Vol. 66
Latest Volume
All Volumes
PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2018-03-26
Fast DOA Estimation in the Spectral Domain and Its Applications
By
Progress In Electromagnetics Research M, Vol. 66, 73-85, 2018
Abstract
This paper presents a direction of arrival (DOA) estimation method. Spectral-domain interferometer equation is first established based on integral transforms of spatial interferometer equations. The direction finding problem in the spatial domain is thereby mapped to that in the spectral domain, relating angular parameters to spatial spectrums. This method is then applied to DOA estimation with circular arrays and spherical arrays. As a result, the elevation angle and azimuth angle are decoupled, giving closed-form and analytical formulae for DOA estimations by discrete phase samples on a sampling aperture. Algebraic relations between angular parameters and phase samples are established, and this method is hence computationally efficient. The Cramer-Rao lower bound (CRLB) of the proposed method is derived, and accuracy analysis demonstrates that the proposed method approaches the CRLB. In addition, mathematical insights into accuracy enhancement by large number of samples are observed via Parseval's theorem. Finally, numerical simulations and experimental measurements are provided to verify the effectiveness and appealing performance of the proposed method.
Citation
Le Zuo Jin Pan Boyuan Ma , "Fast DOA Estimation in the Spectral Domain and Its Applications," Progress In Electromagnetics Research M, Vol. 66, 73-85, 2018.
doi:10.2528/PIERM18011102
http://www.jpier.org/PIERM/pier.php?paper=18011102
References

1. Wu, Y. and H. C. So, "Simple and accurate two-dimensional angle estimation for a single source with uniform circular array," IEEE Antennas Wireless Propag. Lett., Vol. 7, 78-80, 2008.
doi:10.1109/LAWP.2008.920908

2. Wu, Y. W., S. Rhodes, and E. H. Satorius, "Direction of arrival estimation via extended phase interferometry," IEEE Trans. Aerosp. Electron. Syst., Vol. 31, No. 1, 375-381, 1995.
doi:10.1109/7.366333

3. Seidman, L. P., "Bearing estimation error with a linear array," IEEE Trans. Audio & Electroacoust., Vol. 19, No. 2, 147-157, 1971.
doi:10.1109/TAU.1971.1162169

4. Jackson, B. R., S. Rajan, and B. J. Liao, "Direction of arrival estimation using directive antennas in uniform circular arrays," IEEE Trans. Antennas Propag., Vol. 63, No. 2, 736-747, 2015.
doi:10.1109/TAP.2014.2384044

5. Pace, P. E., D. Wickersham, D. C. Jenn, and N. S. York, "High-resolution phase sampled interferometry using symmetrical number systems," IEEE Trans. Antennas Propag., Vol. 49, No. 10, 1411-1423, 2001.
doi:10.1109/8.954930

6. Lee, J. H. and J. M. Woo, "Interferometer direction-finding system with improved DF accuracy using two different array configurations," IEEE Antennas Wireless Propag. Lett., Vol. 14, 719-722, 2015.
doi:10.1109/LAWP.2014.2377291

7. Liu, Z. M., Z. T. Huang, and Y. Y. Zhou, "Computationally efficient direction finding using uniform linear arrays," IET Radar, Sonar, Navigation, Vol. 6, No. 1, 39-48, 2012.
doi:10.1049/iet-rsn.2010.0254

8. Liang, J. and D. Liu, "Two L-shaped array-based 2-D DOAs estimation in the presence of mutual coupling," Progress In Electromagnetics Research, Vol. 112, 273-298, 2011.
doi:10.2528/PIER10071701

9. Liao, B., Y. T. Wu, and S. C. Chan, "A generalized algorithm for fast two-dimensional angle estimation of a single source with uniform circular arrays," IEEE Antennas Wireless Propag. Lett., Vol. 11, No. 2, 984-986, 2012.
doi:10.1109/LAWP.2012.2213792

10. Ioannides, P. and C. A. Balanis, "Uniform circular arrays for smart antennas," IEEE Antennas Propag. Magazine, Vol. 47, No. 4, 192-206, 2005.
doi:10.1109/MAP.2005.1589932

11. Mathews, C. P. and M. D. Zoltowski, "Eigenstructure techniques for 2-D angle estimation with uniform circular array," IEEE Trans. Signal Process., Vol. 42, No. 9, 2395-2407, 1994.
doi:10.1109/78.317861

12. Yang, P., F. Yang, and Z.-P. Nie, "DOA estimation with sub-array divided technique and interporlated ESPRIT algorithm on a cylindrical conformal array antenna," Progress In Electromagnetics Research, Vol. 103, 201-216, 2010.
doi:10.2528/PIER10011904

13. Si, W., L. Wan, L. Liu, and Z. Tian, "Fast estimation of frequency and 2-D DOAs for cylindrical conformal array antenna using state-space and propagator method," Progress In Electromagnetics Research, Vol. 137, 51-71, 2013.
doi:10.2528/PIER12121114

14. Belloni, F. and V. Koivunen, "Beamspace transform for UCA: Error analysis and bias reduction," IEEE Trans. Signal Process., Vol. 54, No. 8, 3078-3089, 2006.
doi:10.1109/TSP.2006.877664

15. Huang, Q., L. Zhang, and Y. Fang, "Two-stage decoupled DOA estimation based on real spherical harmonics for spherical arrays," IEEE/ACM Trans. Audio Speech Lang. Process., Vol. 25, No. 11, 2045-2058, 2017.
doi:10.1109/TASLP.2017.2737235

16. Teutsch, H., Modal Array Signal Processing: Principles and Applications of Acoustic Wavefield Decomposition (Lecture Notes in Control and Information Sciences), Springer, Berlin, Germany, 2007.

