NASAs Cosmic Background Explorer (COBE) satellite mission has provided
a wealth of information about the CMBR. The Far Infrared
Spectrophotometer (FIRAS)
has established the shape of the CMBR spectrum as an almost perfect
black-body corresponding to a
temperature of 
(Fixsen et al. 1996) and the
complete four-year data from the
Differential Microwave Radiometer (DMR) experiment
demonstrate frequency independent RMS temperature fluctuations of the
CMBR with a typical amplitude of 
K
on a 
angular scale (Banday et al. 1997). The fact that the
fluctuations are frequency independent is consistent with the hypothesis,
that they are of cosmological origin (Banday et al. 1997).
These important results
along with power spectrum analysis of the four-year COBE anisotropy maps
(see e.g. Bennett et al. 1996; Tegmark 1996;
Górski et al. 1996)
are however not able to impose
sufficient constraints on theoretical models for
the early Universe. The main objective
for the second generation of CMBR experiments will thus be to
make observations which can allow an unambiguous discrimination between
competing models for the physics of the very early Universe as well as the
formation and evolution of large-scale structure
in the Universe. In order to achieve these goals, sensitivities of
down to a 10' angular scale
covering at least one third of the sky will have to be reached (Bersanelli
et al. 1996). Since the 10' angular scale is smaller than that subtended
by the horizon scale at the surface of last scattering and measurements made
at the level will be limited only by
cosmic variance, such observations will not only be a significant improvement
with respect to the COBE results but will actually be the definitive
observations of the CMBR anisotropies.
For the first generation of CMBR experiments lack of sufficient instrument
sensitivity has been a major obstacle to reaching the above mentioned levels
of sensitivity. In recent years developments in detector technology now
make feasible the construction of CMBR experiments with instrumental
sensitivities for 
in the order of a few times 10-6
(Bersanelli et al. 1996). With these instrument sensitivities
the dominant remaining obstacle
for high sensitivity anisotropy measurements is contamination
by galactic and extragalactic foregrounds.
For any experiment aiming at the detection of the extremely weak temperature
fluctuations in the CMBR it is thus imperative to document how well
this contamination can be overcome.
The choice of optimal frequency bands enters this discussion as a crucial
parameter.
The COBE FIRAS and DMR results along with observations of the infrared (IR) and far infrared (FIR) emission from our Galaxy made by the COBE FIRAS and Diffuse Infrared Background Experiment (DIRBE) has shown that space-based CMBR experiments with full or near full sky coverage have many advantages over ground-based or balloon-borne experiments. Away from atmospheric emission in a thermally stable environment the possibility for low-noise, multifrequency observation dramatically improves the ability to identify and remove hampering foreground effects of galactic and extragalactic nature. This ability is based on the difference in spectral and spatial signatures of the CMBR and the various foregrounds.
Various studies of this issue have been made including the
work of Brandt et al. (1994) and Tegmark & Efstathiou (1996).
Brandt
et al. (1994) identify two 
patches in the sky with the lowest possible foreground fluctuation levels,
and
only carry out their modelling with the limited foreground parameter ranges
given in these patches. They investigate a number of
different idealized experiments with a varying level of noise to establish
at what noise level the anisotropy recovery becomes too difficult or
impossible.
The analysis is based on a single-pixel non-linear least-squares
spectral fitting technique.
They investigate the performance of both ground- and space-based
experiments in various frequency intervals and with various approaches to
the foreground modelling depending on the frequency interval used (i.e.
disregarding
the effect of certain foregrounds in some frequency intervals).
Their work indicates that the ablility of the spectral fitting technique to
extract the CMBR anisotropies depends strongly on the noise level, which
in turn depends in a highly non-linear way on the frequencies observed.
Obviously, the number of frequency bands i.e. data points
must exceed the number of free parameters in the fit. If a given frequency
range is divided into N bands, then the extraction of anisotropies only
weakly depends on N as long as the former condition is met.
They also conclude that a larger frequency coverage
results in a better anisotropy extraction, but note that extending the
frequency range also can have the opposite effect.
If the frequency coverage is extended into regions where one or
more foreground components which gave negligible contributions
in the previous range become important, the amount of data needed to
constrain the fit can increase considerably.
Brandt et al. (1994) indicate that the reason for this
is the highly non-linear character of the extraction process. Attempts
to remove effects from an inadequately constrained foreground component
using this method can introduce errors many times larger than the
fluctuations in the component itself.
Tegmark & Efstathiou (1996)
describe a different approach towards the removal of foreground
effects from multi-frequency CMBR sky maps. They use a generalized Wiener
filtering method to recover CMBR anisotropies in the presence of contaminating
foregrounds from multifrequency data where the subtraction of
foreground templates is optimized in the multipole-frequency (
)
plane in Fourier space. This method exploits the fact that the foregrounds
have both spectral behaviour and angular power spectra which differ substantially
from that of the CMBR.
This very persuasive scheme however has a major weakness, by being very
dependent on the knowledge of the foregrounds, since the highly non-linear
spectral
behaviour of the foregrounds is treated as a linear problem.
If the frequency dependencies of the foregrounds were perfectly known and
independent of the position on the sky, this optimal Wiener filtering method
could recover the CMBR anisotropy power spectrum from observations with
10' angular resolution corresponding to multipoles of about
with an accuracy of about one tenth of a percent
(Tegmark & Efstathiou 1996).
Since, however, the foreground parameters are rather uncertain, and since they are definitely not independent of the position in the sky (see discussion of the different foregrounds below), the accuracy stated above is not directly achievable.
In this work the non-linear single-pixel spectral fitting approach used by Brandt et al. (1994) is applied but we do not restrict ourselves to the limited range of foreground parameters found in selected areas with the lowest possible foreground emission as did Brandt et al. (1994). Instead we apply the method with extreme values for the foreground parameters i.e. modelling almost the entire sky. Furthermore we investigate the effect of our limited knowledge of the foregrounds by fitting functions which differ substantially from those used to create the simulated observations. Thus the ability to recover the CMBR anisotropies in the presence of poorly known foregrounds which can be encountered in most of the sky is tested for the PLANCK CMBR mission, which is selected to be ESAs next medium sized satellite mission. The ability to overcome the difficulties induced by foregrounds is discussed for the PLANCK baseline as well as for alternate configurations in order to assess the question of the optimum set of frequency bands and detector systems. Also the Microwave Anisotropy Probe (MAP), selected as one of the NASA MIDEX missions, is modelled and discussed.