5 - Adaptive Beamforming
Published online by Cambridge University Press: 24 November 2022
Summary
The chapter briefly introduces the main concepts of array signal processing, emphasizing those related to adaptive beamforming, and discusses how to impose linear constraints to adaptive filtering algorithms to achieve the beamforming effect. Adaptive beamforming, emphasizing the incoming signal impinging from a known direction by means of an adaptive filter, is the primary objective of the array signal processing addressed in this chapter. We start this study with the narrowband beamformer. The constrained LMS, RLS, conjugate gradient, and SMAP algorithms are introduced along with the generalized sidelobe canceller, and the Householder constrained structures; sparse promoting adaptive beamforming algorithms are also addressed in this chapter. In the following, it introduces the concepts of frequency-domain and time-domain broadband adaptive beamforming and shows their equivalence. The chapter wraps up with brief discussions and reference suggestions on essential topics related to adaptive beamforming, including the numerical robustness of adaptive beamforming algorithms.
Keywords
- Type
- Chapter
- Information
- Online Learning and Adaptive Filters , pp. 152 - 197Publisher: Cambridge University PressPrint publication year: 2022
References
Oppenheim, A. V. and Schafer, R. W., Discrete-Time Signal Processing, 3rd ed. (Pearson, Upper Saddle River, 2009).Google Scholar
Frost, O. L., III, An algorithm for linearly constrained adaptive array processing, Proceedings of the IEEE 60, pp. 926-935 (1972).Google Scholar
Diniz, P. S. R., Adaptive Filtering: Algorithms and Practical Implementations, 5th ed. (Springer, New York, 2020).Google Scholar
Apolinario Jr., J. A., Werner, S., S. R. Diniz, P., and T. I. Laakso, Constrained normalized adaptive filters for CDMA mobile communications, 9th European Signal Process. Conf. (EUSIPCO 1998), Island of Rhodes, Greece, 1998, pp. 1-4.Google Scholar
Resende, L. S., M. T. Romano, J., and M. G. Bellanger, A fast least-squares algorithm for linearly constrained adaptive filtering, IEEE Transactions on Signal Processing 44, pp. 1168-1174 (1996).Google Scholar
R. de Campos and J. A. Apolinario Jr., M. L., The constrained affine projection algorithm - development and convergence issues, First Balkan Conference on Signal Processing, Communications, Circuits and Systems, Istanbul, Turkey, 2000, pp. 1-4.Google Scholar
Werner, S. and S. R. Diniz, P., Set-membership affine projection algorithm, IEEE Signal Proc. Letters 8, pp. 231-235 (2001).Google Scholar
Werner, S., A. Apolinaario Jr., J., and M. L. R. De Campos, The data-selective constrained affine-projection algorithm, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2001) 6, Salt Lake City, USA, 2001, pp. 3745-3748.Google Scholar
Werner, S., A. Apolinario Jr., J., L. R. de Campos, M., and P. S. R. Diniz, Low- complexity constrained affine-projection algorithms, IEEE Transactions on Signal Processing 53, pp. 4545-4555 (2005).Google Scholar
Galdino, J. F., A. Apolinario Jr., J., and M. L. R. de Campos, A set-membership NLMS algorithm with time-varying error bound, IEEE International Symposium on Circuits and Systems (ISCAS 2006), Island of Kos, Greece, 2006, pp. 277-280.Google Scholar
Griffiths, L. J. and Jim, C. W., An alternative approach to linearly constrained adaptive beamforming, IEEE Transactions on Antennas and Propagation AP- 30, pp. 27-34 (1982).Google Scholar
Werner, S., A. Apolinario Jr., J., and M. L. R. de Campos, On the equivalence of RLS implementations of LCMV and GSC processors, IEEE Signal Processing Letters 10, pp. 356-359 (2003).Google Scholar
Tseng, C.-Y. and Griffiths, L. J., A systematic procedure for implementing the blocking matrix in decomposed form, Twenty-Second Asilomar Conference on Signals, Systems and Computers 2, Pacific Grove, USA, 1988, pp. 808-812.Google Scholar
Chu, Y., Fang, W.-H., and S.-H. Chang, A novel wavelet-based generalized side- lobe canceller, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1998) 4, Seattle, USA, 1998, pp. 2497-2500.Google Scholar
Chang, P. S. and Willson, A. N., Adaptive filtering using modified conjugate gradient, 38th Midwest Symposium on Circuits and Systems, 1, Rio de Janeiro, Brazil, 1995, pp. 243-246.Google Scholar
Chang, P. S. and Willson, A. N., Analysis of conjugate gradient algorithms for adaptive filtering, IEEE Transactions on Signal Processing 48, pp. 409-418 (2000).Google Scholar
Apolinario Jr., J. A., L. R. de Campos, M., and C. P. Bernal O., The constrained conjugate gradient algorithm, IEEE Signal Processing Letters 7, pp. 351-354 (2000).Google Scholar
Wang, L. and C. de Lamare, R., Set-membership constrained conjugate gradient adaptive algorithm for beamforming, IET Signal Processing 6, pp. 789-797 (2012).Google Scholar
R. de Campos, M. L., Werner, S., and J. A. Apolinario Jr., Constrained adaptation algorithms employing Householder transformation, IEEE Transactions on Signal Processing 50, pp. 2187-2195 (2002).Google Scholar
R. de Campos, M. L., Werner, S., and J. A. Apolinario Jr., Householder-transform constrained LMS algorithms with reduced-rank updating, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1999) 4, Phoenix, USA, 1999, pp. 1857-1860.Google Scholar
