Study of Blind Adaptive Beamforming Method for Multiple Sources Based on Genetic Algorithm
Blind adaptive beamforming method for multiple sources is studied. A new method based on genetic algorithm is presented. The algorithm can estimate weight vectors by defining a new cost function. At the same time, a global optimal solution of nonlinear we
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Study of Blind Adaptive Beamforming Method for Multiple Sources Based on Genetic Algorithm Yanwu Liu
Abstract Blind adaptive beamforming method for multiple sources is studied. A new method based on genetic algorithm is presented. The algorithm can estimate weight vectors by defining a new cost function. At the same time, a global optimal solution of nonlinear weighting vector estimation is obtained by complex coding genetic algorithm. The coded parameters in the complex coding genetic algorithm are composed of real parts and imaginary parts of complex weight vectors. The fitness function equivalent to the objective function of the traditional optimization techniques is constructed by the new cost function. Computer simulation proves correctness of this method. Keywords Genetic algorithm • Blind adaptive beamforming • Computer simulation • Multiple sources
262.1
Introduction
In recent years, blind adaptive beamforming has been an important subject of research in signal processing and communication. Many blind adaptive beamforming algorithms are presented based on know signal properties, such as cyclostationarity [1, 2], high-order statistic [3, 4] and constant modulus (CM) [5]. The application of CMA for blind adaptive beamforming was addressed by Agee. It was shown that CMA beamformer can automatically capture a certain class of non-Gaussian signals with negative kurtosis. To capture signals with positive and negative kurtosis, the kurtosis maximization algorithm (KMA) was proposed in [6]. However, in order to force multiple weighting vectors to converge to distinct
Y. Liu (*) School of Information and Electronic Engineering Shandong Institute of Business and Technology, Yantai 264005, China e-mail: [email protected] S. Zhong (ed.), Proceedings of the 2012 International Conference on Cybernetics 2057 and Informatics, Lecture Notes in Electrical Engineering 163, DOI 10.1007/978-1-4614-3872-4_262, # Springer Science+Business Media New York 2014
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maxima, KMA needs the Gram-Schmidt orthogonalization (GSO). This process would increase the algorithm complexity and result in the bias of the beamformer weight vector estimation. In this paper, a new blind adaptive beamforming method for multiple sources based on genetic algorithm is presented. Computer simulation proves correctness of this method.
262.2
Problem Formulation
Consider the case of multiple (P) narrowband signals sj ðtÞ, j ¼ 1,2,. . ., P, arriving at M sensors in the presence of additive noise nm ðtÞ, m ¼ 1,2,. . .,M. Assume that these P independent source signals have nonzero fourth-order cumulant. The received signal vector is given by rðtÞ ¼ ASðtÞ þ nðtÞ
(262.1)
where A is an M P mixing matrix that may be formed by P steering column vectors in beamforming systems as A ¼ ½aðθ1 Þ aðθ2 Þ aðθP Þ The signal vector contains P active sources SðtÞ ¼ ½s1 ðtÞ s2 ðtÞ sP ðtÞT nðtÞ is an additive noise vector, nðtÞ ¼ ½n1 ðtÞ n2 ðtÞ nM ðtÞT My method will lay on the assumptions that the steering vectors are linearly independe
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