  We present the first tests of a new method, the Correlated Component Analysis
(CCA) based on second-order statistics, to estimate the mixing matrix, a key
ingredient to separate astrophysical foregrounds superimposed to the Cosmic
Microwave Background (CMB). In the present application, the mixing matrix is
parameterized in terms of the spectral indices of Galactic synchrotron and
thermal dust emissions, while the free-free spectral index is prescribed by
basic physics, and is thus assumed to be known. We consider simulated
observations of the microwave sky with angular resolution and white stationary
noise at the nominal levels for the PLANCK satellite, and realistic foreground
emissions, with a position dependent synchrotron spectral index. We work with
two sets of PLANCK frequency channels: the low frequency set, from 30 to 143
GHz, complemented with the Haslam 408 MHz map, and the high frequency set, from
217 to 545 GHz. The concentration of intense free-free emission on the Galactic
plane introduces a steep dependence of the spectral index of the global
Galactic emission with Galactic latitude, close to the Galactic equator. This
feature makes difficult for the CCA to recover the synchrotron spectral index
in this region, given the limited angular resolution of PLANCK, especially at
low frequencies. A cut of a narrow strip around the Galactic equator (|b|<3
deg), however, allows us to overcome this problem. We show that, once this
strip is removed, the CCA allows an effective foreground subtraction, with
residual uncertainties inducing a minor contribution to errors on the recovered
CMB power spectrum.
