Research On Underdetermined Blind Source Separation Algorithms And Its Application

With the rapid developments and achievements of information and engineering technology, the use of electronic equipment is becoming more and more widely, which result in the increasingly complex transmission environment. All kinds of signals are mixed with high concentration in time domain and aliasing mutually in frequency domain, so we must separate the signals successfully before do the parameter estimation of the target signal and the subsequent processing. As a kind of effective method for signal separation, Blind Source Separation(BSS) has drawn a wide attention, and has become an important research topic in the field of modern signal processing. It has broad application prospects in biomedical engineering, data communications, speech enhancement and array signal processing, image processing and recognition, etc. After years of development, though the research of blind source separation has a series of remarkable achievements, it is still a challenging task because of the complexity of the mixing model and the diversity of application object. Especially for some certain conditions(such as underdetermined mixing or not sufficient sparse, et al), the blind source separation technology has great study and improving space and practical value. This paper has closely focused on the theme of blind source separation in linear time-delayed underdetermined model, studies the relevant theories of sparse component analysis, independent component analysis and the time-frequency distribution, and the specific implementation in the conditions of not sufficient sparse and mixed signals with different characteristics. At last, we apply it to the moving target detecting in the passive radar system. The specific research contents and achievements have the following several aspects:(1) In view of the conditions when sources are not sufficient sparse and with partial aliasing, a new blind source separation method with enhanced functionality is proposed based on priori information extraction and convex optimization model. Firstly, with the known antenna parameters from receiver end, extract the priori information of mixing matrix, and derive a new standard for single source points detecting, and estimate the underdetermined mixing matrix. Then, use the convex model to do the signal separation. The model takes into account both projection and size of the signal’s subspace(source number), avoids the local mixing matrix’s “over-estimate” problem of traditional subspace projection algorithm, which needs to preset the source number at every time-frequency point as a constant, while adding extra steps to do the source number estimation will increase the computation cost greatly. Simulation results show that the proposed method overcomes the shortage of conventional subspace method and achieves higher separation performance especially in low signal-to-noise ratio conditions.(2) Under the condition of quasi-stationary signal mixing model, as the traditional algorithm based on Khatri-rao product can hardly accurately distinguish the signals with closer directions, a new high resolution identification algorithm is presented based on the decomposition of PARAFAC model. The underdetermined identification model is build firstly using Khatri-rao product by extract the algebraic structure of mixed sources, and then the model is expressed as the third order PARAFAC form. At last, PARAFAC decomposition is applied to do the mixing matrix estimation. Compared with traditional method, the proposed algorithm can make full use of the data’s inner compact algebraic structure, and then we can solve the problem by means of the efficient algebraic algorithm. It uses not only the statistical characteristics of the source signals, but also the inner priori information of inner structure of data. The experimental results show that the method can realize the high resolution of blind identification under the underdetermined mixing model, and has better results especially for the sources coming close with each other.(3) To solve the underdetermined blind source separation of cyclic stationary signals, a new blind separation method based on quadratic time-frequency distribution is proposed after exploit more charactistics of signals, which extract the second-order quadratic to do the preprocessing. Different from traditional methods, we study the inner relations between second-order cyclic statistics and Wigner-Ville Distribution(WVD), and reconstruct the WVD using the piecewise average periodogram method. Then, auto-term TF points are detected after computing the matrixes of TFDs, and a new three-order tensor is folded by the chosen TFD matrixes. At last, PARAFAC decomposition is applied to separate the sources directly, which does not assume that the number of active sources at any TF point is not larger than the sensor number. Simulation results demonstrate that the proposed method can suppress the noise effectively and separate the sources directly with only one step avoiding the superposition of error of “two-step” methods, which improves the performance and efficiency of separation.(4) Take the passive radar moving target detection as the research object, propose a new multi-step clutter suppression structure based on blind source separation, and study the application of the technology in the real environment. Time-domain cancellation algorithm is firstly applied to restrain the direct and multipath interference come from the main base station, and then for the residual mixture of interferences from neighboring stations, blind source separation algorithm is used to preliminary restrain the strong interference signals before adopting the robust adaptive beamforming method for further weak signals elimination. At last, range-doppler coherent processing is used to detect the moving target. With the help of multi-step architecture, the main station interference, strong and weak interferences from adjacent base stations are treated respectively, which overcomes the shortage of traditional method, which uses more degrees of freedom for inhibiting large power signals(direct wave and multipath interference of main base station), and avoids the “shield” effect to weak signals caused by strong ones when using direct beamforming processing. The experimental results show that the proposed method has better performance for clutter interference suppression and target detection.