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Generalized Broadband Beamforming Using a Modal Subspace Decomposition
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 068291 (2006)
We propose a new broadband beamformer design technique which produces an optimal receiver beam pattern for any set of field measurements in space and time. The modal subspace decomposition (MSD) technique is based on projecting a desired pattern into the subspace of patterns achievable by a particular set of space-time sampling positions. This projection is the optimal achievable pattern in the sense that it minimizes the mean-squared error (MSE) between the desired and actual patterns. The main advantage of the technique is versatility as it can be applied to both sparse and dense arrays, nonuniform and asynchronous time sampling, and dynamic arrays where sensors can move throughout space. It can also be applied to any beam pattern type, including frequency-invariant and spot pattern designs. A simple extension to the technique is presented for oversampled arrays, which allows high-resolution beamforming whilst carefully controlling input energy and error sensitivity.
Van Veen BD, Buckley KM: Beamforming: a versatile approach to spatial filtering. IEEE ASSP Magazine 1988,5(2):4–24.
Johnson DH, Dudgeon DE: Array Signal Processing: Concepts and Techniques. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.
Liu C, Sideman S: Digital frequency-domain implementation of optimum broadband arrays. Journal of the Acoustical Society of America 1995,98(1):241–247. 10.1121/1.413771
Godara LC: Application of the fast Fourier transform to broadband beamforming. Journal of the Acoustical Society of America 1995,98(1):230–240. 10.1121/1.413765
Ward DB, Kennedy RA, Williamson RC: Theory and design of broadband sensor arrays with frequency invariant far- field beam patterns. Journal of the Acoustical Society of America 1995,97(2):1023–1034. 10.1121/1.412215
Chan SC, Pun CKS: On the design of digital broadband beamformer for uniform circular array with frequency invariant characteristics. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '02), May 2002, Scottsdale, Ariz, USA 1: 693–696.
Liu W, Weiss S: A new class of broadband arrays with frequency invariant beam patterns. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 2: 185–188.
Harris FJ: On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE 1978,66(1):51–83.
Hansen WW, Woodyard JR: A new principle in directional antenna design. Proceedings of the IRE 1938, 26: 333–345.
Riblet HJ: Note of the maximum directivity of an antenna. Proceedings of the IRE 1948, 36: 620–623.
Taylor TT: A discussion of the maximum directivity of an antenna. Proceedings of the IRE 1948, 25: 1134–1135.
Yaru N: A note on super-gain antenna arrays. Proceedings of the IRE 1951, 39: 1081–1085.
Sharma RR, Van Veen BD: Large modular structures for adaptive beamforming and the Gram-Schmidt preprocessor. IEEE Transactions on Signal Processing 1994,42(2):448–451. 10.1109/78.275626
Poletti MA: A unified theory of horizontal holographic sound systems. Journal of the Audio Engineering Society 2000,48(12):1155–1182.
Debnath L, Mikusinski P: Introduction to Hilbert Spaces with Applications. Academic Press, San Diego, Calif, USA; 1990.
Stroud AH: Approximate Calculation of Multiple Integrals. Prentice-Hall, Englewood Cliffs, NJ, USA; 1971.
Mikhlin SG: Integral Equations and Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology. Pergamon Press, New York, NY, USA; 1957.
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Williams, M.I.Y., Abhayapala, T.D. & Kennedy, R.A. Generalized Broadband Beamforming Using a Modal Subspace Decomposition. EURASIP J. Adv. Signal Process. 2007, 068291 (2006). https://doi.org/10.1155/2007/68291
- Input Energy
- Pattern Type
- Pattern Design
- Sampling Position
- Simple Extension