Golub and C. F. Van Loan, G. H., Matrix Computations, 3rd ed. (The Johns Hopkins University Press, Baltimore, 1996).Google Scholar
Wilkinson, J. H. (ed.), The Algebraic Eigenvalue Problem (Oxford University Press, New York, 1988).Google Scholar
Tseng, C.-Y. and Griffiths, L. J., A systematic procedure for implementing the blocking matrix in decomposed form, Twenty-Second Asilomar Conference on Signals, Systems and Computers 2, Pacific Grove, USA, 1988, pp. 808-812.Google Scholar
Duttweiler, D., Proportionate normalized least-mean-squares adaptation in echo cancelers, IEEE Transactions on Speech and Audio Processing 8, pp. 508-518 (2000).Google Scholar
Benesty, J. and Gay, S. L., An improved PNLMS algorithm, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2002) 2, Orlando, USA, 2002, pp. 1881-1884.Google Scholar
Chen, Y., Gu, Y., and A. O. Hero III, Sparse LMS for system identification, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2009), Taipei, Taiwan, 2009, pp. 3125-3128.Google Scholar
R. de Campos and J. A. Apolinario Jr., M. L., Shrinkage methods applied to adaptive filters, 2010 International Conference on Green Circuits and Systems, Shanghai, China, 2010, pp. 41-45.Google Scholar
Paleologu, C., Benesty, J., and S. Ciochina, An improved proportionate NLMS algorithm based on the l0 norm, IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), Dallas, USA, 2010, pp. 309-312.Google Scholar
Kopsinis, Y., Slavakis, K., and S. Theodoridis, Online sparse system identification and signal reconstruction using projections onto weighted £1 balls, IEEE Transactions on Signal Processing 59, 936-952 (2011).Google Scholar
Lima, M. V. S., Ferreira, T. N., Martins, W. A., and P. S. R. Diniz, Sparsity- aware data-selective adaptive filters, IEEE Transactions on Signal Processing 62, pp. 4557-4572 (2014).Google Scholar
de Andrade Jr., J. F., L. R. de Campos, M., and J. A. Apolinario Jr., An £1- norm linearly constrained LMS algorithm applied to adaptive beamforming, 7th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2012), Hoboken, USA, 2012, pp. 429-432.Google Scholar
de Andrade Jr., J. F., L. R. de Campos, M., and J. A. Apolinario Jr., An £1- constrained normalized LMS algorithm and its application to thinned adaptive antenna arrays, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013), Vancouver, Canada, 2013, pp. 3806-3810.Google Scholar
Andrade Jr., J. F., L. R. de Campos, M., and J. A. Apolinario Jr., ^-constrained normalized LMS algorithms for adaptive beamforming, IEEE Transactions on Signal Processing 63, pp. 6524-6539 (2015).Google Scholar
Andrade Jr., J. F., L. R. Campos, M., and J. A. Apolinario Jr., An^-norm linearly constrained affine projection algorithm, IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2016), Rio de Janeiro, Brazil, 2016, pp. 1-5.Google Scholar
Godara, L. C., Application of the fast Fourier transform to broadband beamform- ing, The Journal of the Acoustical Society of America 98, pp. 230-240 (1995).Google Scholar
Apolinaario Jr. and M. L. R. de Campos, J. A., Sparse broadband acoustic adaptive beamformers for underwater applications, MTS/IEEE Oceans Conference, Aberdeen, Scotland, 2017, pp. 1-6.Google Scholar
Trees, H. L. V., Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory (John Wiley & Sons, Hoboken, 2002).CrossRefGoogle Scholar
Razavizadeh, S. M., Ahn, M., and I. Lee, Three-dimensional beamforming: A new enabling technology for 5G wireless networks, IEEE Signal Processing Magazine 31, pp. 94-101 (2014).Google Scholar
Gong, X. and Lin, Q., Spatially constrained parallel factor analysis for semi- blind beamforming, Seventh International Conference on Natural Computation 1, Shanghai, China, 2011, pp. 416-420.Google Scholar
Miranda, R. K., P. C. L. da Costa, J., Roemer, F., L. F. de Almeida, A., and G. Del Galdo, Generalized sidelobe cancellers for multidimensional separable arrays, IEEE 6th International Workshop on Computational Advances in Multi- Sensor Adaptive Processing (CAMSAP 2015), Cancun, Mexico, 2015, pp. 193196.Google Scholar
Ribeiro, L. N., L. F. de Almeida, A., and J. C. M. Mota, Tensor beamforming for multilinear translation invariant arrays, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), Shanghai, China, 2016, pp. 2966-2970.CrossRefGoogle Scholar
Ramos, A. L. L., A. Apolinario Jr., J., and M. L. R. de Campos, On numerical robustness of constrained RLS-like algorithms, Brazilian Telecommunication Symposium (SBrT 2004), Belem, Brazil, 2004.Google Scholar
Resende, L. S., M. T. Romano, J., and M. G. Bellanger, A fast least-squares algorithm for linearly constrained adaptive filtering, IEEE Transactions on Signal Processing 44, pp. 1168-1174 (1996).Google Scholar
R. de Campos, M. L., Werner, S., A. Apolinario Jr., J., and T. I. Laakso, Constrained guasi-Newton algorithm for CDMA mobile communications, SBrT/IEEE International Telecommunications Symposium (ITS 1998) 1, Sao Paulo, Brazil, 1998, pp. 371-376.Google Scholar
Pi Sheng Chang and A. N. Willson, Analysis of conjugate gradient algorithms for adaptive filtering, IEEE Transactions on Signal Processing 48, pp. 409-418 (2000).Google Scholar
R. de Campos and A. Antoniou, M. L., A new guasi-Newton adaptive filtering algorithm, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 44, pp. 924-934 (1997).Google Scholar