Direction of Arrival (DOA) Estimation Using Kronecker Subspace

Majidian, Sina; Haddadi, Farzan

doi:10.29252/jsdp.15.1.29

Volume 15, Issue 1 (6-2018) JSDP 2018, 15(1): 29-40 | Back to browse issues page

‎ 10.29252/jsdp.15.1.29

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Majidian S, Haddadi F. Direction of Arrival (DOA) Estimation Using Kronecker Subspace. JSDP 2018; 15 (1) :29-40
URL: http://jsdp.rcisp.ac.ir/article-1-410-en.html

Direction of Arrival (DOA) Estimation Using Kronecker Subspace

Sina Majidian ^*

, Farzan Haddadi

Iran University of Science and Technology (IUST)

Abstract: (5021 Views)

This paper proceeds directions of arrival (DOA) estimation by a linear array. These years, some algorithms, e.g. Khatri-Rao approach, Nested array, Dynamic array have been proposed for estimating more DOAs than sensors. These algorithms can merely estimate uncorrelated sources. For Khatri-Rao approach, this is due to the fact that Khatri-Rao product discard the non-diagonal entries of the correlation matrix in opposed to Kronecker product. In this article, an algorithm named as Direction of Arrival (DOA) Estimation using Kronecker Subspace is proposed to solve more correlated sources than sensors via some properties of vectorization operator and Kronecker product. The simulations in different scenarios are presented considering various numbers of frames and correlation values, here. These verify our mathematical analysis. Furthermore, Cramer-Rao bound (CRB) which is a crucial criterion to estimate, is under investigating for DOA problem. Although, CRB for DOA estimation has been proposed before, it is applicable only for fewer sources than sensors. In this paper, CRB for more sources than sensor is derived by extending the dimensions with using both real and imaginary parts of the parameters. This bound is compared to the error of the presented algorithm. The simulations show that the error of the presented algorithm is merely 7 dB far from the CRB.

Keywords: Array signal processing, Direction of Arrival (DOA), Correlated sources, Kronecker

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Type of Study: Research | Subject: Paper
Received: 2016/06/2 | Accepted: 2017/03/5 | Published: 2018/06/13 | ePublished: 2018/06/13

References

1. [1] H. Krim and M. Viberg, "Two decades of array signal processing research, the parametric approach," IEEE Signal Process. Mag., pp. 67-94, Jul. 1996. [DOI:10.1109/79.526899]

2. [2] L. Fulai, et al., "Spatial Differencing Method for DOA Estimation Under the Coexistence of Both Uncorrelated and Coherent Signals," IEEE Trans. Antennas Propag, vol. 60, no. 4, pp. 2052-2062; April 2012. [DOI:10.1109/TAP.2012.2186216]

3. [3] W. K. Ma, T. H. Hsieh, and C. Y. Chi, "DOA Estimation of Quasi-Stationary Signals With Less Sensors Than Sources and Unknown Spatial Noise Covariance: A Khatri–Rao Subspace Approach," IEEE Trans. Signal Process., vol. 58, no. 4, pp. 2168–2180, Apr. 2010. [DOI:10.1109/TSP.2009.2034935]

4. [4] P. Pal and P.P. Vaidyanathan, "Nested arrays: A novel approach to array processing with enhanced degrees of freedom," IEEE Trans. Signal Process., vol. 58, no. 8, pp. 4167–4181, Aug. 2010. [DOI:10.1109/TSP.2010.2049264]

5. [5] P.P. Vaidyanathan and P. Pal, "Sparse sensing with co-prime samplers and arrays," IEEE Trans. Signal Process., vol. 59, no. 2, pp. 573–586, Feb. 2011. [DOI:10.1109/TSP.2010.2089682]

6. [6] D. Ariananda and G. Leus, "Direction of arrival estimation for more correlated sources than active sensors," Signal Process. (Elsevier), Vol.93, pp. 3435–3448, Dec. 2013. [DOI:10.1016/j.sigpro.2013.04.011]

7. [7] S. M. Kay, Fundamentals of Statistical Signal processing: Estimation Theory, Prentice Hall. 1993.

8. [8] P. Stoica, A. Nehorai, "Performance study of conditional and unconditional direction-of-arrival estimation," IEEE Trans. Acoust., Speech, Signal Process, vol. 38, no.10, pp. 1783-1795, Oct 1990. [DOI:10.1109/29.60109]

9. [9] P. Stoica, E.G. Larsson, A.B. Gershman, "The stochastic CRB for array processing: a textbook derivation," IEEE Signal Process. Lett., vol.8, no. 5, pp. 148–150, May 2001. [DOI:10.1109/97.917699]

10. [10] R. Schmidt, "Multiple Emitter Location and Signal Parameter Estimation," IEEE Trans. Antennas Propag., vol. AP-34, No. 3, pp. 276-280, Mar. 1986. [DOI:10.1109/TAP.1986.1143830]

11. [11] A. Roger, R. Charles, Topics in Matrix Analysis, Cambridge University Press, 1991.

12. [12] Y. I. Abramovich, N. K. Spencer, and A. Y. Gorokhov, "DOA estimation for noninteger linear Arrays with More Uncorrelated Sources than Sensors," IEEE Trans. Signal Process., vol. 48, pp. 943-955, Apr. 2000. [DOI:10.1109/78.827529]

13. [13] P. Chevalier, A. Ferreol, and L. Albera, "High-resolution direction finding from higher order statistics: The 2q-MUSIC algorithm," IEEE Trans. Signal Process., vol. 54, pp. 2986–2997, Aug. 2006. [DOI:10.1109/TSP.2006.877661]

14. [14] P. Chevalier, L. Albera, A. Ferreol, and P. Comon, "On the virtual array concept for higher order array processing," IEEE Trans. Signal Process., vol. 53, pp. 1254–1271, Apr. 2005 [DOI:10.1109/TSP.2005.843703]

15. [15] Z. Chen, G, Gokeda, Y. Yu, Introduction to Direction-of-Arrival Estimation, Artech House press., 2010.

16. [16] D. Johnson, D. Dudgeon, "Array signal processing, Concepts and Techniques," Prentice Hall, 1993

17. [17] MH. Kahaei, V. Khanagha, "Localization of Multiple Speakers in Echoic Environments Using BSS and Speech Features for Solution of Global Permutation Ambiguity" JSDP 7 (1) :53-64, . 2010.

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