Comparative analysis of various Matrix Pencil methods for direction of arrival estimation

The Matrix Pencil (MP) method is a direct data domain method that can be used to estimate direction of arrivals (DOA) of coherent or non-coherent signals from a single snapshot of a uniform linear array (ULA). Recently, many variants of MP method have been proposed including Unitary Matrix Pencil (UMP), Single invariance Beamspace Matrix Pencil (SBMP) and Multiple invariance Beamspace Matrix Pencil(MBMP) methods. The main objective of this paper is to compare these algorithms with respect to computational complexity and estimation accuracy. It is shown through computer simulations that although all these methods give comparable performance in terms of average root mean square error of estimated DOA, there is a significant difference in their computational complexity.

I. Introduction

Many methods and techniques have been developed in the last few decades to estimate unknown parameters of plane wave signals using sensor arrays [1]. Supper resolution techniques like MUSIC [2] and ESPRIT [3] are widely used to estimate the unknown parameters by exploiting the eigen structure of the covariance matrix. These techniques are usually suitable for stationary environment and require that the signals are not fully correlated or coherent. Another method for estimating the unknown parameters of sinusoids in noise is the Matrix Pencil (MP) method [4], [5]. The MP method is a direct data domain method that analyzes the data on snapshot-by-snapshot basis; consequently, non-stationary environment can be handled easily [6]. Moreover, this method can find direction of arrival (DOA) in the presence of multi-path coherent signals without performing additional spatial smoothing.