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

Abstract

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.