volume | PIER Journals

Abstract

Super-resolution algorithms used in radar imaging, e.g., MUltiple SIgnal Classification (MUSIC), can help us to get much higher resolution image beyond what is limited by the signal's bandwidth. We focus on MUSIC imaging algorithm in the paper and investigate the uniqueness and effectiveness conditions of the MUSIC algorithm when used in 1-D radar range imaging. Unlike conventional radar resolution analysis, we introduced the concept of resolution threshold from Direction of Arrival (DOA) into the MUSIC radar range imaging, we derive an approximate expression of theoretical resolution threshold for 1-D MUSIC imaging algorithm through the approach of asymptotic and statistical analysis to the null spectrum based on the perturbation theory of algebra and matrix theories. Monte Carlo simulations are presented to verify the work.

1. August, W. R., Principles of High-Resolution Radar, Artech House Publishers, Boston, USA, 1996.

2. Son, J. S., G. Thomas, and B. C. Flores, Range-Doppler Radar Imaging and Motion Compensation, Artech House Publishers, London, UK, 2001.

3. Hamish, D. M., Modern Radar Systems, 2nd edition, Artech House Publishers, Boston, USA, 2008.

4. Odendaal, J. W., E. Barnard, and C. W. I. Pistorius, "Two-dimensional super-resolution radar imaging using the MUSIC algorithm," IEEE Trans. Antennas Propagat., Vol. 42, No. 10, 1386-1391, 1994.
doi:10.1109/8.320744

5. Kim, K., D. Seo, and H. Kim, "Efficient radar target recognition using the MUSIC algorithm and invariant features," IEEE Trans. Antennas Propagat., Vol. 50, No. 3, 325-337, 2002.
doi:10.1109/8.999623

6. Yoon, Y. and M. G. Amin, "High-resolution through-the-wall radar imaging using beamspace MUSIC," IEEE Trans. Antennas Propagat., Vol. 56, No. 6, 1763-1774, 2008.
doi:10.1109/TAP.2008.923336

7. Roy, R., A. Paulraj, and T. Kailath, "ESPRIT - A subspace rotation approach to estimation of parameters of cisoids in noise," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 34, No. 5, 1340-1342, 1986.
doi:10.1109/TASSP.1986.1164935

8. Roy, R. and T. Kailath, "ESPRIT - Estimation of signal parameters via rotational invariance techniques," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 37, No. 7, 984-995, 1989.
doi:10.1109/29.32276

9. Rouquette, S. and M. Najim, "Estimation of frequencies and damping factors by two-dimensional ESPRIT type methods," IEEE Trans. Signal Processing, Vol. 49, No. 1, 237-245, 2001.
doi:10.1109/78.890367

10. Schmidt, R., "Multiple emitter location and signal parameter estimation," Proc. RADC Spectral Estimation Workshop, Rome Air Development Center, New York, October 1979.

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

12. Lee, H. B. and M. S. Wengrovitz, "Resolution threshold of beamspace MUSIC for two closely spaced emitters," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 38, No. 9, 1545-1559, 1990.
doi:10.1109/29.60074

13. Yamada, H., M. Ohmiya, Y. Ogawa, and K. Itoh, "Super-resolution techniques for time-domain measurements with a network analyzer," IEEE Trans. Antennas Propagat., Vol. 39, No. 2, 177-183, 1991.
doi:10.1109/8.68179

14. Li, F., H. Liu, and R. J. Vaccaro, "Performance analysis for DOA estimation algorithms: Unification, simplification, and observations," IEEE Trans. Aerosp. Electron. Syst., Vol. 29, No. 4, 1170-1184, 1993.
doi:10.1109/7.259520

15. Cheng, C. and Y. Hua, "Performance analysis of the MUSIC and pencil-MUSIC algorithms for diversely polarized array," IEEE Trans. Signal Processing, Vol. 42, No. 11, 3150-3165, 1994.
doi:10.1109/78.330374

16. Thompson, J. S., P. M. Grant, and B. Mulgrew, "Performance of spatial smoothing algorithms for correlated sources," IEEE Trans. Signal Processing, Vol. 44, No. 4, 1040-1046, 1996.
doi:10.1109/78.492567

17. Astely, D. and B. Ottersten, "The effects of local scattering on direction of arrival estimation with MUSIC," IEEE Trans. Signal Processing, Vol. 47, No. 12, 3220-3234, 1999.
doi:10.1109/78.806068

18. McCloud, M. L. and L. L. Scharf, "A new subspace identification algorithm for high-resolution DOA estimation," IEEE Trans. Antennas Propagat., Vol. 50, No. 10, 1382-1390, 2002.
doi:10.1109/TAP.2002.805244

19. Charge, P., Y. Wang, and J. Saillard, "An extended cyclic MUSIC algorithm," IEEE Trans. Signal Processing, Vol. 51, No. 7, 1695-1701, 2003.
doi:10.1109/TSP.2003.812834

20. Kim, J.-T., S.-H. Moon, D. Han, and M.-J. Cho, "Fast DOA estimation algorithm using pseudocovariance matrix," IEEE Trans. Antennas Propagat., Vol. 53, No. 4, 1346-1351, 2005.
doi:10.1109/TAP.2005.844459

