the performance and sensitivity of an eigenspace-based interference canceler," IEEE Trans. Antennas Propag., Vol. 48, No. 5, 826-835, May 2000.
9. Lee, J.-H. and Y.-H. Lee, "Two-dimensional adaptive array beamforming with multiple beam constraints using a generalized sidelobe canceller," IEEE Trans. Signal Process.,, Vol. 53, No. 9, 3517-3529, Sep. 2005.
10. Choi, Y.-H., "Duvall-structure-based fast adaptive beamforming for coherent interference cancellation," IEEE Signal Process. Lett., Vol. 14, No. 10, 739-741, Oct. 2007.
11. Yu, L., W. Liu, and R. Langley, "SINR analysis of the subtraction-based SMI beamformer IEEE Trans. Signal Process.,", Vol. 58, No. 11, 5926-5932, Nov. 2010.
12. Steinhardt, A. O., The PDF of adaptive beamforming weights, IEEE Trans. Signal Process., Vol. 39, No. 5, 1232-1235, May 1991.
13. Richmond, C. D., "PDF's confidence regions, and relevant statistics for a class of sample covariance-based array processors," IEEE Trans. Signal Process., Vol. 44, No. 7, 1779-1793, Jul. 1996.
14. Frost, O. L., "An algorithm for linearly constrained adaptive array processing," Proc. IEEE, Vol. 60, No. 8, 926-935, Aug. 1972.
15. Li, R., X. Zhao, and X. W. Shi, "Derivative constrained robust LCMV beamforming algorithm," Progress In Electromagnetics Research C, Vol. 4, 43-52, 2008.
16. 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.
17. Griffiths, L. J. and C. W. Jim, "An alternative approach to linearly constrained adaptive beamforming," IEEE Trans. Antennas Propag., Vol. 30, No. 1, 27-34, Jan. 1982.
18. Trim, D., Calculus for Engineers, Prentice Hall, Toronto, 2008.
19. Sominskii, I. S., The Method of Mathematical Induction, Pergamon, London, 1961.
20. Larson, R., B. H. Edwards, and D. C. Falvo, Elementary Linear Algebra, Brooks Code, CA, 2009.
21. Miller, K. S. and J. B. Walsh, Elementary and Advanced Trigonometry, 212-215, Harper & Brothers, New York, 1962.
22. Jordan, C., Calculus of Finite Differences, 100-107, Chelsea, New York, 1947.