Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2011, Article ID 540275, 12 pages doi:10.1155/2011/540275 Research Article Spatial Correlation for DoA Characterization Using Von Mises, Cosine, and Gaussian Distributions Wamberto J. L. Queiroz, 1 Francisco Madeiro, 2 Waslon Terllizzie A. Lopes, 1 and Marcelo S. Alencar 1 1 Departamento de Engenharia El´ etrica, Universidade Federal de Campina Grande, 58.429-900 Campina Grande, PB, Brazil 2 Escola Polit´ ecnica de Pernambuco, Universidade de Pernambuco, 50.750-470 Recife, PE, Brazil Correspondence should be addressed to Waslon Terllizzie A. Lopes, waslon@ieee.org Received 2 May 2011; Accepted 2 July 2011 Academic Editor: Hoi Shun Lui Copyright © 2011 Wamberto J. L. Queiroz et al. This 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. This paper presents mathematical expressions for the spatial correlation between elements of linear and circular antenna arrays, considering cosine, Gaussian, and Von Mises distributions, for the direction of arrival (DoA) of the electromagnetic waves at the receiver antenna. The expressions obtained for the Von Mises distribution can include or not the mutual coupling effect between the elements and are simpler than those obtained for the cosine and the Gaussian distributions of the angle of arrival. The Von Mises distribution produces spatial correlation expressions in terms of Bessel and trigonometric functions. An exact expression for the spatial correlation, taking into account the mutual coupling, for the circular and linear arrays and an arbitrary number of elements are presented. It can be verified, by numerical evaluation of the expressions, that the coupling between the elements correlates the electromagnetic field, and a separation of half wavelength could not be enough to decorrelate them. 1. Introduction The design of modern communication systems usually requires the statistical characterization of parameters, such as the direction of arrival (DoA) of the electromagnetic wave that reaches the receiver antenna. The knowledge of that parameter is valuable when the target is to limit the effects of interference as well as the gain for undesirable signals [1]. The estimation of DoA has been treated by different authors [1] considering the signal samples captured in the equally spaced elements of antenna arrays. This relevant problem has been addressed in many aspects. A general approach is to consider elements with arbitrary directional characteristics in environments corrupted by noise and inter- ference, characterized by arbitrary covariance matrices. As an example, in [2], the author addresses the spatial processing of signals with respect to the multiplicity of transmitters and presents the algorithm used in the multiple signal classification (MUSIC) method which gives asymptotically nonbiased estimates of different parameters, such as number of arriving waves, direction of arrival, interference, and noise power. A comparative study of methods based on maximum likelihood (ML) and maximum entropy (ME) is presented. The approach presented in the paper for the classification of multiple signals is general and has wide application. The method may be understood in terms of the geometry of an M-dimensional complex vector space in which the eigenvalues of the covariance matrix of the samples play an essential role. Another important contribution for spatial signal pro- cessing is found in the literature [3]. The authors present an efficient algorithm for ML estimation of the DoA considering multiple emission sources and signals captured by the elements of an antenna array. The estimator can be applied to signals that arrive through multipath propagation. The algorithm is based on an iterative technique referred to as alternating projection (AP), which transforms the nonlinear multivariate maximization problem in a set of unidimen- sional problems which are easier to simplify. In spite of the convergence achieved for a wide set of simulations, the authors did not assure the convergence for a general problem. The Estimation of Signal Parameters Via Rotational Invariance Techniques (ESPRIT) algorithm was presented in