Maximum Likelihood-Based Direction-of-Arrival Estimator for Discrete Sources
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Maximum Likelihood-Based Direction-of-Arrival Estimator for Discrete Sources Rafael Krummenauer · Rafael Ferrari · Ricardo Suyama · Romis Attux · Cynthia Junqueira · Pascal Larzabal · Philippe Forster · Amauri Lopes
Received: 2 August 2012 / Revised: 15 March 2013 © Springer Science+Business Media New York 2013
Abstract This paper addresses the problem of direction-of-arrival (DOA) parameter estimation in array processing when the signals are inherently discrete, which is the case mainly in the digital communication context. Based on the particular structure R. Krummenauer () · R. Ferrari · R. Attux · A. Lopes Faculdade de Engenharia Elétrica e de Computação (FEEC)/6101, Universidade Estadual de Campinas—UNICAMP, 13083-852 Campinas, SP, Brazil e-mail: [email protected] R. Ferrari e-mail: [email protected] R. Attux e-mail: [email protected] A. Lopes e-mail: [email protected] R. Suyama Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS), UFABC, Santo André, SP, Brazil e-mail: [email protected] C. Junqueira Instituto de Aeronáutica e Espaço (IAE), Comando-Geral de Tecnologia Aeroespacial (CTA), 12228-904 São José dos Campos, SP, Brazil e-mail: [email protected] P. Larzabal · P. Forster Laboratoire SATIE, ENS de CACHAN, CNRS, Universud, 61 avenue du président Wilson, 94235 Cachan Cedex, France P. Larzabal e-mail: [email protected] P. Forster e-mail: [email protected]
Circuits Syst Signal Process
of the signal space in the data model, a maximum likelihood-based approach is introduced. The strategy consists in transforming the parameter estimation problem into a decision task. It is shown through numerical simulations that the proposed solution closely follows the performance limit given by the Cramér–Rao bound. Some important features of the technique are as follows: (i) it is capable of handling any number of sources, provided that the number of sensors is greater than or equal to two and the number of snapshots is sufficiently greater than the cardinality of the signal space; (ii) the estimation quality is not affected by the angle and phase separation; and (iii) it offers the possibility to deal with uncalibrated arrays. Keywords Array signal processing · Direction-of-arrival estimation · Maximum likelihood criterion · Digital modulation 1 Introduction In any practical parameter estimation case, the more the chosen model matches the available data, the better the estimator should perform, given some fixed optimality criterion. In the statistical sense, this means, inter alia, that the random processes involved in the signal and noise components must assume adequate distributions. For instance, in array signal processing, Gaussianity is by far the most common assumption for both signal and noise probability density functions—sometimes due to mathematical tractability—and many algorithms and bounds have been developed in this line (see [14, 24, 25, 38, 40, 41] and references therein). Although the Gaussian assumption for
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