Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays - part III: detection-estimation nonidentifiability

For pt.II see ibid., vol.51, no.6, p.1492-507 (2003). We investigate nonidentifiability conditions for the detection-estimation problem with multiple uncorrelated plane waves incident upon a nonuniform (sparse) linear antenna array. Specifically, we define conditions under which a given Hermitian covariance matrix has a nonunique (multiple) decomposition into an admissible number of dyads weighted by the source powers and a white-noise identity matrix. Our method is based on the Proukakis-Manikas technique of generating ambiguity generator sets (AGSs) and allows ambiguous sets of sources associated with a given sparse antenna geometry to be determined.

[1]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[2]  James H. McClellan,et al.  Array design for MEM and MLM array processing , 1981, ICASSP.

[3]  Vladimir Gaitsgory,et al.  Stability of manifold ambiguity resolution in DOA estimation with nonuniform linear antenna arrays , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[4]  Alexei Gorokhov,et al.  Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. II. Partially augmentable arrays , 1998, IEEE Transactions on Signal Processing.

[5]  A. Moffet.  Minimum-redundancy linear arrays , 1968 .

[6]  R. Bracewell,et al.  The Stanford five-element radio telescope , 1973 .

[7]  Petre Stoica,et al.  Performance study of conditional and unconditional direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[8]  James P. Reilly,et al.  Some aspects of array signal processing , 1992 .

[9]  Douglas B. Williams,et al.  On resolving 2M-1 narrow-band signals with an M sensor uniform linear array , 1992, IEEE Trans. Signal Process..

[10]  Alexei Gorokhov,et al.  Resolving manifold ambiguities in direction-of-arrival estimation for nonuniform linear antenna arrays , 1999, IEEE Trans. Signal Process..

[11]  Athanassios Manikas,et al.  Investigative study of planar array ambiguities based on "hyperhelical" parameterization , 1999, IEEE Trans. Signal Process..

[12]  Ilan Ziskind,et al.  On unique localization of multiple sources by passive sensor arrays , 1989, IEEE Trans. Acoust. Speech Signal Process..

[13]  Douglas A. Gray,et al.  Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. II. Partially augmentable arrays , 1998, IEEE Trans. Signal Process..

[14]  Athanassios Manikas,et al.  Study of ambiguities of linear arrays , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[15]  Y. Bar-Ness,et al.  A new approach to array geometry for improved spatial spectrum estimation , 1985, Proceedings of the IEEE.

[16]  Athanassios Manikas,et al.  Modeling and estimation of ambiguities in linear arrays , 1998, IEEE Trans. Signal Process..

[17]  Alexei Gorokhov,et al.  Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays .I. Fully augmentable arrays , 2001, IEEE Trans. Signal Process..

[18]  Alexei Gorokhov,et al.  DOA estimation for noninteger linear antenna arrays with more uncorrelated sources than sensors , 2000, IEEE Trans. Signal Process..

[19]  Alexei Gorokhov,et al.  Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays. II. Partially augmentable arrays , 2001, IEEE Trans. Signal Process..

[20]  Mati Wax.  On unique localization of constrained-signals sources , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[21]  Tariq S. Durrani,et al.  Temporal and spatial sampling influence on the estimates of superimposed narrowband signals: when less can mean more , 1996, IEEE Trans. Signal Process..