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Radial Basis Function Networks and their Application in Communication Systems

  • Ascensiòn Gallardo Antolìn
  • Juan Pascual Garcìa
  • Josè Luis Sancho Gòmez
Chapter

Among the different types of Neural Networks (NN), the most popular and frequently used architectures are the Multilayer Perceptron (MLP) and Radial Basis Functions (RBF) due to their approximation capabilities. In this chapter we discuss the use of RBF networks to solve problems in different areas related to communications systems. In the first part of the chapter, we revise the structure of the RBF networks and the main procedures to train them. In the second part, the main applications of RBF networks in communication systems are presented and described. In particular, we will focus our attention in antenna array signal processing (direction-of-arrival estimation and beamforming) and channel equalization (intersymbol interferences and co-channel interferences). Other applications such as coding/decoding, system identification, fault detection in access networks and automatic recognition of wireless standards are also mentioned

Neural networks radial basis functions communication systems channel equalization antenna array signal processing 

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References

  1. Cortes, C. and Vapnik, V.N., Support vector networks. Machine learning, 20: 273–297, 1995.zbMATHGoogle Scholar
  2. Boser, B., Guyon, I. and Vapnik, V.N., A training algorithm for optimal margin classifiers. Fifth annual workshop on computational learning theory, :144–152, San Mateo, CA, 1992.Google Scholar
  3. Bouchired, S., Ibnkahla, M., Roviras, D. and Castaniè, F., Equalization of satellite mobile communication channels using combined self-organizing maps and RBF networks, In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’98), 3377–3380, Seattle, WA, USA, April 1998b.Google Scholar
  4. Bouchired, S., Ibnkahla, M., Roviras, D. and Castaniè, F., “Equalization of satellite UMTS channels using RBF networks”, In Proceedings of IEEE Workshop on Personal Indoor and Mobile Radio Communications (PIMRC), Boston, USA, September 1998a.Google Scholar
  5. Broomhead, D.S. and Lowe, D., Multivariable functional interpolation and adpative networks Complex Systems, 2:321–355, 1988.zbMATHMathSciNetGoogle Scholar
  6. Cid-Sueiro, J. and Figueiras-Vidal, A. R., Recurrent radial basis function networks for optimal blind equalization, In IEEE-SP Workshop on Neural Networks for Signal Processing, 562–571, Baltimore, MA (USA), September 1993.Google Scholar
  7. Cid-Sueiro, J., Artès-Rodrìguez A. and Figueiras-Vidal, A. R., Recurrent radial basis function networks for optimal symbol-by-symbol equalization, In Signal Processing, vol. 40, no. 1, 53–63, October 1994.zbMATHCrossRefGoogle Scholar
  8. Cha, I. and Kassam, S. A., Channel equalization using adaptive complex radial basis function networks, In IEEE Journal on Selected Areas in Communications, vol. 13, no. 1, 122–131, January 1995.CrossRefGoogle Scholar
  9. Chandra Kumar, P., Saratchandran, P. and Sundararajan, N., Non-linear channel equalisation using minimal radial basis function neural networks, In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’98), 3373–3376, Seattle, WA, USA, April 1998.Google Scholar
  10. Chen, S., Cowan, C. F. N. and Grant, P. M., Ortoghonal least squares learning algorithm for radial basis function networks, In IEEE Transactions on Neural Networks, vol. 2, 302–309, March 1991.CrossRefGoogle Scholar
  11. Chen, S. and Mulgrew, B., Overcoming co-channel interference using an adaptive radial basis function equalizer, In EURASIP Signal Processing Journal, vol. 28, no. 1, 91–107, 1992.Google Scholar
  12. Chen, S., Mulgrew, B. and Grant, P. M., A clustering technique for digital communications channel equalization using radial basis function networks, In IEEE Transactions on Neural Networks, vol. 4, no. 4, 570–579, July 1993a.CrossRefGoogle Scholar
  13. Chen, S., Mulgrew, B. and McLaughlin, S., Adaptive bayesian equalizer with decision feedback, In IEEE Transactions on Signal Processing, vol. 41, no. 9, 2918–2927, September 1993b.zbMATHCrossRefGoogle Scholar
