Robustness Beamforming Algorithms

Subject Areas : Telecommunication field and wave

Sajad Dehghani ¹ , Naser Parhizgar ²

1 - Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Fars
2 - 1 Department of Electrical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran

Received: 2013-07-29 Accepted : 2014-04-27 Published : 2014-06-01

Keywords: Uncertainty, Robustness, Minimum Variance Distortionless Response Beamforming, Convex Optimization,

Abstract :

Adaptive beamforming methods are known to degrade in the presence of steering vector and covariance matrix uncertinity. In this paper, a new approach is presented to robust adaptive minimum variance distortionless response beamforming make robust against both uncertainties in steering vector and covariance matrix. This method minimize a optimization problem that contains a quadratic objective function and a quadratic constraint. The optimization problem is nonconvex but is converted to a convex optimization problem in this paper. It is solved by the interior-point method and optimum weight vector to robust beamforming is achieved.

References:

[1] S. Reed, J.D. Mallett, L.E. Brennan, "Rapid  convergence rate in adaptive arrays", IEEE Trens. Aerosp. Electron. Sys., Vol. AES-10, pp. 853-863, Nov. 1974.

[2] L.J. Griffiths, C.W. Jim, "An alternative approach to linearly constrained adaptive beamforming", IEEE Trans. Antennas Propagat., Vol. A P–30, pp. 27–34, Jan. 1982.

[3] E.K. Hung, R.M. Turner, "A fast beamforming algorithm for large arrays", IEEE Trans. Aerosp. Electron. Syst., Vol. AES-19, pp. 598–607, July 1983.

[4] B.D. Carlson, "Covariance matrix estimation errors and diagonal loading in adaptive arrays", IEEE Trans. Aerosp. Electron. Sys., Vol. 24, pp. 397–401, July 1988.

[5] R.A. Monzingo, T.W. Miller, "Introduction to Adaptive Arrays", New York: Wiley, 1980.

[6] D.D. Feldman, L.J. Griffiths, "A projection approach to robust adaptive beamforming", IEEE Trans. Signal Processing, Vol. 42, pp. 867–876, Apr. 1994.

[7] S.D. Hayward, "Effects of motion on adaptive arrays", IEE Pmc. Ruhr Sonar and Navigarion, Vol. 144, pp. 15-20, Feb.1997.

[8] A.B. Gershman, G.V. Serebryakov, J.F. Bohme, "Constrained hung-tumer adaptive heamforming algorithm with additional robustness to wideband and moving jammers", IEEE Trans. Antennas and Propagation, Vol. 44, pp. 361-367, March 1996.

[9] A.B. Gershman. U. Nickel, J.F. Bohme, "Adaptive beamforming algorithms with robustness against jammer motion", IEEE Trans. Signdl Processing, Vol. 45, pp. 1878-1885, July. 1997.

[10] R.I. Goldberg, G. Vazquez, "Robust beamforming. for interference rejection in mobile communications", IEEE Trans. Signal Processing, Vol. 45, pp. 271-275, Jan. 1997.

[11] J.R. Guerci, "Theory and application of covariance matrix tapers for robust adaptive beamforming", IEEE Trans. Signal Processing, Vol. 47, pp. 997-985, Apr. 1999.

[12] N.K. Jablon, "Adaptive beamforming with the generalized sidelobe canceller in the presence of array imperfections", IEEE Trans. Antennas Propagat., Vol. AP-34, pp. 996–1012, Aug. 1986.

[13] A.B. Gershman, "Robust adaptive beamforming in sensor arrays", Int. J. Electron. Commun., Vol. 53, pp. 305–314, Dec. 1999.

[14] H. Cox, R.M. Zeskind, M.H. Owen, "Robust adaptive beamforming", IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-35, pp. 1365–1376, Oct. 1987.

[15] M.H. Er, T. Cantoni, "An alternative formulation for an optimum beamformer with robustness capability", Proc. Inst. Elect. Eng. Radar, Sonar, Navig., pp. 447–460, Oct. 1985.

