مقاوم سازی الگوریتم شکل دهی پرتو

الموضوعات :

سجاد دهقانی ¹ (دانشگاه آزاد اسلامی واحد علوم و تحقیقات فارس)
ناصر پرهیزگار ² (دانشکده مهندسی برق- واحد شیراز، دانشگاه آزاد اسلامی، شیراز، ایران)

تاريخ الإرسال : 21 الإثنين , رمضان, 1434 تاريخ التأكيد : 27 الأحد , جمادى الثانية, 1435 تاريخ الإصدار : 03 الأحد , شعبان, 1435

الکلمات المفتاحية: عدم قطعیت, مقاوم سازی, Convex Optimization, شکل دهنده پرتو حداقل واریانس با پاسخ بدون اعوجاج,

ملخص المقالة :

عملکرد الگوریتم‌های شکل‌دهی پرتو در شرایط عدم قطعیت در بردار هدایت و یا در ماتریس کوواریانس داده، به شدت خراب می‌شوند. در این مقاله یک روش جدید برای مقاوم سازی الگوریتم شکل‌دهی پرتو وفقی حداقل واریانس ارائه می‌شود که هم نسبت به عدم قطعیت در بردار هدایت و هم نسبت به عدم قطعیت در ماتریس کوواریانس داده مقاوم می‌باشد. این روش شامل حداقل‌سازی یک مسأله بهینه سازی با تابع هزینه مرتبه دوم و قید غیر محدب است. در این مقاله نشان داده خواهد شد که مسأله بهینه سازی غیر محدب به یک مسأله محدب تبدیل شده و بردار وزن شکل دهنده پرتو مقاوم سازی شده به دست می‌آید.

المصادر:

[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.