Vol. 38
Latest Volume
All Volumes
PIERB 109 [2024] PIERB 108 [2024] PIERB 107 [2024] PIERB 106 [2024] PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2012-01-26
Direction of Arrival Estimation for Nonuniform Planar Array Based on Piecewise Interpolation Method
By
Progress In Electromagnetics Research B, Vol. 38, 241-259, 2012
Abstract
The problem of direction-of-arrival (DOA) estimation by using spectral search for a non-uniform planar array is addressed. New search methods for DOA estimation based on piecewise interpolation are proposed. The relationships between these methods and Fourier-Domain (FD) root-MUSIC are discussed. The proposed methods are based on dividing the multiple signal classification (MUSIC) null-spectrum function into a number of equal subintervals. These subintervals are interpolated by using low-degree polynomials. Piecewise interpolation methods based on elementary functions are used to reduce the required computations of MUSIC null-spectrum function. This property reduces the computational complexity compared with line-search methods for DOA estimation. The Cramér Rao Lower Bound (CRB) is used as a benchmark to check the accuracy and validity of the proposed methods.
Citation
Wael Elshennawy, Ahmed Attiya, Essam Hashish, and Islam A. Eshrah, "Direction of Arrival Estimation for Nonuniform Planar Array Based on Piecewise Interpolation Method," Progress In Electromagnetics Research B, Vol. 38, 241-259, 2012.
doi:10.2528/PIERB11121412
References

1. Rubsamen, M. and A. B. Gershman, "Direction-of-arrival estimation for nonuniform sensor arrays: From manifold separation to Fourier domain MUSIC methods," IEEE Transactions on Signal Process., Vol. 57, No. 2, 588-599, Feb. 2009.
doi:10.1109/TSP.2008.2008560

2. Belloni, F., A. Richter, and V. Koivunen, "Extension of root-MUSIC to non-ULA array configurations," Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP, IV-IV, France, 2006.

3. Haijie, L., F. Wentao, L. Ying, and L. Jiaxuan, "Research on direction-of-arrival estimation with arbitrary geometry array," Proc. of the IEEE International Conference on Signal Processing, ICSP, 315-318, China, 2010.

4. Rubsamen, M. and A. B. Gershman, "Root-music based direction-of-arrival estimation methods for arbitrary non-uniform arrays," Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, 2317-2320, USA, 2008.

5. Wasylkiwskyj, W. and I. Kopriva, "A modified root polynomial algorithm," Proc. of the IEEE International Conference on Applied Electromagnetics and Communications, ICECom, 1-3, Croatia, 2005.

6. Tuncer, E. and B. Friedlander, Classical and Modern Direction-of-Arrival Estimation, Chapter 5, Elsevier, 2009.

7. Babu, K. V. S., "A fast algorithm for adaptive estimation of root-MUSIC polynomial coefficients," Proc. International Conference Acoustics, Speech, Signal Processing, ICASSP, 2229-2232, Canada, 1991.

8. Wither, Jr., L., "Piecewise root-MUSIC," Proc. International Conference Acoustics, Speech, and Signal Processing, ICASSP, 3305-3308, Canada, 1991.

9. Zhuang, J., W. Li, and A. Manikas, "An IDFT-based root-MUSIC for arbitrary arrays," Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, 2614-2617, USA, 2010.

10. Gross, F., Smart Antennas for Wireless Communications with MATLAB, Chapter 7, McGraw-Hill, 2005.

11. Belloni, F., A. Richter, and V. Koivunen, "DoA estimation via manifold separation for arbitrary array structures," IEEE Transactions on Signal Process., Vol. 55, No. 10, 4800-4810, Oct. 2007.
doi:10.1109/TSP.2007.896115

12. Foutz, J., A. Spanias, and M. K. Banavar, Narrowband Direction of Arrival Estimation for Antenna Array, Chapter 3, Morgan and Claypool Publishers Series, 2008.

13. Balanis, C. A. and P. I. Ioannides, Introduction to Smart Antennas, Chapter 5, Morgan and Claypool Publishers, 2007.

14. Chen, Z., G. Gokeda, and Y. Yu, Introduction to Direction-of-Arrival Estimation, Chapter 3, Artech House, 2010.

15. Hwang, H. K., Z. Aliyazicioglu, M. Grice, and A. Yakovlev, "Direction of arrival estimation using a root-MUSIC algorithm," Proceedings of International MultiConference of Engineers and Computer Scientists, IMECS, Vol. II, Hong Kong, 2008.

16. Rao, B. D. and K. V. S. Hari, "Performance analysis of root-MUSIC," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 37, No. 12, 1939-1949, Dec. 1989.
doi:10.1109/29.45540

17. Shim, H.-T. and C.-H. Park, "Gibbs phenomenon for trigono-metric interpolation," J. of Appl. Math. and Computing, Vol. 16, No. 1--2, 605-612, 2004.

18. Atkinson, K. E., An Introduction to Numerical Analysis, 2nd Ed., Chapter 3, Wilely and Sons, New York, 1988.

19. Pan, C., "Gibbs phenomenon removal and digital filtering directly through the fast Fourier transform," IEEE Transactions on Signal Process., Vol. 49, No. 2, 444-448, Feb. 2001.
doi:10.1109/78.902128

20. Lin, F., Polynomial Interpolation, Chapter 2, National Taiwan Ocean University Pub., Scientific Computing, 2007.

21. Farahmand, K. and T. Li, "Random trigonometric polynomials with nonidentically distributed coefficients," International Journal of Stochastic Analysis, Vol. 2010, 1-10, Hindawi Publishing Cooperation, Feb. 2010.

22. Dumitrescu, B., Positive Trigonometric Polynomials and Signal Processing Application, Chapters 1 and 2, Springer, 2007.
doi:10.1007/978-1-4020-5125-8_1

23. Lobos, T., J. Rezmer, and P. Schegner, "Parameter estimation of distorted signals using Prony method," Proceeding of the Power Tech Conference, PTCF, Vol. 4, 1468-1475, Bologna, Jun. 2003.

24. Alaoui Ismaili, M. and A. Xémard, "Representation of electrical signals by a series of exponential terms," Proceeding of the International Conference on Power Systems Transien, IPST, 93-98, Hungary, Jun. 1999.

25. Abutheraa, M. A. and D. Lester, "Computable function representations using effective Chebyshev polynomial," Proceedings of the World Academy of Science, Engineering, and Technology, PWASET, Vol. 25, 103-109, Nov. 2007.

26. Mason, J. C. and D. C. Handscomb, Chebyshev Polynomials, Chapman and Hall/CRC, 2003.

27. Stoica, P., E. G. Larsson, and A. B. Gershman, "The stochastic CRB for array processing a textbook derivation," IEEE Trans. on Acoustics and Signal Process., Vol. 8, No. 5, 148-150, May 2001.
doi:10.1109/97.917699

28. Satish, A. and R. L. Kashyap, "Cramér-rao bounds and estimation of direction of arrival for narrowband signals," Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Process., ICASSP, 532-535, USA, 2003.

29. Stoica, P. and A. Nehoral, "Performance study of conditional and unconditional direction-of-arrival estimation," IEEE Trans. on Acoustics and Signal Process., Vol. 38, No. 10, 1783-1795, Dec. 1990.
doi:10.1109/29.60109