Advertisement

Multidimensional Systems and Signal Processing

, Volume 24, Issue 3, pp 583–598 | Cite as

Multi-dimensional Capon spectral estimation using discrete Zhang neural networks

  • Abderrazak BenchabaneEmail author
  • Abdelhak Bennia
  • Fella Charif
  • Abdelmalik Taleb-Ahmed
Communication Brief

Abstract

The minimum variance spectral estimator, also known as the Capon spectral estimator, is a high resolution spectral estimator used extensively in practice. In this paper, we derive a novel implementation of a very computationally demanding matched filter-bank based a spectral estimator, namely the multi-dimensional Capon spectral estimator. To avoid the direct computation of the inverse covariance matrix used to estimate the Capon spectrum which can be computationally very expensive, particularly when the dimension of the matrix is large, we propose to use the discrete Zhang neural network for the online covariance matrix inversion. The computational complexity of the proposed algorithm for one-dimensional (1-D), as well as for two-dimensional (2-D) and three-dimensional (3-D) data sequences is lower when a parallel implementation is used.

Keywords

Multi-dimensional spectral estimation Covariance matrix Capon estimator Discrete Zhang neural network 3-D imaging 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benesty, J., Chen, J., & Huang, Y., (2007). Recursive and fast recursive Capon spectral estimators. EURASIP Journal on Advances in Signal Processing. doi: 10.1155/2007/45194.
  2. Capon J. (1969) High resolution frequency wave number spectrum analysis. Proceedings of the IEEE 57(8): 1408–1418CrossRefGoogle Scholar
  3. Eberhardt S. P., Tawel R., Brown T. X., Daud T., Thakoor A. P. (1992) Analog VLSI neural networks: Implementation issues and examples in optimization and supervised learning. IEEE Transactions on Industrial Electronics 39(6): 552–564CrossRefGoogle Scholar
  4. Glentis G. O. (2008) A fast algorithm for APES and Capon spectral estimation. IEEE Transactions on Signal Processing 56(9): 4207–4220MathSciNetCrossRefGoogle Scholar
  5. Glentis G. O. (2010) Efficient algorithms for adaptive Capon and APES spectral estimation. IEEE Transactions on Signal Processing 58(1): 84–96MathSciNetCrossRefGoogle Scholar
  6. Gohberg I., Olshevsky V. (1994) Complexity of multiplication with vectors for structured matrices. Linear Algebra and its Applications 202: 163–192MathSciNetzbMATHCrossRefGoogle Scholar
  7. Kay S., Pakula L. (2010) Convergence of the multidimensional minimum variance spectral estimator for continuous and mixed spectra. IEEE Signal Processing Letters 17(1): 1–4CrossRefGoogle Scholar
  8. Kailath T., Sayed A. H. (1995) Displacement structure: Theory and applications. SIAM Review 37(3): 297–386MathSciNetzbMATHCrossRefGoogle Scholar
  9. Kailath, T., Sayed, A. H. (eds) (1999) Fast reliable algorithms for matrices with structure. SIAM Publications, Philadelphia, PAzbMATHGoogle Scholar
  10. Kailath T., Kung S. Y., Morf M. (1979) Displacement ranks of matrices and linear equations. Journal of Mathematical Analysis and Applications 68(2): 395–407MathSciNetzbMATHCrossRefGoogle Scholar
  11. Larsson E., Stoica P. (2002) Fast implementation of two-dimensional APES and Capon spectral estimators. Multidimensional Systems and Signal Processing 13(1): 35–54zbMATHCrossRefGoogle Scholar
  12. Li H., Li J., Stoica P. (1998) Performance analysis of forward-backward matched-filterbank spectral estimators. IEEE Transactions on Signal Processing 46(7): 1954–1966CrossRefGoogle Scholar
  13. Liu Z. S., Li H., Li J. (1998) Efficient implementation of Capon and APES for spectral estimation. IEEE Transactions on Aerospace and Electronic Systems 34(4): 1314–1319CrossRefGoogle Scholar
  14. Lombardini, F., Cai, F., & Pardini, M. (2009). Parametric differential SAR tomography of decorrelating volume scatterers. In Proceedings of the 6th European Radar conference. doi: 270-273.978-2-87487-014-9.
