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Journal of Applied Mathematics
Volume 2015 (2015), Article ID 638978, 8 pages
http://dx.doi.org/10.1155/2015/638978
Review Article

Evolution of Black-Box Models Based on Volterra Series

Department of Electrical Circuits, Federal University of Juiz de Fora, Campus Universitario, Rua Jose Lourenco Kelmer, s/n, 36030-900 Juiz de Fora, MG, Brazil

Received 26 September 2014; Revised 18 December 2014; Accepted 18 December 2014

Academic Editor: Zhiwei Gao

Copyright © 2015 Daniel D. Silveira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. K. Pearson, “Selecting nonlinear model structures for computer control,” Journal of Process Control, vol. 13, no. 1, pp. 1–26, 2003. View at Publisher · View at Google Scholar · View at Scopus
  2. J. C. Pedro and S. A. Maas, “A comparative overview of microwave and wireless power-amplifier behavioral modeling approaches,” IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 4, pp. 1150–1163, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Zhu and T. J. Brazil, “RF power amplifier behavioral modeling using volterra expansion with laguerre functions,” in Proceedings of the IEEE MTT-S International Microwave Symposium, pp. 963–966, June 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Reina-Tosina, C. Crespo-Cadenas, and M. J. Madero-Ayora, “A compact volterra model for power amplifiers with memory,” in Proceedings of the IEEE MTT-S International Microwave Symposium (IMS '09), pp. 1585–1588, IEEE, Boston, Mass, USA, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. D. D. Silveira, P. L. Gilabert, P. M. Lavrador et al., “Improvements and analysis of nonlinear parallel behavioral models,” International Journal of RF and Microwave Computer-Aided Engineering, vol. 19, no. 5, pp. 615–626, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. D. D. Silveira, P. L. Gilabert, A. B. dos Santos, and M. Gadringer, “Analysis of variations of volterra series models for RF power amplifiers,” IEEE Microwave and Wireless Components Letters, vol. 23, no. 8, pp. 442–444, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. O. Nelles, Nonlinear System Identification, Springer, Berlin, Germany, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  8. D. Lichtblau and E. W. Weisstein, “Condition Number,” MathWorld—A Wolfram Web Resource, December 2004, http://mathworld.wolfram.com/ConditionNumber.html.
  9. J. Vuolevi and T. Rahkonen, Distortion in RF Power Amplifiers, Artech House, Norwood, Mass, USA, 2003.
  10. M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology, and Techniques, Kluwer Academic Publishers, Norwell, Mass, USA, 2000.
  11. R. Raich and G. T. Zhou, “Orthogonal polynomial for complex Gaussian processes,” IEEE Transactions on Signal Processing, vol. 52, no. 10, pp. 2788–2797, 2004. View at Publisher · View at Google Scholar
  12. M. S. O'Droma, “Dynamic range and other fundamentals of the complex Bessel function series approximation model for memoryless nonlinear devices.,” IEEE Transactions on Communications, vol. 37, no. 4, pp. 397–398, 1989. View at Publisher · View at Google Scholar · View at Scopus
  13. Mathworks, “Matlab version 7,” 2005.
  14. V. Z. Marmarelis, Nonlinear Dynamic Modeling of Physiological Systems, John Wiley & Sons, 2004.
  15. W. J. Rugh, Nonlinear System Theory—The Volterra/Wiener Approach, Johns Hopkins University Press, Baltimore, Md, USA, 1981. View at MathSciNet
  16. T. M. Panicker and V. John Mathews, “Parallel-cascade realizations and approximations of truncated Volterra systems,” IEEE Transactions on Signal Processing, vol. 46, no. 10, pp. 2829–2832, 1998. View at Publisher · View at Google Scholar · View at Scopus
  17. M. J. Korenberg, “Parallel cascade identification and Kernel estimation for nonlinear systems,” Annals of Biomedical Engineering, vol. 19, no. 4, pp. 429–455, 1991. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, Krieger Publishing, 1980. View at MathSciNet
  19. V. J. Mathews and G. L. Sicuranza, Polynomial Signal Processing, Wiley Interscience, 2000.
  20. D. D. Silveira and G. Magerl, “Extraction and improvements of a behavioral model based on the wiener-bose structure used for baseband volterra kernels estimation,” in Proceedings of the IEEE MTT-S International Microwave Symposium (IMS '07), vol. 1, pp. 2007–2010, Honolulu, Hawaii, USA, June 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. A. S. Tehrani, H. Cao, S. Afsardoost, T. Eriksson, M. Isaksson, and C. Fager, “A comparative analysis of the complexity/accuracy tradeoff in power amplifier behavioral models,” IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 6, pp. 1510–1520, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Zhu, J. C. Pedro, and T. R. Cunha, “Pruning the volterra series for behavioral modeling of power amplifiers using physical knowledge,” IEEE Transactions on Microwave Theory and Techniques, vol. 55, no. 5, pp. 813–820, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. C. Crespo-Cadenas, J. Reina-Tosina, M. J. Madero-Ayora, and J. Munoz-Cruzado, “A new approach to pruning Volterra models for power amplifiers,” IEEE Transactions on Signal Processing, vol. 58, no. 4, pp. 2113–2120, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. S. Benedetto and E. Biglieri, Principles of Digital Transmission, Kluwer Academic Publishers, Norwell, Mass, USA, 1999.
  25. A. Zhu, P. J. Draxler, J. J. Yan, T. J. Brazil, D. F. Kimball, and P. M. Asbeck, “Open-loop digital predistorter for RF power amplifiers using dynamic deviation reduction-based volterra series,” IEEE Transactions on Microwave Theory and Techniques, vol. 56, no. 7, pp. 1524–1534, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Climate Research, vol. 30, no. 1, pp. 79–82, 2005. View at Publisher · View at Google Scholar · View at Scopus
  27. P. Karras and N. Mamoulis, “One-pass wavelet synopses for maximum-error metrics,” in Proceedings of the 31st International Conference on Very Large Data Bases (VLDB '05), pp. 421–432, September 2005. View at Scopus
  28. M. J. Hall, “How well does your model fit the data?” Journal of Hydroinformatics, vol. 3, pp. 49–55, 2001. View at Google Scholar