Vol. 38

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2012-01-26

Direction of Arrival Estimation for Nonuniform Planar Array Based on Piecewise Interpolation Method

By Wael Elshennawy, Ahmed Attiya, , Essam Hashish, and Islam A. Eshrah
Progress In Electromagnetics Research B, Vol. 38, 241-259, 2012
doi:10.2528/PIERB11121412

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
http://www.jpier.org/PIERB/pier.php?paper=11121412

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, Chapter 6, 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