ROBUST DIRECTION ESTIMATION OF UWB SOURCES IN LAGUERRE-GAUSS BEAMSPACES Elio D. Di Claudio(*), Giovanni Jacovitti(**), and Alberto Laurenti(***) (*)(**) DIET, Dept. of Information Engineering, Electronics and Telecommunications, University of Rome “La Sapienza”, Via Eudossiana, 18, I-00184, Roma, Italy (*)phone: + (39) 06 44585490, fax: + (39) 06 4873300, email: dic@infocom.uniroma1.it (**)phone: + (39) 06 44585838, fax: + (39) 06 4873300, email: gjacov@infocom.uniroma1.it (***) GIAL S.r.l. company, Via Capodistria 12, I-00198, Rome, Italy phone: + (39) 06 39088746, email: a.laurenti@unicampus.it ABSTRACT A novel method for estimating the direction of arrival of ultra-wideband wavefronts impinging on a linear uniform sensor array is proposed. It is based on expanding the space time signals onto a basis of Laguerre-Gauss Circular Harmonic functions, whose peculiar properties lead to a new signal subspace parametric model. This approach allows robust angle of arrival estimation in low signal to noise ratio environments. Index Terms— UWB DOA, space-time array processing, Laguerre-Gauss Circular Harmonic expansion, UWB communications. 1. INTRODUCTION Direction of arrival (DOA) estimation of plane waves is one of the most classical issues of sensor array signal processing, employed for localization of sources in propagating media. Several computationally efficient and accurate methods have been developed for narrow band sources [1] based on amplitude and phase differences of signals received by sensors. These classical methods are extended to the case of ultra- wideband (UWB) sources by focusing, i.e., by coherent combination of many narrowband components [1][2]. However, these techniques turn out to be computationally expensive and critical when the array bandwidth exceeds about one octave [3]. Another classical UWB DOA approach used in the specific case of a single radiating source is space-time (ST) processing, where the set of signals collected by a sensor array are viewed as 1-D patterns, i.e., 2-D signals constant in the direction orthogonal to the DOA. A well known ST estimation method consists on estimating the time difference of arrival (TDOA) between the signals received by any sensor pair [4], [5], [6]. TDOA estimates are prone to large outliers in low SNR environment. The scope of this contribution is to present a method for estimating the DOA of UWB sources robust to high noise contamination. The method is based on expanding the ST signal impinging on a linear array onto a basis of Laguerre- Gauss Circular Harmonic (LG-CH) orthogonal functions [6][7]. These functions have two fundamental properties that make them suited for performing a kind of tomographic analysis of the ST signal, whose optimality for 1-D pattern orientation estimation was discussed in [8]. The first property is that they are polar separable and steer by multiplication by a complex factor [7]. The second one is that they are block-wise linearly related to corresponding sets of Cartesian separable two dimensional Hermite Gauss (2D-HG) orthogonal functions [9], [10], [11]. It is shown here that robust DOA estimates can be performed using a truncated series of coefficients [9], by means of polynomial rooting techniques. 2. NOTATION Matrices are indicated by capital boldface letters, vectors by lowercase, boldface letters. The transpose of matrix A is T A . The Hermitian transpose of the same matrix is H A . I is the identity matrix. >@ . E indicates the expected value. 3. SPACE TIME SIGNAL MODEL A far-field source, located at angle T with respect to the broadside of an uniform linear array (ULA) radiates the UWB signal () s t in a non-dispersive medium with wave propagation speed c . In a Cartesian reference system (,) xt , the real-valued baseband signal received by an unit gain, omni-directional sensor placed at the generic coordinates ( ,0) x is given by 2736 978-1-4577-0539-7/11/$26.00 ©2011 IEEE ICASSP 2011