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.
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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 483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37781-5_20
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DOI: https://doi.org/10.1007/978-3-642-37781-5_20
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