A modular neural network for direction-of-arrival estimation of two sources Gal Ofek , Joseph Tabrikian 1 , Mayer Aladjem 2 Department of ECE, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel article info Article history: Received 29 August 2010 Received in revised form 17 March 2011 Accepted 18 April 2011 Communicated by S. Fiori Available online 26 May 2011 Keywords: Direction-of-arrival estimation Neural networks Neural network applications Maximum likelihood estimation abstract This work addresses the problem of estimating the direction-of-arrival (DOA) of two sources using an array of sensors. This problem is mostly useful in radar applications, where we have few targets at each range bin. Super-resolution algorithms, such as maximum likelihood (ML) estimation and multiple signal classification (MUSIC), have been applied to this problem, but the former involves high computation efforts, while the later has poor estimation performance for coherent sources. In this work, we propose a DOA estimation network, named RBF-AML, which combines the approximated ML (AML) estimator and a radial basis function (RBF) neural network (NN). In the proposed RBF-AML network, the entire two dimensional DOA space is divided into multiple sectors covered by RBF experts. The AML function is then used as a mediator among the experts and selects the most suitable one as the final output of the system. The performance of the RBF-AML network for a two coherent sources case in a Y shape array configuration is evaluated. We show that the performance of the RBF-AML network is similar to the performance of the classical AML DOA estimation for various signal-to-noise ratios (SNRs), phase of the correlation coefficient and signal-to-interference ratios (SIRs). Furthermore, the RBF-AML network requires fewer computational efforts than the classical AML DOA estimation and therefore is an attractive choice for real-time applications. & 2011 Elsevier B.V. All rights reserved. 1. Introduction Estimating direction-of-arrival (DOA) of sources using an array of sensors [1] is of great interest for many applications such as sonar, radar, and cellular communications, which require both real-time processing and high accuracy. Classical methods for DOA estimation include the maximum likelihood (ML) [1] and the multiple signal classification (MUSIC) [2]. The ML method results in a good estima- tion performance for both the coherent [3] and incoherent signals [4], however it is not practical for real-time applications, as it involves high computational complexity due to the multidimen- sional search procedure over all possible DOA combinations. The MUSIC algorithm, on the other hand, is not computationally complicated, but fails for the case of coherent sources [5]. Neural networks have been widely used in array signal processing [6,7]. To solve the DOA estimation problem, both radial basis function (RBF) network [8–10] and multi-layer perceptron (MLP) network [11–13] have been used in the literature. The main difficulty in training a neural network (NN) for DOA estimation is that the training set needs to be large enough to cover different combinations of the DOAs, signal-to-noise ratios (SNRs), phases of the correlation coeffi- cient and signal-to-interference ratios (SIRs). The number of the adjustable parameters of such NN might be very large, implying complicated model and training procedures. To overcome this problem, the modular NNs [14] have been applied to the DOA estimation problem in [15–19]. In this work, we propose a modular network for DOA estimation of two sources, which combines an asymptotic ML (AML) method [1] and RBF-NN. In our network, the two dimensional DOA range is divided into multiple sectors. RBF-NN is trained for each angular sector, while the AML performs as a mediator among the RBF-NNs. The advantages of the proposed network over other DOA estima- tion solutions, which are purely statistical such as ML [1] or purely NN-based such as NMUST [15], are low computational complexity, adaptive learning with generalization capabilities and massive parallelism together with the advantage of the good performance of the ML methods. The proposed method can be applied to any array configuration and is not limited to linear arrays unlike other classical methods (spatial smoothing, method of direction estima- tion (MODE), and forward-backward averaging [1]). In this paper, we considered a problem of two coherent sources impinging a Y shape array of sensors. We train our network to perform in different scenarios, such as large range of SNRs, various angular separations between the sources, different phases of the correlation coefficient and various SIRs. In fact, Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/neucom Neurocomputing 0925-2312/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2011.04.012 Corresponding author. Current address: Micron Technology Inc., Ha’avatz 11 P.O. Box 1320 Kiryat Gat, Israel. Tel.: þ972 547886171. E-mail addresses: galofek@yahoo.com, gofek@micron.com (G. Ofek), joseph@ee.bgu.ac.il (J. Tabrikian), aladjem@ee.bgu.ac.il (M. Aladjem). 1 Tel.: þ972 36477774; fax: þ972 36472949. 2 Tel.: þ972 36472409; fax: þ972 36472949. Neurocomputing 74 (2011) 3092–3102