Particle Filter In The Single Channel Signal Separation

Single channel signal separation (SCSS) is a fundamental and challenging research topic in signal processing field. And it plays an important role in denoising, wireless communication, speech signal processing, biological medical signal processing, and seismic signal processing and so on. Most signal processing problems appearing from phenomenon of nature and society are nonlinear, chaos signal and seismic signal for example. With the rapid improvement of the precision, flexibility and real-time requirement for signal processing, traditional linear technology has not been able to meet the demand of information processing perfectly. Recently, the theory and technology of nonlinear signal processing have been study a lot, and many nonlinear filter are proposed, especially the Particle Filtering which is a novel class Bayesian filter based on Monte Carlo technique, it is powerful and can solve the general nonlinear non-Gaussian problem, it has been widely asserted that Particle Filtering beat the curse of dimensionality.We have analyzed the thesis and literature that are correlated with SCSS problem and carried on further research on it, using Particle Filtering theory as theory background. Some research on the denoising, separation of chaos signal and PCMA (Paired Carrier Multiple Access) signal are provided. The main content of the thesis is:Chapter 1: Introduction. Firstly, the application of single channel signal processing in many fields is introduced, and then the separability of multi-component mixing signal is discussed. Finally, we introduce the main work and contribution of the thesis briefly.Chapter 2: Bayesian filtering. Begin with the Bayesian iterative estimation; we introduce the Kalman Filter which is the optimal solution in linear gaussian model. Then, we review the existing nonlinear filtering algorithms, and the meaning of the Monte Carlo method is also made clear. Finally, the sampling techniques of Monte Carlo are presented.Chapter 3: Particle Filtering. In this chapter, we review the evolution of Particle Filtering from sequential importance sampling, resampling, to Regularized Particle Filter. The idea, algorithm frame and improvement strategies of Particle Filtering are discussed.Chapter 4: Single channel nonlinear signal estimation. Chaos signal is the major research subject in the chapter. According to the number of the mixing signal, the single channel problem is separated into denoising and separation, and we propose two new algorithms based on Particle Filtering for denoising and separation problem respectively. The selection and performance of different importance functions are discussed in detail, while there is state noise in the model or not, the noise is gaussian or not. When there is no state noise, we study the reason of the degeneracy and effective method is proposed. While there is state noise, the general condition when can we chose the optimal importance function is presented and the importance weight formula is deduced, according to the characteristic of different state space model. Finally, a new semi-blind separation is proposed. Kernel smoothing method is used when the unknown parameter is fixed, while we utilizing the AR model deal with the timing problem. Mixture Kalman filter is also applied to realizing the combined parameter and signal estimation.Chapter 5: Single channel blind separation of PCMA signal. For communication signal, the nonlinear is caused by the complex channel. In this chapter, a general model for the single channel blind signal processing of digital modulated signals is introduced, considering transmission delay, timing offset, channel fading factor, and frequency offset, etc. And a Particle Filtering based blind separation algorithm is presented utilizing the differences of the parameters in the model. In this algorithm, blind signal separation is converted into the joint estimation of unknown parameters and the symbols of the PCMA signals. The optimal importance function is deduced, and smoothing step is carried out to improve the separation performance.Chapter 6: Conclusion and prospect. We summarize the thesis, and introduce the development trend of SCSS and problems faced at present briefly in this chapter. And we present the further suggestion of researching on SCSS algorithm.