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Sensors 2013, 13(1), 746-757; doi:10.3390/s130100746
Article

An Improved Direction Finding Algorithm Based on Toeplitz Approximation

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Received: 19 November 2012 / Revised: 29 December 2012 / Accepted: 6 January 2013 / Published: 7 January 2013
(This article belongs to the Section Physical Sensors)
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Abstract

In this paper, a novel direction of arrival (DOA) estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC) algorithm is proposed through combining a fast MUSIC-like algorithm termed the modified fourth order cumulants MUSIC (MFOC-MUSIC) algorithm and Toeplitz approximation. In the proposed algorithm, the redundant information in the cumulants is removed. Besides, the computational complexity is reduced due to the decreased dimension of the fourth-order cumulants matrix, which is equal to the number of the virtual array elements. That is, the effective array aperture of a physical array remains unchanged. However, due to finite sampling snapshots, there exists an estimation error of the reduced-rank FOC matrix and thus the capacity of DOA estimation degrades. In order to improve the estimation performance, Toeplitz approximation is introduced to recover the Toeplitz structure of the reduced-dimension FOC matrix just like the ideal one which has the Toeplitz structure possessing optimal estimated results. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. From the simulations, in comparison with the MFOC-MUSIC algorithm, it is concluded that the TFOC-MUSIC algorithm yields an excellent performance in both spatially-white noise and in spatially-color noise environments.
Keywords: DOA estimation; fourth order cumulants; MUSIC-like; Toeplitz approximation; spatially-white noise; spatially-color noise DOA estimation; fourth order cumulants; MUSIC-like; Toeplitz approximation; spatially-white noise; spatially-color noise
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.

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Wang, Q.; Chen, H.; Zhao, G.; Chen, B.; Wang, P. An Improved Direction Finding Algorithm Based on Toeplitz Approximation. Sensors 2013, 13, 746-757.

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