Research On ICA Algorithm And Its Application In Array Signal Processing

Independent component analysis is one of the most primary methods to solve the problem of blind source separation. By using mutual statistical independence property of source signals, it can separate source signals from mixed signals without any known paraemters of source signals and channel. ICA has large application value in communication system, speech signal processing, image processing, biomedicine, environment analysis, financial data analysis and other fields.ICA can be classified as real valued ICA and complex valued ICA according to the differences of the processed signals. Real valued ICA enjoys the most extensive researching, which is mainly applied in real valued signal processing. Complex valued ICA is proposed by some researchers to process complex valued signal in recent years, which is mainly applied in the fields of array signal processing, frequency domain signal and functional magnetic resonance imaging processing. Although complex valued ICA has some development, comparied with real valued ICA, its research is not mature. Its research on theory and application need to be deeper.In this paper, we mainly research on and analyze the basic theory of complex valued ICA and improve the complex valued ICA algorithms from their scope of application, convergence rate and practical application. At the same time, we also research on and analyze the basic theory of real valued ICA and propose an improved ICA algorithm, which can be realized easily by hardware. The content and innovation of this paper can be summarized as follows:Firstly, to overcome the problem that real valued fast ICA algorithm is difficult to be realized by hardware, while the real valued fast ICA algorithm based on Huber M-estimator is easy, but its robustness is not good enough. We propose a new real valued fast ICA algorithm wich is easy to be realized by hardware based on tukey biweight function. It uses tukey biweight function which has better robustness as nonlinear function of real valued fast ICA algorithm and only involves addition and multiplication operation, so it can be realized easily by hardware. Compared with the FastICA algorithm based on Huber M-estimtor, the new algorithm has better robustness.Secondly, to overcome the problem that strong-uncorrelating transform algorithm is only applicable to the non-circular source signals which have different spectrum coefficients, we propose two complex valued ICA algorithms with wider range of application. They use the property that second-order statistics are not zero to contruct cost function and optimize it by different optimization methods. The new algorithms are not only applicable to non-circular source signals with different spectrum coefficients, but also any statical independent complex valued source signals that contain non-circular signals. They extend the range of application of original algorithm.Thirdly, to overcome the problem that complex valued FastICA algorithm is only applicable to circular source signals, we propose an improved complex valued FastICA algorithm which has wider range of application. It constructs new cost function by modifying the cost function of complex valued fast ICA algorithm, and uses approximate Newton method to optimize the new cost function. The new algorithm is not only applicable to circular signals, but also to any non-Gaussian complex valued source signals. Besides, to overcome the problem that the quadratic convergence rate of complex valued FastICA algorithm is not fast enough, we use complex Newton method that has third order convergence rate to optimize the cost function, and deduce a new complex valued FastiCA algorithm with faster convergence rate and apply it in estimating direction of the arrival signals. It not only has faster convergence rate compared with the original algorithm, but also can directly compute the direction of arrival signals, compared with traditional estimation method of the arrival signal direction with high resolution. It also has better perfeormantce and resolution.Finally, to overcome the problem that complex valued non-Gaussian maximization algorithm need the setting of learning rate, but it is difficult to choose suitable learing rate without any system information. We propose a fixed-point complex valued non-Gaussian maximization algorithm. It constructs cost function by introducing penalty function, which is a separated matrix satisfying normalization condition to original cost function, and optimizes the cost function directly in complex valued field. Besides, kurtosis maximization blind beamforming algorithm also has the same problem of setting learning rate. To overcome the problem, we use complex valued Newton-Like method to ptimize cost function and deduce a fixed point kurtosis maximization blind beamforming algorithm without settig learning rate. The improved complex valued non-Gaussian maximization algorithm and kurtosis maximization blind beamforming algorithm are both fixed point algorithm without setting any learning rate, so they are more suitable for practical application.In conclusion, the real valued ICA, complex valued ICA and kurtosis maximization blind beamforming algorithm are researched in this paper, and improved algorithms are proposed to overcome the problems existing in the algorithms. Experimental results indicate that all the improved algorithms could attain good results.