Utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival

• Published in: IEEE transactions on antennas and propagation Vol. 54; no. 1; pp. 175 - 181
• Main Authors: Yilmazer, N., Jinhwan Koh, Sarkar, T.K.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computation; Computational efficiency; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Digital signal processors; Direction of arrival; Direction of arrival (DOA); Direction of arrival estimation; Exact sciences and technology; Frequency estimation; Information, signal and communications theory; Karhunen-Loeve transforms; Mathematical analysis; Matrices; Matrix converters; Matrix methods; matrix pencil (MP); Multiple signal classification; Pencils; Phased arrays; Signal and communications theory; Signal processing; Signal processing algorithms; Signal resolution; Signal, noise; Studies; Telecommunications and information theory; Transformations; unitary transformation; Cost minimization; matrix pencil (MP); Direction-of-arrival estimation; Parameter estimation; Unitary matrix; Eigenvector; Direction of arrival (DOA); Hermite interpolation; Signal estimation; Covariance matrix; Computational complexity; Implementation; Accuracy; Simulation; Matrix method; unitary transformation; Real time processing; Digital signal processor; Cramer Rao inequality
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2005.861567

In this study, we use the matrix pencil (MP) method to compute the direction of arrival (DOA) of the signals using a very efficient computational procedure in which the complexity of the computation can be reduced significantly by using a unitary matrix transformation. This method applies the technique directly to the data without forming a covariance matrix. Simulation results show that the variance of the estimate approaches to the Cramer-Rao lower bound. Using real computations through the unitary transformation for the MP method leads to a very efficient computational methodology for real time implementation on a digital signal processor chip. A unitary transform can convert the complex matrix to a real matrix along with their eigenvectors and thereby reducing the computational cost at least by a factor of four without sacrificing accuracy. This reduction in the number of computations is achieved by using a transformation, which maps centro-hermitian matrices to real matrices. This transformation is based on Lee's work on centro-hermitian matrices.