  AIMS: The separation of foreground contamination from cosmic microwave
background (CMB) observations is one of the most challenging and important
problem of digital signal processing in Cosmology. In literature, various
techniques have been presented, but no general consensus about their real
performances and properties has been reached. This is due to the
characteristics of these techniques that have been studied essentially through
numerical simulations based on semi-empirical models of the CMB and the
Galactic foregrounds. Such models often have different level of sophistication
and/or are based on different physical assumptions (e.g., the number of the
Galactic components and the level of the noise). Hence, a reliable comparison
is difficult. What actually is missing is a statistical analysis of the
properties of the proposed methodologies. Here, we consider the "Internal
Linear Combination" method (ILC) which, among the separation techniques,
requires the smallest number of "a priori" assumptions. This feature is of
particular interest in the context of the CMB polarization measurements at
small angular scales where the lack of knowledge of the polarized backgrounds
represents a serious limit. METHODS: The statistical characteristics of ILC are
examined through an analytical approach and the basic conditions are fixed in a
way to work satisfactorily. RESULTS: ILC provides satisfactory results only
under rather restrictive conditions. This is a critical fact to take into
consideration in planning the future ground-based observations (e.g., with
ALMA) where, contrary to the satellite experiments, there is the possibility to
have a certain control of the experimental conditions.
