Fast gradient algorithm with toral decomposition for complex ICA

Abstract

The article introduces the new gradient descent/ascent algorithm for independent component analysis for complex valued data (cICA). This algorithm uses toral decomposition of skew-Hermitian gradient matrix and very simple and computationally inexpensive method of projection based on Lie structure of optimization landscape. Toral decomposition is the diagonalization of the gradient matrix. In this stage a very fast Schur decomposition was used. The algorithm was tested for complex communication signals and compared to several classes of algorithms as gradient descent, quasi-Newton and complex JADE. The simulations showed very good results in terms of speed of operation and separation quality, as well as the highest versatility of applications in the context of the cost functions used among all the tested algorithms. The specificity of gradient methods characterized by quick response to changes in the signal indicates the practical usage potential of this method in on-line applications.