A New Approach for Estimating the Number of Sources Under the Coexistence of Circular and Various Noncircular Sources
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A New Approach for Estimating the Number of Sources Under the Coexistence of Circular and Various Noncircular Sources Weijian Si · Tong Zhu · Mengying Zhang
Received: 14 October 2012 / Revised: 27 March 2013 © Springer Science+Business Media New York 2013
Abstract Estimation of source number is a fundamental problem of direction-ofarrival (DOA) estimation. In the problem of DOA estimation under the coexistence of circular and various noncircular signals, the source number should be estimated in order to distinguish the signal subspace from the noise subspace. Thus, a new method for source number estimation is proposed in this paper. Using the approach of k-means clustering, the projections of a one-dimensional reduced covariance matrix are divided into two categories. Then the signal subspace and the noise subspace are separated by the optimal classification boundary of those two categories so as to obtain the equivalent source number. Simulation results show that the proposed method has relatively better performance even in low SNR or in a colored noise environment. Keywords Source number estimation · k-Means clustering · Noncircular source · Array signal processing
1 Introduction Noncircular sources are widely applied in modern communication systems [2, 3, 5, 12], such as binary phase shift keying (BPSK), minimum shift keying (MSK), and W. Si · T. Zhu () · M. Zhang Department of Information and Communication Engineering, Harbin Engineering University, Harbin, China e-mail: [email protected] W. Si e-mail: [email protected] M. Zhang e-mail: [email protected]
Circuits Syst Signal Process
Gaussian filtered minimum shift keying (GMSK) modulated signals. As the noncircular properties of signals can improve the performance of direction-of-arrival (DOA) estimation, DOA estimation of noncircular sources has become the focus of recent research in array signal processing. In 1998, a convenient DOA estimation algorithm was presented for noncircular sources (NC-MUSIC) [5] by Gounon. After that, improved MUSIC algorithms [2–4, 12], improved ESPRIT algorithms [6, 9–11, 19], and improved Cramér–Rao bounds [1, 7] for noncircular sources were subsequently proposed by scholars of all nations. Most of the algorithms based on eigensubspace must precisely estimate the number of sources, namely the number of eigenvalues of the signal subspace; otherwise, the estimation accuracy will be significantly deteriorated. M. Wax and T. Kailath first introduced information theoretic criteria to source number estimation algorithms, and presented algorithms based on the Akaike information criterion (AIC) and the minimum description length (MDL) criterion [15]. A source number estimation algorithm based on Gerschgorin’s disk estimation (GDE) [16] was proposed by H.T. Wu. The information theoretic criteria were applied to noncircular sources processing, and then Non-Circular Information Theoretic Detect (NC-ITD) and Non-Circular Minimum Description Length (NC-MDL) criteria were proposed by C.D. Zheng [17, 18]. However, those criteria can dem
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