Published in IET Radar, Sonar and Navigation Received on 19th July 2008 Revised on 2nd December 2008 doi: 10.1049/iet-rsn.2008.0118 ISSN 1751-8784 Computationally efficient two-dimensional direction-of-arrival estimation of electromagnetic sources using the propagator method J. He Z. Liu Department of Electronic Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, People’s Republic of China E-mail: andrie1111@hotmail.com Abstract: The authors develop a propagator-based algorithm for two-dimensional (2D) direction finding of electromagnetic sources under spatially correlated noise here. The planar-plus-an-isolated array geometry, first defined by Li et al. (1996) is adopted. The authors propose to replace the planar pressure-sensors in Li et al. (1996) by electromagnetic vector sensors, thus exploiting the benefits inherent in the additional measurements made by a vector sensor. Compared with the algorithm in Li et al. (1996), the presently proposed algorithm can offer closed-form automatically paired azimuth-elevation angle estimates, without costly 2D iterative searching. Moreover, the proposed algorithm can achieve the unambiguous direction estimates with enhanced accuracy by setting the planar electromagnetic vector sensors to space much farther apart than a half-wavelength. Therefore the proposed algorithm constitutes a distinct improvement over (Li et al., 1996) 1 Introduction Estimation of two-dimensional (2D) direction-of-arrival (DOA) of multiple narrowband sources using sensor array techniques has played a fundamental role in many applications involving radar, sonar, wired/wireless communications and seismic sensing. Subspace-based algorithms such as MUSIC [1] and ESPRIT [2–8] have been intensively investigated for 2D direction finding because of their high-resolution and computational simplicity. Traditionally, these algorithms use the eigen-decomposition (or singular value decomposition) to decompose the column space of the data correlation matrix into a signal subspace and a noise subspace, and these algorithms are always implemented in batch mode. Unfortunately, the computational costs involved in the eigen-decomposition process are huge especially when the number of sensors is large. To alleviate the computational burden of the eigen-decomposition, many efficient techniques such as computing only principal eigenvectors, or recursively updating the eigenvectors have been proposed [6, 7]. Recently, it is found that the so-called propagator method, first proposed in [8], has become a possible alternative to MUSIC and ESPRIT because the propagator method offers almost equivalent performance to MUSIC and ESPRIT, but needs a much reduced computational cost [9]. For example, the multiplication operations required for ESPRIT in calculating the eigen-decomposition for a covariance matrix with an array of size L and snapshots N are in the order of O(L 3 þ 2L 2 N ). In contrast, the computational load of the propagator method is in O(2LNK), where K is the number of incident sources. For 2D direction finding with propagator, [10] and [11] have, respectively, applied the parallel shape array and the L-shape array [12] has used arbitrarily spaced electromagnetic vector sensors. Most of the above mentioned propagator-based algorithms assume the incoherent sources and spatially white noise. However, for real world applications, we may often encounter the coherent sources (which arise in scenarios due to multipath propagation [13]), and spatially correlated IET Radar Sonar Navig., 2009, Vol. 3, Iss. 5, pp. 437–448 437 doi: 10.1049/iet-rsn.2008.0118 & The Institution of Engineering and Technology 2009 www.ietdl.org