The estimation of directions of arrival is formulated as the decomposition of a 3-way array into a sum of rank-one terms, which is possible when the receive array enjoys some geometrical structure. The main advantage is that this decomposition is essentially unique under mild assumptions, if computed exactly. The drawback is that a low-rank approximation does not always exist. Therefore, a coherence constraint is introduced that ensures the existence of the latter best approximate, which allows

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... to localize and estimate closely located or highly correlated sources. Then Cramér-Rao bounds are derived for localization parameters and source signals, assuming the others are nuisance parameters; some inaccuracies found in the literature are pointed out. Performances are eventually compared with unconstrained reference algorithms such as ESPRIT, in the presence of additive complex Gaussian noise, with possibly non circular distribution. Index Terms multi-way array, coherence, tensor decomposition, source localization, antenna array processing, low-rank approximation, complex Cramér-Rao bounds, non circularity I. INTRODUCTION Estimation of Directions of Arrival (DoA) is a central problem in antenna array processing, including in particular radar, sonar, or telecommunications [2]. Over the last decades, several DoA estimation tools have been developed, ranging from nonparametric Fourier-based methods to parametric high-resolution techniques. The latter techniques, including linear prediction-based methods and subspace methods, are often preferred to nonparametric ones since they achieve high resolution estimates. Recently, methods based on sparse approximations have been proposed, which are considered as semi-parametric [3], [4]. Traditional subspace approaches such as MUSIC (multiple signal classification) are based on low-rank approximation of the covariance matrix of observations, and on detecting points of minimal distance with the so-called array manifold [5] [6] . These approaches hence assume that (i) the measurements are weakly stationary over sufficiently long observation lengths, (ii) the number of sources of interest is smaller than the number of sensors, and (iii) spatial