An Adaptive Nonlinear Function Controlled by Estimated Output Pdf for Blind Source Separation

In blind source separation, convergence and separation performance are highly dependent on a relation between a probability density function (pdf) of the output signals y and nonlinear functions f(y) used in updating coefficients of a separation block. This relation was analyzed based on kurtosis κ4 of the output signals. The nonlinear functions, tanh(y) and y have been suggested for super-Gaussian (κ4 ≥ 0) and sub-Gaussian (κ4 < 0) distributions, respectively. Furthermore, an adaptive nonlinear function, which can be continuously controlled, was proposed. The nonlinear function is formed as a linear combination of y and tanh(y). Their linear weights are controlled by the estimated κ4. Although the latter can improve separation performance, its performance is still limited especially in difficult separation problems. In this paper, a new method is proposed. Nonlinear functions are directly controlled by the estimated pdf p(y) of the separation block outputs y. p(y) is expressed by a mixture Gaussian model, whose parameters are iteratively estimated sample by sample. f(y) and p(y) are related by the stability condition f(y) = −(dp(y)/dy)/p(y). Blind source separation using 2∼ 5 channel music signals are simulated. The proposed method is superior to the above conventional methods. Three Gaussian functions are enough to express the output pdf.