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# Accession Number:

## ADA200112

# Title:

## Extensions to the Matrix Pencil Approach for Direction Finding

# Descriptive Note:

## Final rept. May 1986-May 1987

# Corporate Author:

## SYRACUSE UNIV NY DEPT OF ELECTRICAL AND COMPUTER ENGINEERING

# Report Date:

## 1988-07-01

# Pagination or Media Count:

##
104.0

# Abstract:

## This work deals with the problem of direction finding using the matrix-pencil approach. Consider a linear array of m sensor and assume there are d narrowband sources. Having collected the data at the m sensors, the problem is to estimate the direction of arrival of these sources. The matrix-pencil approach is a non-search procedure, thus very easy to use. In this study, a generalization of the method to a linear array of m identical sensors with some arbitrary beam pattern was performed. It is also shown that the method still works when using different windows. The only restriction is that at least d elements of the window be non-zero to ensure the validity of the algorithm. A perturbation analysis due to equal sensor spacing was also performed. The concept of the chordal metric was introduced. It is shown that the bound derived on the chordal metric is equivalent to the chordal metric itself. The problem of estimating both the angular frequencies and the angles of arrival of the sources was then posed. It is proven that the method still works i.e., the angular frequencies and the locations of the sources were estimated using two matric pencils. The rank values of these matrices is shown to contain both the angles of arrival and the angular frequencies of the sources. A computer simulation was performed each time to ensure the effectiveness of the method.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#