A fast second‐order signal separation algorithms with on‐line capabilities

Abstract

SUMMARYIn correlation-based signal separation algorithms, the received mixed signals are fed to a de-coupling system designed to minimize the output cross-correlation functions. If minimizaion is perfect, each of the system's outputs carries only one signal independent of the others. In these algorithms, the computation burden of the output cross-correlation functions normally slows down the separation algorithm. This paper, describes a computationally e cient method for o -line pre-computation of the needed crosscorrelation functions. Explicit formulas have been derived for the output cross-correlation functions in terms of the received input signals and the de-coupling system parameters. Then, it is shown that signal separation amounts to the least-squares solution of a system of linear equations describing these output cross-correlation functions, evaluated over a batch of lags. Next, a fast RLS-type adaptive algorithm is devised for on-line signal separation. In this respect, an algorithm is derived for updating the de-coupling parameters as data comes in. This update is achieved recursively, along the negative of the steepest descent directions of an objective cost function describing the output cross-correlation functions over a batch of lags, subject to equal output power constraints. Illustrative examples are given to demonstrate the e ectiveness of the proposed algorithms.

Blind Source Separation Technique for Linear Mixtures Based on Accurate Estimation of Probability Density Function

“…The sources are assumed to be mutually independent and no information exits about their distribution. This subject has been extensively studied for the linear memoryless mixture, where separation algorithms are mainly based on Independent Component Analysis (ICA), [1][2][3][4][5][6][7]11]. The basic concept of ICA techniques stems from the fact that separation is achieved if the output's negentropy is maximized.…”

Blind source separation using time-frequency concepts

“…The ambiguity functions in (4) are computed at positive and negative lags. This tums out to right and left different cross terms points.…”

“…This tums out to right and left different cross terms points. Update the parameters h, of the decoupling system through setting equations (4) to zero at the m s sterms' points and solving the resulting system of linear equations in the least squares sense. 3.…”

“…The function of this system is to make the outputs yip) completely independent. In [3,4], this condition has been achieved through decorrelating the output time signals. However un-correlation doesn't mean independence.…”