[16] D.D. Feldman, L.J. Griffiths, "A projection approach to robust adaptive beamforming", IEEE Trans. Signal Processing, Vol. 42, pp. 867–876, Apr. 1994.

[17] L. Chang, C.C. Yeh, "Performance of DMI and eigenspace-based beamformers", IEEE Trans. Antennas Propagat., Vol. 40, pp. 1336–1347, Nov. 1992.

[18] K.I. Pedersen, P.E. Mogensen, B.H. Fleury, "A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments", IEEE Trans. Veh. Technol., Vol. 49, pp. 437–447, Mar. 2000.

[19] J. Goldberg, H. Messer, "Inherent limitations in the localization of a coherently scattered source", IEEE Trans. Signal Processing, Vol. 46, pp. 3441–3444, Dec. 1998.

[20] O. Besson, P. Stoica, "Decoupled estimation of DOA and angular spread for a spatially distributed source", IEEE Trans. Signal Processing, Vol. 48, pp. 1872–1882, July 2000.

[21] D. Astely, B. Ottersten, "The effects of local scattering on direction of arrival estimation with MUSIC", IEEE Trans. Signal Processing, Vol. 47, pp. 3220–3234, Dec. 1999.

[22] Y. Nesterov, A. Nemirovsky, "Interior point polynomial algorithms in convex programming", Philadelphia, PA: SIAM, 1994.

[23] M. Lobo et al., "Applications of second-order cone programming", Linear Algebra Applicat., pp. 193–228, Nov. 1998.

[24] J.F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones", Optim. Meth. Softw., Vol. 11–12, pp. 625–653, Aug. 1999.

[25] J. Li, P. Stoica, "Robust adaptive beamforming", John Wiley, Inc. Hoboken, New Jersey, 2006.

[26] A. Elnashar, S.M. Elnoubi, H.A. El-Mikati. "Further study on robust adaptive beamforming with optimum diagonal loading", IEEE Trans. Antennas Propagation, Vol. AP-54, No.12, pp. 3647-3658, Dec.2006.

[27] F. Vincent, O. Besson. "Steering vector errors and diagonal loading", IEE Proceedings.- Radar Sonar Navig., Vol. 151, No.6, pp. 337-343, Dec. 2004.

[28] J. Li, P. Stoica, Z. Wang, "On robust Capon beamforming and diagonal loading", IEEE Trans. on Sig. Proc., Vol. 51, pp. 1702–1715, 2003.

[29] L. Congfeng. "Robust Beamforming and DOA Estimation, Fourier Transform Applications", Dr Salih Salih (Ed.), ISBN: 978-953-51-0518-3, InTech, 2012.

[30] R.A. Monzingo, T.W. Miller. "Introduction to adaptive arrays", New York: Wiley, 1980.

[31] S.P. Boyd, L. Vandenberghe. "Convex Optimization", Cambridge University Press,2011.

[32] S.A. Vorobyov, A.B. Gershman, Z-Q. Luo. "Robust adaptive Beamforming using worst-case performance optimization: a solution to the signal mismatch problem", IEEE Trans. Signal Processing. Vol.51, No.2, pp. 313-324, Feb. 2003.

[33] Z.L. Yu, M.H. Er, "A robust capon beamformer against uncertainty of nominal steering vector", Hindawi Publishing Corporation, EURASIP J. on App. Sig. Proc., Article ID 62327, pp. 1–8, 2006.

[34] R.G. Lorenz, S.P. Boyd. "Robust minimum variance beamforming", Sig. Proc. IEEE Trans. on, Vol. 53, No.5, pp.1684,1696, May 2005.

[35] C.Y.Chen, P.P.Vaidyanathan, "Quadratically constrained beamformingrobust against direction-of- arrival mismatch", IEEE Trans. Sig. Proc., Vol.55, No.8, pp: 4139-4150, Aug.2007.