A simple geometric blind source separation method for bounded magnitude sources

A novel blind source separation approach and the corresponding adaptive algorithm is presented. It is assumed that the observation mixture is obtained through an unknown memoryless linear mapping of independent and bounded magnitude sources. We further assume an initial adaptive prewhitening of the original observation vector which transforms it into a white vector with the same dimension as the original source vector. Our approach is centered around the basic geometric fact that, under a certain boundedness assumption, the unitary mapping which transforms the whitening output vector into an independent vector has the minimum value of maximum (real component) magnitude output over the ensemble of all output components. Therefore, the related criterion is the minimization of the infinity norm of the real component of the unitary separator's output over all possible output combinations. For the minimization of the corresponding nondifferentiable cost function, we propose the use of subgradient optimization methods to obtain a low complexity iterative adaptive solution. The resulting algorithm is fairly intuitive and simple, and provides a low complexity solution especially to a class of multiuser digital communications problems. We provide examples at the end of this paper to illustrate the performance of our algorithm.