Time delay estimation from the time series for optical chaos systems using deep learning

We propose a model-free time delay signature (TDS) extraction method for optical chaos systems. The TDS can be identified from time series without prior knowledge of the actual physical processes. In optical chaos secure communication systems, the chaos carrier is usually generated by a laser diode subject to opto-electronic/all-optical time delayed feedback. One of the most important factors to security considerations is the concealment of the TDS. So far, statistical analysis methods such as autocorrelation function (ACF) and delayed mutual information (DMI) are usually used to unveil the TDS. However, the effectiveness of these methods will be reduced when increasing the nonlinearity of chaos systems. Meanwhile, certain TDS concealment strategies have been designed against statistical analysis. In our previous work, convolutional neural network shows its effectiveness on TDS extraction of chaos systems with high loop nonlinearity. However, this method relies on the knowledge of detailed structure of the chaos systems. In this work, we formulate a blind identification method based on long short-term memory neural network (LSTM-NN) model. The method is validated against the two major types of optical chaos systems, i.e. opto-electronic oscillator (OEO) chaos system and laser chaos system based on internal nonlinearity. Moreover, some security enhanced chaotic systems are also studied. The results show that the proposed method has high tolerance to additive noise. Meanwhile, the data amount needed is less than existing methods. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement