Chapter 7 - Second-order methods based on color

Abstract

Random processes with second-order temporal statistical structures are classically divided into two broad classes—wide-sense stationary (WSS) processes and nonstationary processes. WSS processes are characterized by the property that the statistical correlation between any two samples thereof depends only on the time-difference between the sampling instants. Such processes exhibit many significant properties in the time and frequency domains, which can be conveniently exploited. The second-order statistics (SOS)-based separation approaches for WSS sources can roughly be divided into two categories—approaches exploiting the special structure of the correlation matrices through (approximate) joint diagonalization and approaches based on the principle of maximum likelihood (ML). ML estimation is based on more than SOS in general, but under the assumption of Gaussian sources, the ML estimate takes a relatively simple form and is indeed based on SOS alone. Using the Gaussianity assumption, it is also possible to apply optimal weighting to the joint-diagonalization based approach, thus obtaining estimates which are asymptotically optimal, and are thus asymptotically equivalent to the ML estimate.