17. De Witte, E., H. Griffith, and P. Brennan, "Phase mode processing for spherical arrays," Electron. Lett., Vol. 39, No. 20, 1430-1431, 2003.
doi:10.1049/el:20030922

18. Meyer, J. and G. Elko, "A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield," Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Vol. 2, 1781-1784, May 2002.

19. Rafaely, B., "Analysis and design of spherical microphone arrays," IEEE Trans. Speech Audio Process., Vol. 13, 135-143, 2005.
doi:10.1109/TSA.2004.839244

20. Rafaely, B., "The spherical-shell microphone array," IEEE Trans. Audio, Speech, Lang. Process., Vol. 16, No. 4, 740-747, 2008.
doi:10.1109/TASL.2008.920059

21. Rafaely, B., Fundamentals of Spherical Array Processing, (Springer Topics in Signal Processing), Springer-Verlag, Berlin, Germany, 2015.
doi:10.1007/978-3-662-45664-4

22. Rafaely, B., "Plane-wave decomposition of the pressure on a sphere by spherical convolution," J. Acoust. Soc. Amer., Vol. 116, 2149-2157, 2004.
doi:10.1121/1.1792643

23. Moore, A., C. Evers, and P. Naylor, "Direction of arrival estimation in the spherical harmonic domain using subspace pseudo-intensity vectors," IEEE/ACM Trans. Audio Speech Lang. Process., Vol. 25, No. 1, 178-192, 2017.
doi:10.1109/TASLP.2016.2613280

24. Costa, M., A. Richter, and V. Koivunen, "Unified array manifold decomposition based on spherical harmonics and 2-D Fourier basis," IEEE Trans. Signal Process., Vol. 58, No. 9, 4634-4645, 2010.
doi:10.1109/TSP.2010.2050315

25. Goossens, R. and H. Rogier, "Unitary spherical ESPRIT: 2-D angle estimation with spherical arrays for scalar fields," IET Signal Process., Vol. 3, No. 3, 221-231, 2008.
doi:10.1049/iet-spr.2008.0101

26. Goossens, R. and H. Rogier, "A hybrid UCA-RARE/Root-MUSIC approach for 2-D direction of arrival estimation in uniform circular arrays in the presence of mutual coupling," IEEE Trans. Antennas Propag., Vol. 55, No. 3, 841-849, 2007.
doi:10.1109/TAP.2007.891848

27. Wang, B. H., H. T. Hui, and M. S. Leong, "Decoupled 2D direction of arrival estimation using compact uniform circular arrays in the presence of elevation-dependent mutual coupling," IEEE Trans. Antennas Propag., Vol. 58, No. 3, 747-755, 2010.
doi:10.1109/TAP.2009.2039323

28. Harrington, R. F., Time-harmonic Electromagnetic Fields, McGraw-Hill, 2001.
doi:10.1109/9780470546710

29. Driscoll, J. R., D. M. Healy, and Jr., "Computing Fourier transforms and convolutions on the 2-sphere," Adv. Appl. Math., Vol. 15, No. 2, 202-250, 1994.
doi:10.1006/aama.1994.1008

30. Williams, E. G., Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography, 1st Ed., Academic, London, U.K., 1999.

31. Kay, S. M., "A fast and accurate single frequency estimator," IEEE Trans. Acoustics, Speech, Signal Process., Vol. 37, No. 12, 1987-1990, 1989.
doi:10.1109/29.45547

32. Tretter, S. A., "Estimating the frequency of a noisy sinusoid by linear regression," IEEE Trans. Inf. Theory, Vol. 31, No. 6, 832-835, 1985.
doi:10.1109/TIT.1985.1057115

33. Rife, D. and R. Boorstyn, "Single tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory, Vol. 20, No. 5, 591-598, 1974.
doi:10.1109/TIT.1974.1055282

34. Mcaulay, R., "Interferometer design for elevation angle estimation," IEEE Trans. Aerosp. Electron. Syst., Vol. 13, No. 5, 486-503, 1977.
doi:10.1109/TAES.1977.308414

35. Kay, Kay, S. M., Fundamentals of Statistical Signal Processing: Estimation Theory, PTR Prentice Hall, 1993.

36. Robert, J. M., II, Handbook of Fourier Analysis and Its Applications, Oxford University Press, 2009.