## 2 Understanding the Impact of RFI in Synthetic Aperture Microwave Radiometry Imagery  
Figures 7 to 10 show different SMOS L1b imagery corresponding to different RFI scenarios on March 3, 2010. In these figures, the hexagon in the (\(\xi\), \(\eta\)) domain corresponds to the full hexagonal period in which the synthetic image is formed by a kind of Fourier synthesis process from the (\(u\), \(v\)) visibility samples (cross-correlations from the signals collected by pairs of antennas) acquired over a hexagonal grid determined by the characteristic Y-array of the MIRAS instrument aboard the SMOS mission [7]. In the imaging process, replicas (\"aliases\") of the unit circle (\(\varsigma^{2}+\eta^{2}\!=\!1\), all directions in front of the array) appear centered at a distance \(2\!\cdot\!\lambda/(\!3\!\cdot\!d)\) from the origin, being \(d\) the spacing between consecutive antennas in the array. Since in MIRAS/SMOS \(d=0.875\)\(\lambda\), aliases are centered at \(1.32\!\leq\!2\) and overlap with the main image (centered at 0) restricting the instrument's alias-free field-of-view (FOV) [11]. In Figures 7 to 10, the dashed lines correspond to the unit circle and its aliases, and the solid lines to the Earth-sky horizon and its aliases.  
Plots (a) and (c) correspond to Y-polarization, while (b) and (d) to X-polarization, acquired sequentially every 1.2 s in dual-polarization mode. Figures 7 to 9 show a typical behavior in which  
Figure 6: Probability of RFI around the world as observed by SMOS (ascending and descending orbits): (**a**) January 7, 2010–March 16, 2010; (**b**) March 16, 2010–April 10, 2010 [10].  
RFI sources appear in the Earth-sky horizon (over the solid lines) and have a very well defined polarization characteristics: RFI sources are stronger at Y-polarization, than they are at X-polarization, which in this part of the FOV approximately correspond to the vertical and horizontal polarizations, respectively. It is worth noting that they are very variable with time (see Figures 8a _vs._8c, and Figure 9a _vs._9c, and to less extent Figures 9b _vs._9d). In some cases (Figure 9c) RFI is so strong that it completely corrupts the whole brightness temperature (BT) image, not only appearing as a strong point source, but eventually corrupting the denormalization coefficients of the visibility samples as well and corrupting the whole image. Figure 10 shows a snap-shot around the Caspian Sea with strong RFI sources, but most of them are in the alias regions.  
Figure 8: _Cont._  
Figure 9: RFI in SMOS (dual-pol mode): Scenario 3. Similar behavior to Figure 8 showing the polarization- and time-dependent behavior of RFI sources in consecutive snap-shots (1.2 s apart), present mostly at Y-pol (**a** and **c**), while at X-pol (**b** and **d**) they are less important. Note how some RFI sources have disappeared from (a) to (c), and from (b) to (d), while others appear or become stronger (**d**).  
As a consequence, it can be concluded that:  
1. Since RFI sources are usually very time-dependent and polarization-dependent as well, RFI detection and mitigation algorithms must operate on a snap-shot basis only, independently for each polarization. Averaging of RFI estimates from different snap-shots as a way to improve the estimated RFI power is, therefore, not possible; and
2. Since most RFI sources appear in the alias regions, but their impact extends over the \"alias-free\" FOV, RFI detection and mitigation algorithms must operate in the whole hexagonal period.