## 1 Introduction  
The European Space Agency (ESA) mission \"Soil Moisture and Ocean Salinity\" (SMOS) was successfully launched on November the 2, 2009. Its main objectives are the determination of Soil Moisture (SM) over land [1] and Sea Surface Salinity (SSS) over the oceans [2], with an accuracy of 0.04 m\({}^{3}\)/m\({}^{3}\) every three days with a spatial resolution of 50 km [3] (R-4.6.1-002 to 004) at level 2, and 0.1 psu every 10 days with a spatial resolution of 200 km [3] (G-4.7.2-005) at level 3. Unfortunately, the first SMOS images [4] using calibration data from the on-ground Image Validation Tests showed a large amount of radio-frequency interference (RFI), specially over land in Europe and Asia, but in some small areas of Africa and Greenland as well (Figure 1). A refined analysis using on-board calibration data allowed to \"focus\" the brightness temperature images (_i.e._, get sharper details). However, even though RFI regions became more localized, the amount of RFI was on many occasions so large that the tails of the \"impulse response\" of a quasi-point RFI source (see Figures 15b and 21) extended over the whole image, hampering the retrieval of geophysical parameters, mainly over land, but not exclusively (Figure 2). Figure 1: First data (calibrated using ground measurements) sent by the MIRAS instrument on European Space Agency’s (ESA) Soil Moisture and Ocean Salinity (SMOS) satellite [4], on March 16, 2010. In [6], a theoretical study of the impact of RFI in SMOS demonstrated that, when the measured normalized cross-correlations (\(\mu\)) among all pairs of signals collected by the interferometric radiometer array are small, for a sinusoidal RFI source in the (\(\zeta_{i}\), \(\eta_{i}\)) = (sin \(\theta_{i}\)\(\cdot\)cos \(\Phi_{i}\), sin \(\theta_{i}\)\(\cdot\)sin \(\Phi_{i}\)) direction, and power \(A_{i}^{2}\)/2, the error is approximately a correlation offset given by:  
\[\mu_{12}^{\text{offset}}\approx\frac{\text{A}_{i}^{2}}{\sigma^{2}}\cos(\phi_{i} )\cdot e^{i\phi}\cdot e^{-i\cdot 2\pi(u_{12}\zeta_{i}+v_{12}\eta_{i})} \tag{1}\]  
where \(\Phi_{i}\) is the RFI signal's phase, \(\sigma^{2}\) is the noise power, (\(u_{12}\), \(v_{12}\)) is the baseline formed by the two antennas whose signals are being correlated, and the (\(\zeta_{i}\), \(\eta_{i}\)) directions are expressed in the director cosines domain with respect to the X and Y axes of the antenna array (+Z being normal to the array plane), where the Fourier synthesis process forms the synthetic brightness temperature image [7]. Figure 3 shows plots of \(\mu_{r,12}\) (for \(\Phi_{i}\)= 0\({}^{\circ}\)), and for different values of 20\(\cdot\)log(\(A\)/\(\sigma\)). Note that, the error in the measured normalized visibilities (\(e_{\mu}\)) is mainly an offset term (Equation 1) whose maximum amplitude is approximately equal to \(\left(A\)/\(\sigma\right)^{2}\). Therefore, in the synthetic aperture brightness temperature image the RFI source will appear as a point source in the (\(\zeta_{i}\), \(\eta_{i}\)) direction, as determined by the phase term in the second exponential term of Equation 1.  
An analysis of the potential sources of RFI and their impact was also performed [6], including:  
1. nearby emissions from L-band radars, non-GSO (non Geo-Stationary Orbit) and GSO MSS (Geo-Stationary Orbit Mobile Satellite Services),
2. harmonics of lower frequency emissions, and
3. possible jamming, which may or may not be deliberately generated. Table 1 from [6] summarizes the potential interferences from nearby emissions and harmonics that can affect an L-band synthetic aperture radiometer. From all possible interferences, the most important ones were predicted to be those generated by:  
Figure 2: Image over Europe after in-orbit calibration [5]. Note that, as compared to Figure 1, radio-frequency interference (RFI) sources are focused, appearing as dots. 1.