21. Abeida, H. and J.-P. Delmas, "MUSIC-like estimation of direction of arrival for noncircular sources," IEEE Trans. Signal Processing, Vol. 54, No. 7, 2678-2690, 2006.
doi:10.1109/TSP.2006.873505

22. Ye, Z. and C. Liu, "2-D DOA estimation in the presence of mutual coupling," IEEE Trans. Antennas Propagat., Vol. 56, No. 10, 3150-3158, 2008.
doi:10.1109/TAP.2008.929446

23. Zhang, Y. and B. P. Ng, "MUSIC-like DOA estimation without estimating the number of sources," IEEE Trans. Signal Processing, Vol. 58, No. 3, 1668-1676, 2010.
doi:10.1109/TSP.2009.2037074

24. Barabell, A., "Improving the resolution performance of eigenstructure-based direction-finding algorithms," IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP'83 , 336-339, 1983.
doi:10.1109/ICASSP.1983.1172124

25. Rao, B. D. and K. V. S. Hari, "Performance analysis of Root-Music," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 37, No. 12, 1939-1949, 1989.
doi:10.1109/29.45540

26. Krim, H., P. Forster, and J. G. Proakis, "Operator approach to performance analysis of root-MUSIC and root-min-norm," IEEE Trans. Signal Processing, Vol. 40, No. 7, 1687-1696, 1992.
doi:10.1109/78.143441

27. Shan, T., M. Wax, and T. Kailath, "On spatial smoothing for direction-of-arrival estimation of coherent signals," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 33, No. 4, 806-811, 1985.
doi:10.1109/TASSP.1985.1164649

28. Haber, F. and M. Zoltowski, "Spatial spectrum estimation in a coherent signal environment using an array in motion," IEEE Trans. Antennas Propagat., Vol. 34, No. 4, 301-310, 1986.
doi:10.1109/TAP.1986.1143831

29. Rao, B. D. and K. V. S. Hari, "Weighted subspace methods and spatial smoothing: Analysis and comparison," IEEE Trans. Signal Processing, Vol. 41, No. 2, 788-803, 1993.
doi:10.1109/78.193218

30. Wang, H. and K. J. R. Liu, "2-D spatial smoothing for multipath coherent signal separation," IEEE Trans. Aerosp. Electron. Syst., Vol. 34, No. 2, 391-405, 1998.
doi:10.1109/7.670322

31. Li, F. and R. J. Vaccaro, "Sensitivity analysis of DOA estimation algorithms to sensor errors," IEEE Trans. Aerosp. Electron. Syst., Vol. 28, No. 3, 708-717, 1992.
doi:10.1109/7.256292

32. Ferreol, A., P. Larzabal, and M. Viberg, "On the resolution probability of MUSIC in presence of modeling errors," IEEE Trans. Signal Processing, Vol. 56, No. 5, 1945-1953, 2008.
doi:10.1109/TSP.2007.911482

33. Kaveh, M. and A. Barabell, "The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 34, No. 2, 331-341, 1986.
doi:10.1109/TASSP.1986.1164815

34. Kaveh, M. and A. Barabell, "The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 34, No. 3, 633-633, 1986.
doi:10.1109/TASSP.1986.1164841

35. Choi, J. and I. Song, "Asymptotic distribution of the MUSIC null spectrum," IEEE Trans. Signal Processing, Vol. 41, No. 2, 985-988, 1993.
doi:10.1109/78.193240

36. Messer, H. and Y. Rockah, "On the eigenstructure of the signal-only tempo-spatial covariance matrix of broad-band sources using a circular array," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 38, No. 3, 557-559, 1990.
doi:10.1109/29.106876

37. Friedlander, B. and A. J. Weiss, "Direction finding using spatial smoothing with interpolated arrays," IEEE Trans. Aerosp. Electron. Syst., Vol. 28, No. 2, 574-587, 1992.
doi:10.1109/7.144583

38. Gardner, W. A., "Simplification of MUSIC and ESPRIT by exploitation of cyclostationarity," Proceedings of the IEEE, Vol. 76, No. 7, 845-847, 1988.
doi:10.1109/5.7152

39. Stoica, P. and A. Nehorai, "Performance comparison of subspace rotation and MUSIC methods for direction estimation," IEEE Trans. Signal Processing, Vol. 39, No. 2, 446-453, 1991.
doi:10.1109/78.80828

40. Yu, X. and K. M. Buckley, "Bias and variance of direction-of-arrival estimates from MUSIC, MIN-NORM, and FINE," IEEE Trans. Signal Processing, Vol. 42, No. 7, 1812-1816, 1994.
doi:10.1109/78.298288

41. Yeh, C.-C., J.-H. Lee, and Y.-M. Chen, "Estimating two-dimensional angles of arrival in coherent source environment," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 37, No. 1, 153-155, 1989.
doi:10.1109/29.17520

