Research Article Tensor-Based Methods for Blind Spatial Signature Estimation in Multidimensional Sensor Arrays Paulo R. B. Gomes, 1 André L. F. de Almeida, 1 João Paulo C. L. da Costa, 2,3,4 João C. M. Mota, 1 Daniel Valle de Lima, 2 and Giovanni Del Galdo 3,4 1 Department of Teleinformatics Engineering, Federal University of Cear´ a, Fortaleza, CE, Brazil 2 Department of Electrical Engineering, University of Bras´ ılia, DF, Bras´ ılia, Brazil 3 Institute for Information Technology, Ilmenau University of Technology, Ilmenau, Germany 4 Fraunhofer Institute for Integrated Circuits IIS, Erlangen, Germany Correspondence should be addressed to Paulo R. B. Gomes; paulo@gtel.ufc.br Received 10 September 2016; Accepted 15 January 2017; Published 15 February 2017 Academic Editor: Elias Aboutanios Copyright © 2017 Paulo R. B. Gomes et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te estimation of spatial signatures and spatial frequencies is crucial for several practical applications such as radar, sonar, and wireless communications. In this paper, we propose two generalized iterative estimation algorithms to the case in which a multidimensional (-D) sensor array is used at the receiver. Te frst tensor-based algorithm is an -D blind spatial signature estimator that operates in scenarios where the source’s covariance matrix is nondiagonal and unknown. Te second tensor-based algorithm is formulated for the case in which the sources are uncorrelated and exploits the dual-symmetry of the covariance tensor. Additionally, a new tensor-based formulation is proposed for an -shaped array confguration. Simulation results show that our proposed schemes outperform the state-of-the-art matrix-based and tensor-based techniques. 1. Introduction High resolution parameter estimation plays a fundamental role in array signal processing and has practical applications in radar, sonar, mobile communications, and seismology. In light of this, several techniques have been developed to increase the accuracy of the estimated parameters, from which we may cite the classical Multiple Signal Classifca- tion (MUSIC) [1] and Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) [2]. However, their performance can be further improved by exploiting the multidimensional structure of the data by means of tensor modeling, which can include several signal dimensions such as space, time, frequency, and polarization. Tensor decom- positions have been successfully employed in array signal processing for parameters estimation since they provide bet- ter identifability conditions when compared to conventional matrix-based methods. Another advantage of tensor-based methods is the so-called “tensor gain” which manifests itself with more precise parameter estimates due to the good noise rejection capability of tensor-based signal processing, as shown in [3–6]. In regards to tensor-based methods for blind spatial signatures estimation, the Parallel Factor (PARAFAC) anal- ysis decomposition [7] is widely applied due to its well- defned conditions for uniqueness [8]. As seen in [9], an iterative technique for PARAFAC decomposition such as Trilinear Alternating Least Squares (TALS) can be applied to estimate the directions of arrival of the sources. Closed-form solutions such as the Standard Tensor ESPRIT (STE) [10] and Closed-Form PARAFAC [11] are also appealing, since these exploit the multidimensional structure in a noniter- ative fashion. Recently in [12], an iterative algorithm was proposed in a manner similar to Independent Component Analysis (ICA) based on the Orthogonal Procrustes Problem (OPP) and Khatri-Rao factorization [13] for a PARAFAC decomposition with dual-symmetry. Tis solution exploits the dual-symmetry property of the data tensor and can be applied in covariance-based array signal processing tech- niques. Te method proposed in [14] is based on the Tucker Hindawi International Journal of Antennas and Propagation Volume 2017, Article ID 1615962, 11 pages https://doi.org/10.1155/2017/1615962