Application of the least squares approach to fixed beamformer design with frequency-invariant constraints
Application of the least squares approach to fixed beamformer design with frequency-invariant constraints
- Author(s): Y. Zhao ; W. Liu ; R. Langley
- DOI: 10.1049/iet-spr.2009.0300
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- Author(s): Y. Zhao 1 ; W. Liu 1 ; R. Langley 1
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View affiliations
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Affiliations:
1: Communications Research Group, Department of Electronic and Electrical Engineering, University of Sheffield, UK
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Affiliations:
1: Communications Research Group, Department of Electronic and Electrical Engineering, University of Sheffield, UK
- Source:
Volume 5, Issue 3,
June 2011,
p.
281 – 291
DOI: 10.1049/iet-spr.2009.0300 , Print ISSN 1751-9675, Online ISSN 1751-9683
An application of the least squares (LS) approach to the design of frequency-invariant beamformers is proposed, based on three different formulations of the problem. The first one is the traditional linearly constrained LS formulation with its solution given by the Lagrange multipliers method. The second and the third ones, which are formulated as an unconstrained LS problem and a constrained total LS problem, respectively, can be considered as extensions of the traditional total LS method and their solutions are obtained by finding the minimum generalised eigenvector of two matrices. Compared with the conventional LS-based methods, a frequency-invariance controlling element is incorporated into the proposed cost functions. Design examples including both broadside and off-broadside main beams are provided with a satisfactory frequency invariant property and sidelobe attenuation. The proposed approach is general and can be applied to different array structures.
Inspec keywords: array signal processing; least squares approximations
Other keywords:
Subjects: Signal processing and detection
References
-
-
1)
- S.C. Pei , C.C. Tseng . A new eigenfilter based on total least squares error criterion. IEEE Trans. Circuit Syst. I, Regul. Pap. , 699 - 709
-
2)
- W. Liu , S. Weiss . (2010) Wideband beamforming: concepts and techniques.
-
3)
- P. Vaidyanathan , T.Q. Nguyen . Eigenfilters: a new approach to least-squares FIR filter design and applications including Nyquist filters. IEEE Trans. Circuits Syst. , 1 , 11 - 23
-
4)
- Chan, S.C., Chen, H.H.: `Theory and design of uniform concentric spherical arrays with frequency invariant characteristics', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Process, May 2006, Toulouse, France, 4, p. 1057–1060.
-
5)
- H. Duan , B.P. Ng , C.M. See , J. Fang . Applications of the SRV constraint in broadband pattern synthesis. Signal Process. , 1035 - 1045
-
6)
- S.C. Chan , H.H. Chen . Uniform concentric circular arrays with frequency-invariant characteristics – theory, design, adaptive beamforming and DOA estimation. IEEE Trans. Signal Process. , 165 - 177
-
7)
- E.L. Hixson , K.T. Au . Widebandwidth constant beamwidth acoustic array. J. Acoust. Soc. Am. , 1
-
8)
- L.C. Parra . Steerable frequency-invariant beamforming for arbitrary arrays. J. Acoust. Soc. Am. , 3839 - 3847
-
9)
- Goodwin, M.M., Elko, G.W.: `Constant beamwidth beamforming', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Process, April 1993, Minneapolis, USA, 1, p. 169–172.
-
10)
- D.B. Ward , R.A. Kennedy , R.C. Williamson . Theory and design of broadband sensor arrays with frequency invariant far-field beam patterns. J. Acoust. Soc. Am. , 2 , 1023 - 1034
-
11)
- J.F. Sturm . Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. , 625 - 653
-
12)
- H.L. Van Trees . (2002) Optimum array processing, part IV of detection, estimation, and modulation theory.
-
13)
- T. Sekiguchi , Y. Karasawa . Wideband beamspace adaptive array utilizing FIR fan filters for multibeam forming. IEEE Trans. Signal Process. , 1 , 277 - 284
-
14)
- Zhao, Y., Liu, W., Langley, R.J.: `Efficient design of frequency invariant beamformers with sensor delay-lines', Proc. IEEE Workshop on Sensor Array and Multichannel Signal Process, July 2008, Darmstadt, Germany, p. 335–339.
