Blind separation of discrete sources

Abstract

A polynomial criterion is proposed to perform blind source separation, extending previous works to MIMO systems. The criterion is proved to be asymptotically MAP-equivalent in presence of PSK sources. An efficient minimization algorithm dedicated to polynomial criteria is then developed, improving on the fixed-step stochastic gradient previously utilized in this framework.

Comparative Speed Analysis of FastICA

“…Exact line search is in general computationally intensive and presents other limitations [15], which explains why, despite being a well-known optimization method, it is very rarely used. However, for criteria that can be expressed as rational functions of μ, such as the kurtosis, the constant modulus [16], [17] and the constant power [18], [19] contrasts, the optimal step size μ opt can easily be determined by finding the roots of a low-degree polynomial. At each iteration, optimal step-size (OS) optimization performs the following steps: S1) Compute OS polynomial coefficients.…”

Iterative algorithms

“…This idea constitutes the basis for the RobustICA algorithm. The technique is also applicable to any other contrasts that can be expressed as polynomials or rational functions of µ, such as the constant modulus [37,83] or the constant power [39,81] criteria used for blind equalization of digital communication channels, even in the semi-blind case (Chapter 15). The RobustICA algorithm repeats the following steps until convergence:…”

Semi-blind methods for communications

“…However, it has been observed in [14,34] that, for a number of equalization criteria including the CM, the CP and their semi-blind versions studied herein, functional Υ(f−µg) is a rational function in the step size µ. This allows us to find µ opt algebraically, so that it is possible to globally minimize the cost function in the descent direction while reducing complexity.…”

“…These strategies are not exclusive to the equalization principles considered in this chapter (CM, CP), but can also profit other criteria such as the KM [96] (see also Chapter 6) or those of [34].…”