Study On Separation And Parameter Estimation For Multicomponent Signals

In modern information age, the signal environment is complicated and varying. The receiver always receives the mixture of many multicomponent signals. Separating these signals in order to extract the information implied in the useful signal, becomes a research task with significance both in theory and in practice. However, unlike the processing technologies specified for the monocomponent signal, the ones for the multicomponent signals are more difficult, and have heavier computational complexity. Aiming at this multicomponent case, this paper sorts the separation problem into different categories according to the relationship between the number of channels and the number of components. Further, the coherence of separation and parameter estimation of multicomponent signals in single channel case is illustrated. On this basis, this paper proposes a series of algorithms for the multicomponent signal separation and parameter estimation in a single channel. Besides, for the determined separation problem, this paper improves the traditional independent component analysis method. The main contributions of this paper are as follows:1. For the single channel case, a mixing vector estimation algorithm of multicomponent angle modulated signals based on cumulant system of equations is proposed. This algorithm derives the equivalent probability density function of the angle modulated signals, computes the corresponding statistics, and establishes the cumulant system of equations. Then the mixing vector estimation is achieved through the solution of the system of equations. This algorithm does not require specific information about the modulation types of these angle modulated signals, and can be used in a wide range of applications.2. For the single channel case, a joint parameter estimation algorithm based on importance sampling is proposed, where each component signal has the same expression. The importance sampling estimators for the multicomponent polynomial phase signals and for the multicomponent sinusoidal frequency modulated signals, respectively, are derived. This algorithm has two decoupling operations. The first one is to decouple the parameters linearly related to the data and those nonlinearly related to the data in maximum likelihood estimation, while the other one is to decouple multicomponent signals using importance sampling. As a non-iterative algorithm, this algorithm avoids getting the local maxima from an inappropriate choice of the initial value. Besides, as opposed to the global optimization algorithm where the joint grid search is directly applied on the multicomponent signals, this algorithm decreases the searching dimension via the decoupling of the multicomponent signals.3. For the single channel case, the multicomponent pulse train signal separation algorithm based on the signal model and the one based on singular value decomposition are proposed, respectively. The algorithm based on the signal model uses characteristics of the pulse train signal to model the signal and the mixing system as the form of the linear system of equations. Subsequently, the component signals are recovered via the solution of the system of equations. This algorithm has two versions, one is for the fixed pulse repetition interval signals, and the other is for the varying pulse repetition interval signals. Besides, the algorithm based on singular value decomposition uses the periodicity of the fixed pulse repetition interval signal to reconstruct the mixing signal to a matrix form. Subsequently, the multicomponent signal separation is achieved based on singular value decomposition. These algorithms do not have the specific request for the intra-pulse information.4. For the determined case, a blind source separation algorithm is presented, as an improvement for the traditional independent component analysis. As opposed to the blind source separation based on the fourth statistics or the temporal structure, this algorithm is from the concept of correntropy in information theoretic learning. Using the information of even order statistics implied in correntropy, the cost function is established based on the relationship between the parameterized center correntropy and the test of independence. Subsequently, the demixing matrix and the recovered sources are obtained by using the optimization algorithm.