Abstract
Since the pioneer work of Hopfield on the computational capabilities of recurrent neural networks (RNNs), they have been applied to solve classification and optimization problems in many scientific disciplines. This can be done, either by using conventional training algorithms like back propagation through time, or by investigating the Lyapunov stability of these RNNs and comparing the corresponding Lyapunov function with the cost function of the optimization problem to be solved. The later method is especially interesting in the field of engineering because no training phase is needed, which is always associated with computational effort and time. In this chapter we focus on an application of RNNs in communications engineering, namely the vector equalization. The importance of this procedure arises from the fact that there is no need for training. The parameters of the RNN to act as vector equalizer can be obtained by investigating the stability properties of these networks and by choosing a suitable activation function, which will be the core of this work.
Keywords
Preview
Unable to display preview. Download preview PDF.
References
Engelhart, A.: Vector detection techniques with moderate complexity. Dissertation, university of Ulm, institute of information technology, VDI Verlag GmbH, Düsseldorf (2003)
Engelhart, A., Teich, W.G., Lindner, J., Jeney, G., Imre, S., Pap, L.: A Survey of multiuser/multisubchannel detection schemes based on recurrent neural networks. In: Wireless Communications and Mobile Computing, special issue on Advances in 3G Wireless Networks, vol. 2(3), pp. 269–284. John Wiley & Sons, Ltd. (2002)
Fogelman-Soulié, F., Mejia, C., Goles, E., Martinez, S.: Energy functions in neural networks with continuous local functions. Complex Systems 3, 269–293 (1989)
Frey, T., Reinhardt, M.: Signal estimation for interference cancellation and decision feedback equalization. In: Proceeding IEEE Vehicular Technology Conference, VTC 1997, pp. 155–159 (1997)
Haykin, S.: Neural Networks: A Comprehensive Foundation, pp. 545–548. Macmillan College Publishing Company, Inc., USA (1994)
Hill, T., Lewicki, P.: Statistics: Methods and applications: A comprehensive reference for science, industry and data mining. StatSoft, Inc., USA (2006)
Hiriart-Urruty, J.-B., Lemaréchal, C.: Fundamentals of convex analysis, pp. 110–117. Springer, USA (2001)
Hopfield, J.J.: Neural networks and physical systems With emergent collective computational abilities. Proceeding of Natural Academic Science 79, 2554–2558 (1982)
Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proceeding of Natural Academic Science 81, 3088–3092 (1984)
Hu, S., Wang, J.: Global stability of a class of discrete-time recurrent neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49(8), 1104–1117 (2002)
Kechriotis, G.I., Manolakos, E.S.: Hopfield neural networks implementation of the optimal CDMA multiuser detector. IEEE Transactions on Neural Networks 7(1), 131–141 (1996)
Kuroe, Y., Hashimoto, N., Mori, T.: On energy function for complex-valued neural networks and its applications. In:Proceeding of the 9th International Conference on Neural Information Processing, ICONIP 2010, vol. 3, pp. 1079–1083 (2002)
Lindner, J.: MC-CDMA in the context of general multiuser/multisubchannel transmission methods. European Transactions on Telecommunications 10(4), 351–367 (1999)
Lindner, J.: Informationsübertragung: Grundlagen der Kommunikationstechnik. ch.8. Springer, Heidelberg (2005)
Luenberger, D.G.: Optimization by vector space method. John Wiley, NY (1969)
Lupas, R., Verdu, S.: Near-far resistance of multiuser detectors in asynchronous channels. IEEE Transactions on Communications 38(4), 496–508 (1990)
Mostafa, M., Teich, W.G., Lindner, J.: A modified recurrent neural network as vector detector. In: Proceeding of Asia-Pacific Conference on Circuits and Systems, APCCAS 2010, pp. 620–623 (2010)
Mostafa, M., Teich, W.G., Lindner, J.: Stability analysis of recurrent neural networks with time-varying activation functions. In: Proceeding of the International Workshop on Nonlinear Dynamical Systems, INDS 2011, pp. 239–244 (2011)
Mostafa, M., Teich, W.G., Lindner, J.: Global vs. local stability for recurrent neural networks as vector equalizer. In: International Conference on Signal Processing and Communication Systems ICSPCS (2011)
Sgraja, C., Engelhart, A., Teich, W.G., Lindner, J.: Combined equalization and decoding for general BFDM packet transmission schemes. In: Proceeding of the 1st international OFDM-Workshop, pp. 1–6 (1999)
Sgraja, C., Engelhart, A., Teich, W.G., Lindner, J.: Equalization with recurrent neural networks for complex-valued modulation schemes. In: Proceeding of the 3rd Workshop Kommunikationstechnik, pp. 7–12 (1999)
Sahoo, P.K., Riedel, T.: Mean value theorems and functional equations. ch.4. World Scientific, USA (1998)
Spivak, M.: Calculus on Mainfolds, pp. 35–37. Addison-Wesley (1965)
Teich, W.G., Seidl, M.: Code division multiple access communications: Multiuser detection based on a recurrent neural network structure. In: Proceeding of the International Symposium on Spread Spectrum Techniques and Applications, ISSSTA 1996, vol. 3, pp. 979–984 (1996)
Teich, W.G., Engelhart, A., Schlecker, W., Gessler, R., Pfleiderer, H.-J.: Towards an efficient hardware implementation of recurrent neural network based multiuser detection. In: 6th International Symposium on Spread Spectrum Techniques and Applications ISSSTA 2000, pp. 662–665 (2000)
Verdu, S.: Computational complexity of optimum multiuser detection. Algorithmica, 303–312 (1989)
Yoshida, M., Mori, T.: Complex-valued neural networks: Utilizing high-dimensional parameterss, pp. 104–114. IGI Global (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mostafa, M., Teich, W.G., Lindner, J. (2013). Stability Analysis of Vector Equalization Based on Recurrent Neural Networks. In: Kyamakya, K., Halang, W., Mathis, W., Chedjou, J., Li, Z. (eds) Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering. Studies in Computational Intelligence, vol 459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34560-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-34560-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34559-3
Online ISBN: 978-3-642-34560-9
eBook Packages: EngineeringEngineering (R0)