Constrained adaptive filtering algorithms based on conjugate gradient techniques for beamforming

This article proposes constrained adaptive algorithms based on the conjugate gradient (CG) method for adaptive beamforming. The proposed algorithms are derived for the implementation of the beamformer according to the minimum variance and constant modulus criteria subject to a constraint on the array response. A CG-based weight vector strategy is created for enforcing the constraint and computing the weight expressions. The devised algorithms avoid the covariance matrix inversion and exhibit fast convergence with low complexity. A complexity analysis compares the proposed algorithms with the existing ones. The convergence properties of the CCM criterion are studied, conditions for convexity are established and a convergence analysis for the proposed algorithms is derived. Simulation results are conducted for both stationary and non-stationary scenarios, showing the convergence and tracking ability of the proposed algorithms.

[1]  Richard W. Hamming,et al.  Numerical Methods for Scientists and Engineers , 1963 .

[2]  Richard W. Hamming,et al.  Numerical Methods for Scientists and Engineers , 1962 .

[3]  O. L. Frost,et al.  An algorithm for linearly constrained adaptive array processing , 1972 .

[4]  T. J. Rivlin.  The Chebyshev polynomials , 1974 .

[5]  David F. Shanno,et al.  Conjugate Gradient Methods with Inexact Searches , 1978, Math. Oper. Res..

[6]  D. Godard,et al.  Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems , 1980, IEEE Trans. Commun..

[7]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[8]  M. Al-Baali.  Descent Property and Global Convergence of the Fletcher—Reeves Method with Inexact Line Search , 1985 .

[9]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[10]  Henry Cox,et al.  Robust adaptive beamforming , 2005, IEEE Trans. Acoust. Speech Signal Process..

[11]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[12]  M. Srinath,et al.  Conjugate gradient techniques for adaptive filtering , 1989, IEEE International Symposium on Circuits and Systems,.

[13]  David S. Watkins,et al.  Fundamentals of matrix computations , 1991 .

[14]  M. Srinath,et al.  Conjugate gradient techniques for adaptive filtering , 1992 .

[15]  Alan N. Willson,et al.  Adaptive filtering using modified conjugate gradient , 1995, 38th Midwest Symposium on Circuits and Systems. Proceedings.

[16]  Tamal Bose,et al.  Conjugate gradient method in adaptive bilinear filtering , 1995, IEEE Trans. Signal Process..

[17]  John Litva,et al.  Digital beamforming in wireless communications , 1996 .

[18]  J. Litva,et al.  Adaptive beamforming for wireless communications , 1996 .

[19]  A. N. Willson,et al.  Analysis of conjugate gradient algorithms for adaptive filtering , 1997, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97.

[20]  Sergio Verdu,et al.  Multiuser Detection , 1998 .

[21]  Bernard Fino,et al.  Multiuser detection: , 1999, Ann. des Télécommunications.

[22]  Dimitris A. Pados,et al.  Auxiliary-vector filters and adaptive steering for DS/CDMA single-user detection , 1999 .

[23]  Theodore S. Rappaport,et al.  Smart Antennas for Wireless Communications: Is-95 and Third Generation Cdma Applications , 1999 .

[24]  Alan N. Willson,et al.  Analysis of conjugate gradient algorithms for adaptive filtering , 2000, IEEE Trans. Signal Process..

[25]  José Antonio Apolinário,et al.  The constrained conjugate gradient algorithm , 2000, IEEE Signal Processing Letters.

[26]  Dimitris A. Pados,et al.  An iterative algorithm for the computation of the MVDR filter , 2001, IEEE Trans. Signal Process..

[27]  K. Kwak,et al.  A modified constrained constant modulus approach to blind adaptive multiuser detection , 2001, IEEE Trans. Commun..

[28]  Michael L. Honig,et al.  Adaptive reduced-rank interference suppression based on the multistage Wiener filter , 2002, IEEE Trans. Commun..

[29]  Zhengyuan Xu,et al.  Code-constrained blind detection of CDMA signals in multipath channels , 2002 .

[30]  Zhengyuan Xu,et al.  Code-constrained blind detection of CDMA signals in multipath channels , 2002, IEEE Signal Processing Letters.

[31]  Harry L. Van Trees,et al.  Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory , 2002 .

[32]  Karim Abed-Meraim,et al.  Reduced-Rank Adaptive Filtering Using Krylov Subspace , 2002, EURASIP J. Adv. Signal Process..

[33]  M.E. Weippert,et al.  Insights from the relationship between the multistage Wiener filter and the method of conjugate gradients , 2002, Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002.

[34]  Tho Le-Ngoc,et al.  Recursive least squares constant modulus algorithm for blind adaptive array , 2004, IEEE Transactions on Signal Processing.

[35]  Fambirai Takawira,et al.  Performance analysis of the linearly constrained constant modulus algorithm-based multiuser detector , 2005, IEEE Transactions on Signal Processing.

[36]  Petre Stoica,et al.  Robust Adaptive Beamforming: Li/Robust Adaptive Beamforming , 2005 .

[37]  Rodrigo C. de Lamare,et al.  Blind adaptive code-constrained constant modulus algorithms for CDMA interference suppression in multipath channels , 2005, IEEE Commun. Lett..

[38]  J. Dicapua.  Chebyshev Polynomials , 2019, Fibonacci and Lucas Numbers With Applications.

[39]  Martin Haardt,et al.  Blind Adaptive Constrained Reduced-Rank Parameter Estimation Based on Constant Modulus Design for CDMA Interference Suppression , 2008, IEEE Transactions on Signal Processing.

[40]  Michael D. Zoltowski,et al.  Subspace Expansion and the Equivalence of Conjugate Direction and Multistage Wiener Filters , 2008, IEEE Transactions on Signal Processing.