Vol. 112
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2011-01-20
Two L-Shaped Array-Based 2-d DOAs Estimation in the Presence of Mutual Coupling
By
Progress In Electromagnetics Research, Vol. 112, 273-298, 2011
Abstract
Recent research on the array geometrical configuration shows that the two L-shaped array (TLSA) has a lower Cramer-Rao Low-Bound (CRLB) of two-dimensional (2-D) directions-of-arrival (DOAs) estimation than other array configurations. However, in this array configuration, there are some problems to note: i) three electric angles are independently obtained from three uniformly linear subarrays on three axes, so they must be matched before solving elevation and azimuth angles from them; ii) Similar to other array geometries, the effect of mutual coupling in the TLSA on the estimation performance cannot be ignored; and iii) the conventional elevation estimators may encounter estimation failure. In this paper, we develop a new TLSA-based 2-D DOAs estimation algorithm. The key points of this paper are: i) using some particularly selecting matrices, a trilinear model is constructed to compensate the effect of mutual coupling on three subarrays. In addition, the steering vector is restored using the trilinear alternating least square method; ii) 2-D DOAs are estimated from the properly chosen elements of the restored steering vector to avoid pairing parameters and the severe performance degradation resulted from the failure in pairing; and iii) a new elevation estimator is designed to avoid estimation failure. Simulation results are presented to validate the performance of the proposed method.
Citation
Junli Liang, and Ding 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
References

1. Pillai, S. U., Array Signal Processing, Springer-Verlag, 1989.
doi:10.1007/978-1-4612-3632-0

2. Krim, H. and M. Viberg, "Two decades of array signal processing research: The parameter approach," IEEE Signal Process. Mag., Vol. 13, No. 4, 67-94, Jul.1996.
doi:10.1109/79.526899

3. Kedia, Y. S. and B. Chandna, "A new algorithm for 2-D DOA algorithm," Signal Processing, Vol. 60, No. 3, 325-332, Mar.1997.
doi:10.1016/S0165-1684(97)00082-0

4. Zoltowski, M. D., M. Haardt and C. P. Mathews, "Closed-form 2-D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT," IEEE Trans. Signal Processing, Vol. 44, No. 2, 316-328, Feb.1996.
doi:10.1109/78.485927

5. Ramos, J., C. P. Mathews and M. D. Zoltowski, "FCA-ESPRIT:A closed-form 2-D angle estimation algorithm for filled circular arrays with arbitrary sampling lattices," Signal Processing, Vol. 47, No. 1, 213-217, Jan.1997.

6. Harabi, F., A. Gharsallah and S. Marcos, "Three-dimensional antennas array for the estimation of direction of arrival," IET Microwaves, Antennas and Propagation, Vol. 3, No. 5, 843-849, 2009.
doi:10.1049/iet-map.2008.0234

7. Hua, Y., T. K. Sarkar and D. D. Weiner, "An L-shape array for estimation 2-D directions of wave arrival," IEEE Trans. Antennas and Propagation, Vol. 39, No. 2, 143-146, Feb.1991.
doi:10.1109/8.68174

8. Tayem, N., H. M. Kwon, and , "L-shape 2-dimensional arrival angle estimation with propagator method," IEEE Trans. Antennas and Propagation, Vol. 53, No. 5, 1622-1630, May 2005.
doi:10.1109/TAP.2005.846804

9. Marcos, S., A. Marsal and M. Benidir, "The propagator method for source bearing estimation," Signal Processing, Vol. 42, No. 2, 121-138, 1995.
doi:10.1016/0165-1684(94)00122-G

10. Munier, J. and G. Y. Delisle, "Spatial analysis using new properties of the cross-spectral matrix," IEEE Trans. Signal Processing, Vol. 39, No. 3, 746-749, Jul.1991.
doi:10.1109/78.80863

11. Roy, R. and T. Kailath, "ESPRIT-estimation of signal parameters via rotational invariance techniques," IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. 37, No. 3, 746-749, Jul.1989.

12. Schmidt, R., "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas and Propagation., Vol. 34, No. 3, 276-280, Mar.1986.
doi:10.1109/TAP.1986.1143830

13. Kikuchi, S., H. Tsuji and A. Sano, "Pair-matching method for estimating 2-D angle of arrival with a cross-correlation matrix," IEEE Antennas and Wireless Propagation Letters, Vol. 5, 35-40, 2006.
doi:10.1109/LAWP.2005.863610

14. Del Rio, J. E. F. and M. F. Catedra-Perez, "The matrix pencil method for two-dimensional direction of arrival estimation employing an L-shape array ," IEEE Trans. Antennas and Propagation, Vol. 45, No. 11, 1693-1694, Nov.1997.
doi:10.1109/8.650082

15. Shu, T., X. Liu and J. Lu, "Comments on `L-shape 2-dimensional arrival angle estimation with propagator method'," IEEE Trans. Antennas and Propagation, Vol. 56, No. 5, 1502-1503, May 2008.
doi:10.1109/TAP.2008.922891

16. Liu, T. H. and J. M. Mendel, "Azimuth and elevation direction finding using arbitrary array geometries," IEEE Trans. Signal Processing, Vol. 46, No. 7, 2061-2065, Jul.1998.

