Matrix pencil method for simultaneously estimating azimuth and elevation angles of arrival along with the frequency of the incoming signals

doi:10.1016/j.dsp.2006.05.009

Digital Signal Processing

Volume 16, Issue 6, November 2006, Pages 796-816

https://doi.org/10.1016/j.dsp.2006.05.009 Get rights and content

Abstract

In this paper we describe a method for simultaneously estimating the direction of arrival (DOA) of the signal along with its unknown frequency. In a typical DOA estimation problem it is often assumed that all the signals are arriving at the antenna array at the same frequency which is assumed to be known. The antenna elements in the array are then placed half wavelength apart at the frequency of operation. However, in practice seldom all the signals arrive at the antenna array at a single pre-specified frequency, but at different frequencies. The question then is what to do when there are signals at multiple frequencies, which are unknown. This paper presents an extension of the matrix pencil method to simultaneously estimate the DOA along with the operating frequency of each of the signals. This novel approach involves approximating the voltages that are induced in a three-dimensional antenna array, by a sum of complex exponentials by jointly estimating the direction of arrival (both azimuth and elevation angles) along with the carrier frequencies of multiple far-field sources impinging on the array by using the three-dimensional matrix pencil method. The matrix pencil method is a direct data domain method for approximating a function by a sum of complex exponentials in the presence of noise. The variances of the estimates computed by the matrix pencil method are quite close to the Cramer–Rao bound. Finally, we illustrate how to carry out the broadband DOA estimation procedure using realistic antenna elements located in a conformal array. Some numerical examples are presented to illustrate the applicability of this methodology in the presence of noise. It is shown that the variance decreases as the SNR increases. The Cramer–Rao bound for the estimators are also provided to illustrate the accuracy and the computational efficiency of this new methodology.

Section snippets

Nuri Yilmazer was born in Silifke, Turkey. He received the B.S. degree from Cukurova University, Adana, Turkey, in 1996, and the M.S. degree from University of Florida, Gainesville, Florida, in 2000. He is currently working towards the Ph.D. degree in the Department of Electrical Engineering at Syracuse University, Syracuse, New York. His current research interests include adaptive signal processing and smart antennas. He received the Outstanding Teaching Assistant award from Syracuse

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Citation Excerpt :
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Raul Fernandez-Recio was born in Madrid, Spain, in 1978. He received the Ingeniero de Telecomunicacion degree from the Universidad Politecnica de Madrid (UPM), Madrid, Spain, in 2001. He was research assistant in Syracuse University from 2001 to 2002. He was in Universidad de Alcala from 2002 to 2006. He is currently working towards the Ph.D. degree at Universidad Carlos III, Madrid, Spain. His research activities and interests are in the area of adaptive antenna problems and numerical methods in electromagnetics.

Tapan K. Sarkar received the B.Tech. degree from the Indian Institute of Technology, Kharagpur, in 1969, the M.Sc.E. degree from the University of New Brunswick, Fredericton, NB, Canada, in 1971, and the M.S. and Ph.D. degrees from Syracuse University, Syracuse, NY, in 1975. He was a Research Fellow at the Gordon McKay Laboratory, Harvard University, Cambridge, MA, from 1977 to 1978. He is now a Professor in the Department of Electrical and Computer Engineering, Syracuse University. His current research interests deal with numerical solutions of operator equations arising in electromagnetics and signal processing with application to system design.

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Matrix pencil method for simultaneously estimating azimuth and elevation angles of arrival along with the frequency of the incoming signals

Abstract

Section snippets

Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise

IEEE Trans. Acoust. Speech Signal Process.

A high resolution technique for multidimensional NMR spectroscopy

IEEE Trans. Biomed. Eng.

Azimuth and elevation computation in high resolution DOA estimation

IEEE Trans. Signal Process.

An adaptive array utilizing an adaptive spatial averaging technique for multi-path environments

IEEE Trans. Antennas Propagat.