Study Of A Joint(Block) Diagonalization Blind Source Separtion Algorithm Excluding Degenerate Soulutions With Its Application

Blind source separation(BSS) is a kind of signal processing which can separate the source signal just corroding to the receive signal and some assumptions about source signal. With the development of BSS, it is widely used in the area such as complex electromagnetic environment, radar design, communications systems and so on. So, BSS is becoming one of the hotspot in signal processing. Hence, as a critical method to solve the problem of BSS, matrix joint(block) diagonalization algorithm has received a great deal of concern. In this paper, we will focus on this topic and do the following work.Firstly, we will probe the relationship between instantaneous signal mixing model(convolution mixture model) and the matrix joint(block) diagonalization model. It will be convenient for us to apply the matrix joint(block) diagonalization algorithm into the separating of the real speech signal.Secondly, in general, the target matrix pencil of joint diagonalization is not able to satisfy the theorem of perfect diagonalization. As a result, the joint diagonalization is always approximate. So we will discuss the commonly used target function to measure the diagonality of the target matrix pencil. What’s more, due to the discussion of the convergence behavior of the joint diagonalization algorithm is highly difficult. Hence, it is impossible to elaborate their advantages and disadvantages in theory. So, we will list the classical joint diagonalization algorithm and compare the performance of the classical algorithm in four aspect.Lastly, for the reason that non-orthogonal joint block diagonalization will converge to the trivial and degenerate solution sometimes, the finally result of the BSS will suffer a huge impact. So,we will describe the status of the study of the degenerate solution and discuss the reason why the joint block diagonalization algorithm always converges to the degenerate solution. Furthermore, we will add a penalty function to the target function based on least squares problem and propose a new non-orthogonal joint block diagonalization algorithm which cloud exclude the degenerate solution. At last, the numerical simulation will be performed to deliberate the effectiveness of the algorithm.