Signal Processing for Arbitrary Sensor Array Configurations: Theory and Algorithms

Fabio Belloni

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on the 12^th of October, 2007, at 12 o'clock noon.

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Abstract

Sensor array systems are employed in many application areas such as multi-antenna wireless communications, radar and biomedicine. Among the research areas of sensor array signal processing, the problem of finding the direction-of-arrival (DoA) at which a propagating wavefield impinges on a sensor array is a popular research field. Applications explicitly needing directional information include beamforming, localization, surveillance, and channel sounding.

Most high-resolution and computationally efficient sensor array processing algorithms have been developed for ideal sensor arrays with regular geometry and known sensor response. In practice, the geometry of the array can not be chosen freely and the array response is always an unknown quantity which can be estimated only through noisy calibration measurements. Consequently, the above algorithms are not applicable on real-world arrays with arbitrary configuration.

This thesis focuses on deriving and analyzing novel algorithms providing high-resolution, optimal or close to optimal statistical performance, and low computational complexity, despite the antenna array geometry and imperfections. In particular, the problem of reformulating the array signal processing model so that computationally efficient high-resolution DoA estimation algorithms can be used with sensor arrays of arbitrary configuration is addressed. The contributions in this thesis are in the areas of array transform techniques, antenna modelling, and signal processing algorithms using sensor arrays of arbitrary configurations.

In this thesis, the key ideas and performance of the most common array transform techniques are investigated. The transformation errors and their impact on the DoA estimates are analyzed. Novel algorithms developed for reducing the bias and mitigating the excess variance in the DoA estimates are introduced. Furthermore, an alternative approach to the above techniques known as manifold separation technique (MST) is analyzed. The introduced MST exploits the effective aperture distribution function (EADF) and it is a method for modelling the azimuthal response of sensor arrays with arbitrary configurations by using Vandermonde structured models. A novel MST-based polynomial rooting DoA algorithm is proposed and the effect of noisy calibration data on its statistical performance is also studied. Implementation issues and the use of the developed techniques in real-world arrays are discussed as well.

This thesis consists of an overview and of the following 8 publications:

1. F. Belloni, and V. Koivunen, Unitary root-MUSIC technique for Uniform Circular Array, in Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology (ISSPIT 2003), Darmstadt, Germany, December 14-17, 2003. © 2003 IEEE. By permission.
2. F. Belloni, and V. Koivunen, Reducing bias in beamspace methods for Uniform Circular Array, in Proceedings of the 30th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2005), Philadelphia, PA, USA, March 19-23, 2005. © 2005 IEEE. By permission.
3. F. Belloni, A. Richter, and V. Koivunen, Reducing excess variance in beamspace methods for Uniform Circular Array, in Proceedings of the 13th IEEE Workshop on Statistical Signal Processing (SSP 2005), Bordeaux, France, July 17-20, 2005. © 2005 IEEE. By permission.
4. F. Belloni, A. Richter, and V. Koivunen, Avoiding bias in circular arrays using optimal beampattern shaping and EADF, in Proceedings of the 39th Annual Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, USA, October 30 - November 2, 2005. © 2005 IEEE. By permission.
5. F. Belloni, A. Richter, and V. Koivunen, Extension of root-MUSIC to non-ULA array configurations, in Proceedings of the 31st IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, May 14-19, 2006. © 2006 IEEE. By permission.
6. F. Belloni, and V. Koivunen, Beamspace transform for UCA: error analysis and bias reduction, IEEE Transactions on Signal Processing, vol. 54, no. 8, pp. 3078-3089, August 2006. © 2006 IEEE. By permission.
7. F. Belloni, A. Richter, and V. Koivunen, Performance of root-MUSIC algorithm using real-world arrays, in Proceedings of the 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006. © 2006 by authors.
8. F. Belloni, A. Richter, and V. Koivunen, DoA estimation via manifold separation for arbitrary array structures, IEEE Transactions on Signal Processing, vol. 55, no. 10, pp. 4800-4810, October 2007. © 2007 IEEE. By permission.

Errata of publications 5 and 6

Keywords: direction of arrival estimation, array transform techniques, manifold separation, error analysis

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© 2007 Helsinki University of Technology