  14. Chen, S., McLaughlin, S. and Mulgrew, B., Complex-valued radial basis function networks, Part II: Application to digital communication channel equalization, In Signal Processing, vol. 36, no. 2, 175–188, March 1994.zbMATHCrossRefGoogle Scholar
  15. Chen, S., McLaughlin, S. and Mulgrew, B. and Grant, P. M., Bayesian decision feedback equalizer for overcoming co-channel interference, In Proc. Inst. Elect. Eng., vol. 143, 219–225, August 1996.Google Scholar
  16. Chen, S., Multi-output regression using a locally regularised orthogonal least-squares algorithm. IEE proceedings-vision image and signal processing, 149 (4): 185–195, 2002.CrossRefGoogle Scholar
  17. Chen, S., Mulgrew, B. and Hanzo, L., “Least bit error rate adaptive nonlinear equalisers for binary signalling”, In IEE Proc. Communications, vol. 150, no. 1, 29–36, February 2003.CrossRefGoogle Scholar
  18. Cover, T.M., Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Transactions on Electronic computers, EC-14:326–334, 1995.CrossRefGoogle Scholar
  19. Du, K.-L., Lai, A. K. Y., Cheng, K. K. M. and Swamy, M. N. S., Neural methods for antenna array signal processing: a review, In Signal Processing, vol. 82, 547–561, 2002.CrossRefzbMATHGoogle Scholar
  20. El Zooghby, A. H., Christodoulou, C. G. and Georgiopoulos, M., Performance of radial basis function with antenna arrays, In IEEE Transactions on Antennas and Propagation, vol. 45, no. 11, 1611–1617, 1997.CrossRefGoogle Scholar
  21. El Zooghby, A. H., Christodoulou, C. G. and Georgiopoulos, M., Neural network-based adaptive beamforming for one- and two-dimensional antenna arrays, In IEEE Transactions on Antennas and Propagation, vol. 46, no. 12, 1891–1893, 1998.CrossRefGoogle Scholar
  22. El Zooghby, A. H., Christodoulou, C. G. and Georgiopoulos, M., A neural network-based smart antenna for multiple source tracking, In IEEE Transactions on Antennas and Propagation, vol. 48, no. 5, 768-776, May 2000.CrossRefGoogle Scholar
  23. Gan, Q., Saratchandran, P., Sundararajan, N. and Subramanian, K. R., A complex valued radial basis function network for equalization of fast time varying channels, In IEEE Transactions on Neural Networks, vol. 10, no. 4, 958–960, July 1999.CrossRefGoogle Scholar
  24. Golub,G.H. and Van Loan, C.G., Matrix computantions Johns Hopkins University Press, 1996.Google Scholar
  25. Gomes, J. and Barroso, V., Using a RBF network for blind equalization: desing and performance evaluation, In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’97), vol. 4, 3285–3288, April 1997.Google Scholar
  26. Gomm, B.J. and Yu, D.L., Selecting radial basis function network centers with recursive orthogonal least squares training. IEEE transactions on neural networks, 11 (2) :306–314, 2000.CrossRefGoogle Scholar
  27. Haykin, S., Neural Networks: a comprehensive foundation Prentice-Hall, New York, 1999.zbMATHGoogle Scholar
  28. Haykin, S., Adaptive Filter Theory Prentice Hall, New Jersey, 2002.Google Scholar
  29. Hochstadt, H., Integral equations. Wiley Classics Library. John Wiley and Sons Inc., New York, 1989. ISBN 0-471-50404-1. Reprint of the 1973 original, A Wiley-Interscience Publication. Google Scholar
  30. Ibnkahla, M., Applications of neural networks to digital communications - a survey, In Signal Processing, vol. 80, 1185–1215, 2000.zbMATHCrossRefGoogle Scholar
  31. Jianping, D., Sundararajan, N. and Saratchandran, P., Communication channel equalization using complex-valued radial basis function neural networks, In IEEE Transactions on Neural Networks, vol. 13, no. 3, 687–696, May 2002.CrossRefGoogle Scholar
  32. Kaminsky, E. J. and Deshpande, N., TCM decoding using neural networks, In Engineering Applications of Artificial Intelligence, vol. 16, 473-489, 2003.CrossRefGoogle Scholar
  33. Kohonen, T., The Self-Organizing Map. Proceedings IEEE, 78 (9) :1464–1480, 1990.CrossRefGoogle Scholar
  34. Leong, T. K., Saratchandran, P. and Sundararajan, N., Real-time performance evaluation of the minimal radial basis function network for identification of time varying nonlinear systems, In Computers and Electrical Engineering, vol. 28, 103–117, 2002.zbMATHCrossRefGoogle Scholar
  35. Lin, H. and Yamashita, K., Blind RBF equalizer for received signal constellation independent channel, In Proceedings of 8th International Conference on Communication Systems (ICCS’02), 82–86, 2002.Google Scholar
