1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 46 Number 11, November 1998

Table of Contents for this issue

Complete paper in PDF format

Linear Dependence of Steering Vectors Associated with Tripole Arrays

Kwok-Chiang Ho, Kah-Chye Tan, Senior Member, IEEE, and B. T. G. Tan

Page 1705.

Abstract:

We are concerned with the linear independence of steering vectors associated with tripoles, each of which provides measurements of the three components of electric field induced by electromagnetic signals. We first establish that for a single tripole, any steering vector is linearly dependent on at least one other steering vector corresponding to a different direction-of-arrival (DOA) for a general problem where signals may arrive from anywhere in a three-dimensional (3-D) space, but every two steering vectors with distinct DOA's are linearly independent if the signals are nonlinearly polarized and arrive from a strictly hemispherical space. We then obtain a series of upper bounds for the number of linearly independent steering vectors associated with a tripole array with general sensor configurations. We also show that for applications where signals are known to be linearly polarized in the same direction, the ability to estimate DOA's using a tripole array is identical to that using a scalar-sensor array if both of them have identical sensor configurations.

References

  1. A. Nehorai and E. Paldi, "Vector sensor array processing for electromagnetic source localization," IEEE Trans. Signal Processing, vol. 42, pp. 376-398, Feb. 1994.
  2. K.-C. Tan, K.-C. Ho, and A. Nehorai, "Linear independence of steering vectors of an electromagnetic vector sensor," IEEE Trans. Signal Processing, vol. 44, pp. 3099-3107, Dec. 1996.
  3. K.-C. Ho, K.-C. Tan, and W. Ser, "A study of the resolvability of vector-sensor array in direction-of-arrival estimation," in Proc. Int. Conf. Commun. Syst.'94, Singapore, Nov. 1994, vol. 1, pp. 35-39.
  4. B. Hochwald and A. Nehorai, "Identifiability in array processing models with vector-sensor applications," IEEE Trans. Signal Processing, vol. 44, pp. 83-95, Jan. 1996.
  5. K.-C. Ho, K.-C. Tan, and W. Ser, "An investigation on number of signals whose directions-of-arrival are uniquely determinable with an electromagnetic vector sensor," Signal Processing, vol. 47, no. 1, pp. 41-54, 1995.
  6. J. Li, "Direction and polarization estimation using arrays with small loops and short dipoles," IEEE Trans. Antenna Propagation, vol. 41, pp. 379-387, Feb. 1993.
  7. K. T. Wong and M. D. Zoltowski, "High accuracy 2-D angle estimation with extended aperture vector sensor arrays," in Proc. Int. Conf. Acoust., Speech, Signal Processing, Atlanta, GA, May 1996, vol. 5, pp. 2789-2792.
  8. K.-C. Ho, K.-C. Tan, and B. T. G. Tan, "Estimation of directions-of-arrival of partially polarized signals with electromagnetic vector sensors," in Proc. Int. Conf. Acoust., Speech, Signal Processing, Atlanta, GA, May 1996, vol. 5, pp. 2900-2903.
  9. M. Wax and I. Ziskind, "On unique localization of multiple sources by passive sensor arrays," IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 996-1000, July 1989.
  10. A. Nehorai, D. Starer, and P. Stoica, "Direction-of-arrival estimation in applications with multipath and few snapshots," Circuits Syst. Signal Processing, vol. 10, no. 3, pp. 327-342, 1991.
  11. R. T. Compton Jr., "The tripole antenna: An adaptive array with full polarization flexibility," IEEE Trans. Antennas Propagat,, vol. AP-29, pp. 944-952, June 1981.
  12. K.-C. Ho, K.-C. Tan, and B. T. G. Tan, "A study of the resolvability of tripole arrays," in Proc. Int. Conf. Commun. Syst., Singapore, Nov. 1996, vol. 1, pp. 302-306.
  13. R. O. Schmidt, "A signal subspace approach to multiple emitter location and spectral estimation," Ph.D. dissertation, Dept. Elect. Eng., Stanford Univ., Stanford, CA, 1981.
  14. K.-C. Tan, G.-L. Oh, and M. H. Er, "A study of the uniqueness of steering vectors in array processing," Signal Processing, vol. 34, no. 3, pp. 245-256, 1993.
  15. K.-C. Tan and Z. Goh, "A detailed derivation of arrays free of higher rank ambiguities," IEEE Trans. Signal Processing, vol. 44, no. 2, pp. 351-359, Feb. 1996.
  16. K.-C. Tan, S.-S. Goh, and E.-C. Tan, "A study of the rank ambiguity issues in direction-of-arrival estimation," IEEE Trans. Signal Processing, vol. 44, no. 4, pp. 880-887, Apr. 1996.
  17. K.-C. Tan, E.-C. Tan, and S.-S. Goh, "Counter-examples to a conjecture for characterizing higher rank ambiguities," IEEE Trans. Signal Processing, vol. 44, no. 4, pp. 1028-1029, Apr. 1996.