# Identification of C-Band Radio Frequency Interferences from Sentinel-1 Data
## 4 Sensitivity
In order to compare the two detectors, we have implemented the Z test in (2) with a very conservative _threshold of 4\(\sigma\)_, which was tuned to the data to exclude false alarms, then we integrated the probability of tails exceeding the threshold:  
\[Z=\int_{\mu+4\sigma}^{\infty}p\Big{(}H_{f}\Big{)}dH_{f} \tag{9}\]  
A comparison between the factor Z and the KL divergence, K, is provided in the bidimensional histogram in Figure 8a, whereas the two values sorted for all the bursts are shown in Figure 8b. In both cases it is possible to notice a two-class behavior, where the thresholds separating the data most likely to be RFI from the good one have been found experimentally from the marginal PDF, plotted on the right, as \(\log_{10}(Z_{th})=-3\) and \(\log_{10}(K_{th})=-1.6\). In order to appreciate the complementarity between Z and K test, we have plotted a set of histograms exceeding the threshold for K, but not for Z (Figure 9a), and vice versa (Figure 9b). In the total of 32,000 bursts, 3800 were classified RFI according to K, then 12% and 4300 according to Z, 14%, whereas the union of K and Z classified 17% of the bursts. Figure 8: (a) Bidimensional histogram, counting the power spectra as function of Kullback-Leibler divergence (K), horizontal, and Fisher figure of merit, (Z), vertical, both in log scale. The two classes, marked as noise and RFI, can be separated better in the 2D than by a single figure of merit, either Z, or K; (b) Marginal histograms representing the RFI pdf with respect to Fisher and KL divergence. \[P_{n}=K_{B}\cdot T_{S}\cdot B_{RFI}, \tag{5}\]0 Example of histograms where RFI can be identified only by KL divergence (a); and of RFI that can be identified by Fisher Z test (b). This confirm the quality of \(Z\) test, however, suggests the use of both (at practically the same cost) if searching for very small RFI, like to RLAN [13]. A map of RFI power has been computed by averaging over the rank echoes and over successive passes, both ascending and descending. The map, shown in Figure 10, reports the highest values measured in the whole spectrum. Detection has been made by assuming a very low threshold in order to visualize the slightest RFI, which would include many false alarms. However, one can appreciate that there is a nearly homogeneous background floor below 0 dBm. The power seems loosely correlated with urban areas, therefore not due to RLAN, whereas there are few occurrences co-located with Radar installations, placed as pinpoints in the map, from those listed in [16]. That power map does not reproduce the spectral occurrence of the RFI. Therefore, we represented in Figure 11, the cumulated histograms of detected RFI power, normalized with respect to S1 noise power, for each frequency bin. The histograms have been normalized so that the figure shows, for each frequency bin, the probability that a certain power level is exceeded. One can notice that, in the majority of the cases, when they are present, the RFI contribute as an additional noise factor less than a figure five, that corresponds to an equivalent temperature of \(\sim\)4000 K.  
\[P_{n}=K_{B}\cdot T_{S}\cdot B_{RFI}, \tag{5}\]1 Map of RFI power, averaged in approximately 6 ms. The label superposed marks a part of weather Radar listed in [16].