17. Van der Veen, A. J., P. Ober and E. F. Deprettere, "Azimuth and elevation computation in high resolution DOA estimation," IEEE Trans. Signal Processing, Vol. 40, No. 4, 1828-1832, Feb.1992.
doi:10.1109/78.143456

18. Van der Veen, A. J. and E. F. Deprettere, "Parallel VLSI matrix pencil algorithm for high resolution direction finding," IEEE Trans. Signal Processing, Vol. 39, No. 2, 383-394, Feb.1991.
doi:10.1109/78.80822

19. Krim, H. and M. Viberg, "Two decades of array signal processing research: The parameter approach," IEEE Signal Process. Mag., Vol. 13, No. 4, 67-69, Jul.1996.
doi:10.1109/79.526899

20. Zoltowski, M. D. and K. T. Wong, "ESPRIT-based 2-D direction finding with a sparse uniform array of electromagnetic vector array," IEEE Trans. Signal Processing, Vol. 48, No. 8, 2195-2304, Aug.2000.
doi:10.1109/78.852000

21. Zoltowski, M. D. and K. T. Wong, "Closed-form eigenstructure-based direction finding using arbitrary but identical subarrays on a sparse uniform cartesian array grid ," IEEE Trans. Signal Processing, Vol. 48, No. 8, 2205-2210, Aug.2000.
doi:10.1109/78.852001

22. Hua, Y., "A pencil-MUSIC algorithm for finding two-dimensional angles and polarizations using crossed dipoles," IEEE Trans. Antennas and Propagation, Vol. 41, No. 3, 370-376, Mar.1993.
doi:10.1109/8.233122

23. Li, J. and R. T. Compton, "Angle and polarization estimation using ESPRIT with a polarization sensitive array," IEEE Trans. Antennas and Propagation, No. 40, 550-555, May 1992.
doi:10.1109/8.142630

24. Veen, A., P. Ober and E. Deprettere, "Azimuth and elevation computation in high resolution DOA estimation," IEEE Trans. Acoust. Speech, Signal Processing,, Vol. 40, No. 7, 1828-1832, 1992.

25. Liang, J. and D. Liu, "Joint elevation and azimuth direction finding using L-shaped array," IEEE Trans. Antennas and Propagation, Vol. 58, No. 6, 2136-2141, Jun.2010.
doi:10.1109/TAP.2010.2046838

26. Swindlehurst, A. and T. Kailath, "Azimuth/elevation direction finding using regular array geometries," IEEE Trans. Aerosp.Electron. Syst., Vol. 29, No. 1, 145-156, Jan.1993.
doi:10.1109/7.249120

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

28. Goossens, B. 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 and Propagation, Vol. 55, No. 3, 841-849, 2007.
doi:10.1109/TAP.2007.891848

29. Lin, M. and L. Yang, "Blind calibration and DOA estimation with uniform circular arrays in the presence of mutual coupling," IEEE Antennas and Wireless Propagation Letters, Vol. 5, No. 1, 315-318, 2006.
doi:10.1109/LAWP.2006.878898

30. Ye, Z. and C. Liu, "2-D DOA estimation in the presence of mutual coupling," IEEE Trans. Antennas and Propagation, No. 56, 3150-3158, 2008.
doi:10.1109/TAP.2008.929446

31. Liu, C., Z. Ye and Y. Zhang, "Autocalibration algorithm for mutual coupling of planar array," Signal Processing, Vol. 90, No. 3, 784-794, Mar.2010.
doi:10.1016/j.sigpro.2009.08.014

32. Friedlander, B. and A. J. Weiss, "Direction finding in the presence of mutual coupling," IEEE Trans. Antennas and Propagation, Vol. 39, No. 3, 273-284, Mar.1991.
doi:10.1109/8.76322

33. Ng, B. C. and C. M. S. See, "Sensor-array calibration using a maximum-likelihood approach," IEEE Trans. Antennas and Propagation, Vol. 44, No. 6, 827-835, Jun.1996.
doi:10.1109/8.509886

34. Ye, Z. and C. Liu., "On the resiliency of MUSIC direction finding against antenna sensor coupling," IEEE Trans. Antennas and Propagation, Vol. 56, No. 2, 371-380, 2008.
doi:10.1109/TAP.2007.915461

35. Liu, C., Z. Ye and Y. Zhang, "DOA estimation based on fourth-order cumulants with unknown mutual coupling," Signal Processing, Vol. 89, No. 9, 1839-1843, 2009.
doi:10.1016/j.sigpro.2009.03.035

36. Svantesson, T., "Modeling and estimation of mutual coupling in a uniform linear array of dipoles," Proc. Int. Conf. Acoustics, Speech, Signal Processing, Vol. 5, 2961-2964, Mar.1999.

37. Saventesson, T., "Mutual coupling compensation using subspace fitting," Proc. IEEE Sensor Array and Multichannel Signal Process, Workshop, 494-498, 2000.

38. Harshman, R. A., "Foundation of the PARAFAC procedure:Model and conditions for an `explanatory' multi-mode factor analysis ," UCLA Working Papers in Phonetics, Vol. 16, 1-84, 1970.

39. Smilde, A., R. Bro and P. Geladi, Multi-way Analysis with Applications in the Chemical Sciences,, John Wiley & Sons Ltd., 2004.
doi:10.1002/0470012110

40. Sidiropoulos, N. D., G. B. Giannakis and R. Bro, "Parallel factor analysis in sensor array processing," IEEE Trans. on Signal Processing, Vol. 48, No. 8, 2377-2388, 2000.
doi:10.1109/78.852018

41. Sidiropoulos , N. D., G. B. Giannakis and R. Bro, "Blind PARAFAC Receiver for DS-CDMA systems," IEEE Trans. Signal Processing, Vol. 48, No. 3, 810-823, 2000.
doi:10.1109/78.824675

42. Sidiropoulos, N. D., COMFAC: Matlab code for LS fit-ting of the complex PARAFAC model in 3-D, 1998, http://www.telecom.tuc.gr/~nikos.

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