Research On Underdetermined Blind Signal Separation

Blind signal separation (BSS) can process signals with only a little priori information, so it has been widely used in the fields of digital communication, speech signal processing, image processing, radar and communication systems, information retrieval, data mining, biomedicine. BSS is a research hotspot of signal processing.It is usually supposed that the number of observation signals is equal to or larger than that of sources, which means the mixed process is complete or overcomplete. Independent component analysis (ICA) is an effective way to solve the above problem, whose key point is estimation of the inverse matrix of mixing matrix. At present, many kinds of ICA algorithms with superior performance have been proposed. However, in the practical application of BSS, such as speech signal collecting and wireless communication, there inevitably exists the case that the number of observation signals is less than that of sources, which is called underdetermined BSS (UBSS). Because the underdetermined mixing matrix is not inverse, classical ICA methods can't be used to resolve UBSS problem any more, thus theory and algorithms of UBSS are still needed to explore.Underdetermined BSS is mainly studied in this thesis.At first, the method of underdetermined blind mixing matrix estimation based on sparse component analysis (SCA) is studied, which relaxes demand of sources sparsity. Generally, the algorithm of underdetermined blind mixing matrix estimation based on SCA firstly clusters the hyperplanes generated by the mixing vector, and then estimates the mixing matrix. However, when sources are not strictly sparse, the cluster of hyperplanes has heavy computation load and low efficiency. A new mixing matrix estimation algorithm based on the normal vector of hyperplane is proposed. A method of calculating the normal vector of hyperplane is presented, which replaces the cluster of hyperplanes, and then the mixing matrix is estimated. Because of avoiding hyperplane cluster, the proposed algorithm has lower computational cost and the efficiency of the estimation of mixing matrix is well improved. Since the demand of sources sparsity is relaxed, the proposed algorithm is more practical.Then, the UBSS algorithms based on nonnegative matrix factorization (NMF) are researched. When NMF is applied to resolve the problem of BSS, in order to obtain unique factorization, the mixing matrix has to be complete or overcomplete, which means NMF can't be used to resolve the UBSS problem. In this thesis, new algorithms of UBSS based on constraint NMF are proposed. In order to realize the unique factorization of mixing matrix and sources, minimization of mixing matrix determinant, spasity and uncorrelated features of sources are used to constrain results of NMF, thereby NMF is successfully expanded to underdetermined BSS. Besides, the separation accuracy can be improved when constraint NMF is used in the complete or overcomplete BSS. The simulation results show that proposed algorithms can successfully separate underdetermined mixed signals by relaxed sparse sources.At last, the application of BSS in PCMA is discussed. In order to obtain signals from the opposite side, the method of signal suppression is adopted in traditional realization of PCMA, which requires to know local signal and to accurately estimate local downgoing signal's parameters. This method has two problems, one is very hard to accurately estimate parameters, the other is it can't be used in non-cooperative communications. To overcome the drawbacks of signal suppression method, a blind separation algorithm of single channel PCMA signal based on ICA is proposed. With orthogonal receiver, underdetermined mixing model of single channel PCMA signal is transformed to complete mixing model, and then an existing ICA algorithm is used for separating signals from both communication parties. This algorithm doesn't need moulds of parameter estimation and adjustment in which error is easily produced, and can be used in blind receiving. The simulation results verify the effectiveness and superiority of proposed algorithm.