  36. Lo, T., Leung, H. and Litva, J., Radial basis function neural network for direction-of-arrivals estimation, In IEEE Signal Processing Letters, vol. 1, no. 2, 45–47, February 1994.CrossRefGoogle Scholar
  37. Micchelli, C.A., Interpolation of scattered data: distance matrices and conditionally positive definite fucntions, 2:11–22, 1986.zbMATHMathSciNetGoogle Scholar
  38. Mimura, M., Furukawa, T., A recurrent RBF network for non-linear channel, In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’01), 1297–1300, 2001.Google Scholar
  39. Müller, A. and Elmirghani, J. M. H., “Novel approaches to signal transmission based on chaotic signals and artificial neural networks”, In IEEE Transactions on Communications, vol. 50, no. 3, 384–390, March 2002.CrossRefGoogle Scholar
  40. Mukai, R., Vilnrotter, V. A., Arabshahi, P. and Jamnejad, V., Adaptive acquisition and tracking for deep space array feed antennas, In IEEE Transactions on Neural Networks, vol. 13, no. 5, 1149–1162, September 2002.CrossRefGoogle Scholar
  41. Mulgrew, B., Applying radial basis functions, In IEEE Signal Processing Magazine, vol. 13, no. 2, 50–65, March 1996.CrossRefGoogle Scholar
  42. Mulgrew, B., Nonlinear signal processing for adaptive equalisation and multi-user detection, In Proc. IX European Signal Processing Conference (EUSIPCO’98), 537–544, Rhodes, Greece, September 1998.Google Scholar
  43. Palicot, J. and Roland, C., A new concept for wireless reconfigurable receivers, In IEEE Communication Magazine, 124–132, July 2003.Google Scholar
  44. Park, J., and Sandberg, I.W., Universal approximation using radial basis function networks. Neural Computation,3 :246–257, 1991.Google Scholar
  45. Poggio, T. and Girosi, F., Networks for approximation and learning. Proceedings of the IEEE, 78: 1481–1497, 1990.CrossRefGoogle Scholar
  46. Powell, M.J.D., Radial basis function approximations to polynomials Numerical Analysis 1987 proceedings, :223–241, 1988.Google Scholar
  47. Proakis, J. G., Digital communications, McGraw-Hill, Boston, 4th edition, 2001.Google Scholar
  48. Qureshi, S. U. H., Adaptive equalization, In Proc. IEEE, vol. 73, 1349–1387, 1985.CrossRefGoogle Scholar
  49. Schmidt, R., Multiple emitter location and signal parameter estimation In Antennas and Propagation, IEEE Transactions on (legacy, pre - 1988) Volume 34, Issue 3, Mar 1986 Page(s):276–280CrossRefGoogle Scholar
  50. Shertinsky, A. and Picard, R.W., On the efficiency of the orthogonal least squares training method for radial basis function networks. IEEE transactions on neural networks, 7 (1) :195–200, 1996.CrossRefGoogle Scholar
  51. Southall, H. L., Simmers, J. A. and O’Donnel, T. H., Direction finding in phased arrays with a neural network beamformer, In IEEE Transactions on Antennas and Propagation, vol. 43, no. 12, 1369–1374, 1995.CrossRefGoogle Scholar
  52. Vapnik, V.N, The nature of statistical learning theory. Wiley, New York, 1995.zbMATHGoogle Scholar
  53. Vapnik, V.N., Statistical learning theory. Wiley, New York, 1998.zbMATHGoogle Scholar
  54. Xu, C. Q., Law, C. L. and Yoshida, S., Interference rejection in non-Gaussian noise for satellite communications using non-linear beamforming, In International Journal of Satellite Communications and Networking, vol. 21, 13–22, 2003.CrossRefGoogle Scholar
  55. Yingwei, L., Sundararajan, N. and Saratchandran, P., Adaptive nonlinear system identification using minimal radial basis function neural networks, In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’96), vol. 6, 3521–3524, 1996.Google Scholar
  56. Zhou, P. and Austin, J., Neural network approach to improving fault location in local telephone networks, In Proc. Artificial Neural Networks, 958–963, 1999.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Ascensiòn Gallardo Antolìn
    • 1
  • Juan Pascual Garcìa
    • 2
  • Josè Luis Sancho Gòmez
    • 3
  1. 1.Departamento de Teorìa de la Senal y ComunicacionesEPS-Universidad Carlos III de Madrid, Avda. de la Universidad30, 28911-Leganès (Madrid)Spain
  2. 2.Departamento de las Tecnologìas de la Informaciòn y las ComunicacionesUniversidad Politècnica de Cartagena Campus de la Muralla del Mars/n, 30202Spain
  3. 3.Departamento de las Tecnologìas de la Informaciòn y las ComunicacionesUniversidad Politècnica de Cartagena Campus de la Muralla del Mars/n, 30202Spain

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