Reconstruction of chaotic signals with application to channel equalization in chaos-based communication systems

A number of schemes have been proposed for communication using chaos over the past years. Regardless of the exact modulation method used, the transmitted signal must go through a physical channel which undesirably introduces distortion to the signal and adds noise to it. The problem is particularly serious when coherent-based demodulation is used because the necessary process of chaos synchronization is difficult to implement in practice. This paper addresses the channel distortion problem and proposes a technique for channel equalization in chaos-based communication systems. The proposed equalization is realized by a modified recurrent neural network (RNN) incorporating a specific training (equalizing) algorithm. Computer simulations are used to demonstrate the performance of the proposed equalizer in chaos-based communication systems. The Hénon map and Chua's circuit are used to generate chaotic signals. It is shown that the proposed RNN-based equalizer outperforms conventional equalizers as well as those based on feedforward neural networks for noisy, distorted linear and non-linear channels.