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

43. Wang, Y.-Y., L.-C. Lee, S.-J. Yang, and J.-T. Chen, "A tree structure one-dimensional based algorithm for estimating the two-dimensional direction of arrivals and its performance analysis," IEEE Trans. Antennas Propagat., Vol. 56, No. 1, 178-188, 2008.
doi:10.1109/TAP.2007.912945

44. Wang, H. and K. J. R. Liu, "2-D spatial smoothing for multipath coherent signal separation," IEEE Trans. Aerosp. Electron. Syst., Vol. 34, No. 2, 391-405, 1998.
doi:10.1109/7.670322

45. Lei, Z. and T. J. Lim, "Estimation of directions of arrival of multipath signals in CDMA systems," IEEE Trans. Commun., Vol. 48, No. 6, 1022-1028, 2000.
doi:10.1109/26.848564

46. Chiang, C.-T. and A.-C. Chang, "DOA estimation in the asynchronous DS-CDMA system," IEEE Trans. Antennas Propagat. , Vol. 51, No. 1, 40-47, 2003.
doi:10.1109/TAP.2003.808547

47. Li, J., Z.-S. Liu, and P. Stoica, "3-D target feature extraction via interferometric SAR," Radar, Sonar & Navigation, IET, Vol. 144, No. 2, 71-80, 1997.
doi:10.1049/ip-rsn:19970970

48. Kim, K.-T., S.-W. Kim, and H.-T. Kim, "Two-dimensional ISAR imaging using full polarisation and super-resolution processing techniques," Radar, Sonar & Navigation, IET, Vol. 145, No. 4, 240-246, 1998.
doi:10.1049/ip-rsn:19982033

49. Kim, K.-T., D.-K. Seo, and H.-T. Kim, "Radar target identification using one-dimensional scattering centres," Radar, Sonar & Navigation, IET, Vol. 148, No. 5, 285-296, 2001.
doi:10.1049/ip-rsn:20010473

50. Miwa, T. and I. Arai, "Super-resolution imaging for point reflectors near transmitting and receiving array," IEEE Trans. Antennas Propagat., Vol. 52, No. 1, 220-229, 2004.
doi:10.1109/TAP.2003.820975

51. Quinquis, A., E. Radoi, and F. C. Totir, "Some radar imagery results using Super-resolution techniques," IEEE Trans. Antennas Propagat., Vol. 52, No. 5, 1230-1244, 2004.
doi:10.1109/TAP.2004.827541

52. Gini, F., F. Lombardini, and M. Montanari, "Layover solution in multibaseline SAR interferometry," IEEE Trans. Aerosp. Electron. Syst., Vol. 38, No. 4, 1344-1356, 2002.
doi:10.1109/TAES.2002.1145755

53. Urazghildiiev, I., R. Ragnarsson, and A. Rydberg, "High-resolution estimation of ranges using multiple-frequency CW radar," IEEE Trans. Intell. Transport. Syst., Vol. 8, No. 2, 332-339, 2007.
doi:10.1109/TITS.2007.895287

54. Secmen, M. and G. Turhan-Sayan, "Radar target classification method with reduced aspect dependency and improved noise performance using multiple signal classification algorithm," Radar, Sonar & Navigation, IET, Vol. 3, No. 6, 583-595, 2009.
doi:10.1049/iet-rsn.2008.0112

55. Li, L., W. Zhang, and F. Li, "A novel autofocusing approach for real-time through-wall imaging under unknown wall characteristics," IEEE Trans. Geosci. Remote Sensing, Vol. 48, No. 1, 423-431, 2010.
doi:10.1109/TGRS.2009.2024686

56. Zhang, W., A. Hoorfar, and L. Li, "Through-the-wall target localization with time reversal music method," Progress In Electromagnetics Research, Vol. 106, 75-89, 2010.
doi:10.2528/PIER10052408

57. Lazarov, A. D., "Iterative MMSE method and recurrent Kalman procedure for ISAR imaging reconstruction," IEEE Trans. Aerosp. Electron., Vol. 37, 1432-1441, 2001.
doi:10.1109/7.976978

58. Li, L., W. Zhang, and F. Li, "Tomographic reconstruction using the distorted rytov iterative method with phaseless data," IEEE Geoscience and Remote Sensing Letters, Vol. 5, 479-483, 2008.
doi:10.1109/LGRS.2007.907306

59. Zhang, W., A. Hoorfar, and C. Thajudeen, "Polarimetric through-the-wall imaging," 2010 URSI International Symposium on Electromagnetic Theory (EMTS), 471-474, Berlin, Germany, 2010.

60. Zhang, W., L. Li, and F. Li, "Multifrequency imaging from intensity-only data using the phaseless data distorted Rytov iterative method," IEEE Trans. Antennas Propagat., Vol. 53, 290-294, 2009.
doi:10.1109/TAP.2008.2009785

61. Hudson, J. E., Adaptive Array Principle, Peter Peregrinus Ltd., London, UK, 1981.

62. Wilkinson, J. H., The Algebraic Eigenvalue Problem, Oxford University Press, Inc., New York, USA, 1965.

Dr. Xiang Gu

Prof. Yunhua Zhang