  15. Lombardini, F., Pardini, M., & Verrazzani, L. (2008). A robust multibaseline sector interpolator for 3D SAR imaging. In Proceedings of the EUSAR 2008, Friedrichshafen, Germany.Google Scholar
  16. Marple, S. L., Jr. Adeli, M., & Liu, H. (2010). Super-fast algorithm for minimum variance (Capon) spectral estimation. In Conference on signals, systems and computers (ASILOMAR). doi: 10.1109/ACSSC.2010.5757893.
  17. McClellan J. H. (1982) Multidimensional spectral estimation. Proceeding of the IEEE 70(9): 1029–1039CrossRefGoogle Scholar
  18. Musicus B. R. (1985) Fast MLM power spectrum estimation from uniformly spaced correlations. IEEE Transactions on Acoustics, Speech and Signal Processing 33(4): 1333–1335CrossRefGoogle Scholar
  19. Pan V. Y., Barel M. V., Wang X., Codevico G. (2004) Iterative inversion of structured matrices. Theoretical Computer Science 315(2-3): 581–592MathSciNetzbMATHCrossRefGoogle Scholar
  20. Pan V. Y. (2001) Structured matrices and polynomials: Unified superfast algorithms. Birkhäser/Springer, Boston/New YorkzbMATHCrossRefGoogle Scholar
  21. Pan, V. Y., Rami, Y., & Wang, X. (2002). Structured matrices and Newton’s iteration: unified approach. In Linear algebra and its applications, (343–344), 233–265Google Scholar
  22. Raj P C. P., Pinjare S. L. (2009) Design and analog VLSI implementation of neural network architecture for signal processing. European Journal of Scientific Research 27(2): 199–216Google Scholar
  23. Rahman S. A., Ansari M. S. (2011) A neural circuit with transcendental energy function for solving system of linear equations. Analog Integrated Circuit and Signal Processing 66(3): 433–440. doi: 10.1007/s10470-010-9524-2 CrossRefGoogle Scholar
  24. Xiao L., Zhang Y. (2011) Zhang neural network versus Gradient neural network for solving time-varying linear inequalities. IEEE Transactions on Neural Networks 22(10): 1676–1684MathSciNetCrossRefGoogle Scholar
  25. Zhang, Y., Cai, B., Liang, M. & Ma, W. (2008). On the variable step-size of discrete-time Zhang neural network and Newton iteration for constant matrix inversion. In Second international symposium on intelligent information technology application. doi: 10.1109/IITA.2008.128.
  26. Zhang, Y., Chen, K., Ma, W., & Xiao, L. (2007). MATLAB simulation of gradient-based neural network for online matrix inversion. In D. S., Huang, L., Heute & Loog, M. (Eds.), ICIC 2007, LNCS(LNAI), (Vol. 4682, pp. 98–109). Heidelberg: Springer.Google Scholar
  27. Zhang Y., Ge S. S. (2005) Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Transaction on Neural Networks 16(6): 1477–1490CrossRefGoogle Scholar
  28. Zhang Y., Jiang D., Wang J. (2002) A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Transactions on Neural Networks 13(5): 1053–1063CrossRefGoogle Scholar
  29. Zhang Y., Li Z. (2009) Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear equality constraints. Physics Letters A 373(18-19): 1639–1643zbMATHCrossRefGoogle Scholar
  30. Zhang Y., Ma W., Cai B. (2009) From Zhang neural network to Newton iteration for matrix inversion. IEEE Transactions on Circuits and Systems I 56(7): 1405–1415MathSciNetCrossRefGoogle Scholar
  31. Zhang, Y., Ma, W., & Yi, C., (2008). The link between Newton iteration for matrix inversion and Zhang neural network (ZNN). In Proceeding of IEEE international conference on industrial technology, Chengdu, China. doi: 10.1109/ICIT.2008.4608578.
  32. Zhang Y., Xiao L., Ruan G., Li Z. (2011) Continuous and discrete time Zhang dynamics for time-varying 4th root finding. Numerical Algorithms 57(1): 35–51MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Abderrazak Benchabane
    • 1
    Email author
  • Abdelhak Bennia
    • 2
  • Fella Charif
    • 1
  • Abdelmalik Taleb-Ahmed
    • 3
  1. 1.Département d’Électronique, Faculté des Sciences et de la Technologie et Sciences de la MatièreUniversité Kasdi MerbahOuarglaAlgeria
  2. 2.Département d’Electronique, Faculté des Sciences de l’ingénieurUniversité Mentouri de ConstantineConstantineAlgeria
  3. 3.Laboratoire LAMIH, FRE CNRS 3304 UVHCUniversité de ValenciennesValenciennesFrance

Personalised recommendations