-
15)
- Scholnik, D.P., Coleman, J.O.: `Formulating wideband array-pattern optimizations', Proc. IEEE Int. Conf. on Phased Array Systems and Technology, May 2000, Dana Point, California, p. 489–492.
-
16)
- H.W. Chen , W. Ser . Design of robust broadband beamformers with passband shaping characteristics using Tikhonov regularization. IEEE Trans. Audio, Speech, Lang. Process. , 4 , 665 - 681
-
17)
- W. Liu , S. Weiss . Design of frequency invarint beamformers for broadband arrays. IEEE Trans. Signal Process. , 2 , 855 - 860
-
18)
- I.D. Dotlić . Minimax frequency invariant beamforming. Electron. Lett. , 19 , 1230 - 1231
-
19)
- S.F. Yan , Y.L. Ma , C.H. Hou . Optimal array pattern synthesis for broadband arrays. J. Acoust. Soc. Am. , 11 , 2686 - 2696
-
20)
- H.H. Chen , S.C. Chan , K.L. Ho . Adaptive beamforming using frequency invariant uniform concentric circular arrays. IEEE Trans. Circuits Syst. I, Regul. Pap. , 9 , 1938 - 1949
-
21)
- A. Tkacenko , P.P. Vaidyanathan , T.Q. Nguyen . On the eigenfilter design method and its applications: a tutorial. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. , 497 - 517
-
22)
- D.B. Ward , Z. Ding , R.A. Kennedy . Broadband DOA estimation using frequency invariant beamforming. IEEE Trans. Signal Process. , 1463 - 1469
-
23)
- W. Liu , D. McLernon , M. Ghogho . Design of frequency invariant beamformer without temporal filtering. IEEE Trans. Signal Process. , 2 , 798 - 802
-
24)
- Chou, T.: `Frequency-independent beamformer with low response error', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Process, May 1995, Detroit, USA, 5, p. 2995–2998.
-
25)
- H.H. Chen , S.C. Chan . Adaptive beamforming and DOA estimation using uniform concentric spherical arrays with frequency invariant characteristics. J. VLSI Signal Process. , 1 , 15 - 34
-
26)
- Chan, S.C., Chen, H.H.: `Theory and design of uniform concentric circular arrays with frequency invariant characteristics', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Process, March 2005, Philadelphia, USA, 4, p. 805–808.
-
27)
- W. Liu , R. Wu , R. Langley . Design and analysis of broadband beamspace adaptive arrays. IEEE Trans. Antennas Propag. , 12 , 3413 - 3420
-
28)
- W. Liu , S. Weiss , J.G. McWhirter , I.K. Proudler . Frequency invariant beamforming for two-dimensional and three-dimensional arrays. Signal Process. , 2535 - 2543
-
29)
- S. Doclo , M. Moonen . Design of broadband beamformers robust against gain and phase errors in the microphone array characteristics. IEEE Trans. Signal Process. , 10 , 2511 - 2526
-
30)
- A. Trucco , M. Crocco , S. Repetto . A stochastic approach to the synthesis of a robust frequency-invariant filter-and-sum beamformer. IEEE Trans. Instrum. Meas. , 4 , 1407 - 1415
-
31)
- Korompis, D., Yao, K., Lorenzelli, F.: `Broadband maximum energy array with user imposed spatial and frequency constraints', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Process, 1994, Adelaide, SA, Australia, 4, p. 529–532.
-
32)
- Chen, T.: `Unified eigenfilter approach: with applications to spectral/spatial filtering', Proc. IEEE Int. Symp. on Circuits and Systems, 1993, Chicago, USA, 1, p. 331–334.
-
33)
- Y. Zhao , W. Liu , R.J. Langley . Subband design of fixed wideband beamformers based on the least squares approach. Signal Process. , 4 , 1060 - 1065
-
34)
- Lofberg, J.: `YALMIP: a toolbox for modeling and optimization in MATLAB', Proc. IEEE Int. Symp. on Computer Aided Control Systems Design, September 2004, Taipei, Taiwan, p. 284–289.
-
35)
- R. Smith . Constant beamwidth receiving arrays for broad band sonar systems. Acustica , 21 - 26
-
1)