Chaotic signals are non-periodic signals which are sensitive to initial conditions and occupying a wide bandwidth in frequency domain. These characteristics make chaotic signals potentially applicable in communications. Since the discovery of self-synchronization phenomenon in chaotic systems, many kinds of communication systems and schemes based on chaos have been proposed. But none of them is applicable in real communication environments. The reasons are: (1) For coherent detection, channel interferences and the mismatching of system parameters make chaos synchronization not realizable. The minus effect of channels, especially interferences in wireless communication channels severely degrade the performance of chaos-based communication systems. (2) For non-coherent detection, two factors influence the feasibility of real applications: the threshold of decision blocks is a function of the noise power and the variance of per bit energy increases with the noise power. If we can separate the chaotic signals, we can solve these problems both in coherent communication systems and non-coherent communication systems. It has significant sense to chaos-based communication systems.Separation of chaotic signals is a basic problem in signal processing and communications. This thesis focuses on the separation of chaotic signals and its applications-detection of chaotic signals, blind separation of chaotic signals and their applications in communications.Motivated by the backward iteration method applying for blind separation of chaotic signals, we propose and realize a non-coherent chaos-based digital communication scheme based on backward iteration. We simulate the performance of the scheme under the condition of binary, 4-ary, and parameter mismatch. The simulation results show that the performance of the scheme is good even in low signal to noise ratio. The method is still effective in weak parameter mismatch. Traditionally, separating a deterministic signal from noise or reducing noise for a noisy corrupted signal is a basic problem in signal processing and communications. Conventional methods such as filtering make use of the differences between the spectra of the signal and noise to separate them, or to reduce noise. Most often the noise and the signal do not occupy distinct frequency bands, but the noise energy is distributed over a large frequency interval, while the signal energy is concentrated in a small frequency band. Therefore, applying a filter whose output retains only the signal frequency band can reduce the noise considerably. When the signal and noise share exactly the same frequency band, the conventional spectrum-based methods are no longer applicable. The early separation methods for chaotic signals usually utilize the intrinsic properties of chaotic signals. They can be realized provided that all source signals are chaotic and their map equations are known. Later a method is proposed to extract an interested chaotic signal by utilizing the map equation of it based on an optimization algorithm. Though it does not require all source signals are chaotic, it needs to know the map equation of the interested source signal. In addition, a method is proposed utilizing the cross-correlation property of source signals to estimate the separating matrix and reconstruct the source signals by the method of solving an eigen-problem. It can separate chaotic signals without knowing the map equations of chaotic signals and mixing matrix. However, it does not take noise into consideration and all source signals are chaotic in it. The requirement of calculating the inverse of matrices in solving the eigen-problem makes it complex and less accurate. Chaotic signals are noise-like and their cross-correlation is weak. Their higher order cumulants may not equal to zero. Under the condition of unknown map equations and mixing matrix, the above methods may be not applicable. Based on the embedding theory and utilizing the weak cross-correlation of source chaotic signals, we estimate the separating matrix and reconstruct the source chaotic signals directly by the approach of solving eigen-problem. The method has some advantages: (1) It belongs to the field of blind separation. The chaotic signals can be separated from the mixture without the prior knowledge about the chaotic map equations and mixing matrix; (2) In noisy background (including Gaussian white noise, uniformly distributed noise and colored noise), the approach is applicable. In this case the noise is simply taken as a source. (3) In strong noise background, the approach is still effective.Blind source separation(BSS) has attracted much attention in the field of signal process. The separability has been solved to some extent, and a number of BSS methods have been proposed in certain conditions. Conventional BSS methods based on the assumption that all source signals are statistically independent and the number of sensors is more than or equal to that of the sources. In underdetermined conditions (the number of sensors is less than that of the sources), blind extraction methods are usually adopted to partially extract sources. In real circumstance, sources may be sparse or their decomposing coefficients may have sparse characteristics, then the sparse characteristics can be utilized to solve the underdetermined BSS problem. For chaotic signals, their autocorrelation function attenuates fast with the increasing of correlation time, their spectrum is broad band and continuous and their cross-correlation is very weak, so they do not have sparse characteristics. The commonly used BSS method for underdetermined mixtures would not work for chaotic source signals. Therefore underdetermined BSS problem has been routinely considered as an obstacle for source separation. Based on the fact that underdetermined BSS problem for linear mixed chaotic signals are intractable, we construct an underdetermined BSS scheme, furthermore, we apply it to secure communication. Analysis and simulation results demonstrate that the proposed method has excellent secure performance and high decryption precision even when channel noise is very high. |