# Identification of C-Band Radio Frequency Interferences from Sentinel-1 Data
## 3 RFI Detection and Estimation  
The estimation of RFI is carried out according to the method summarized in Figure 3. It comprises a calibration step (on the left in the figure), that runs once in the long term, by exploiting a large amount of data, and an estimation step, on the right, performed on each single data-take. The aim of calibration is the identification of spurious tones and the precise receiver power spectrum profile. In principle, all the combinations of swaths, polarizations, sensors (S1A and S1B) and modes (IW and EW) should be calibrated. In the present study, we focused to IW mode and S1A sensor: the power spectra for the three sub-swaths and the two polarizations are plotted in Figure 4, after averaging over 10,000 bursts in each of the two polarizations, acquired all over the world from November 2016, up to April 2017. S1 demonstrated very good stability in gain, ripples and spurious locations, and this suggest the use of noise data to speed up calibration. A total of 100-200 spectral samples of the whole \(\sim\)20,000, were found affected by spurious tones, which can be easily detected by a median filter. Once removed, the spectral profiles are estimated and stored. Figure 4: Mean power spectrum density, dB, measured from the “rank” pulses at beginning of each swaths in V (_a,c,e_) and H (_b,d,f_) polarizations, for sub-swaths IW1 (_a,b_), _IW2 (c,d_) and IW3 (_e,f_), averaged on 10,000 bursts. Notice the spurious tones and the ripples. Figure 3: Schematic block diagram for the identification of RFI. In the processing step, first the data spectrogram _H(f,t)_ is estimated as the squared amplitude of the Fourier Transform of each echo. The frequencies corresponding to the spurious previously identified are nulled. Ripples are then removed in both frequency and time by modelling the expectation of the spectrogram as:  
\[E[H(f)]=H_{0}(f)\times G(t), \tag{1}\]  
where _H0(f)_ is the mean power spectrum estimated by the calibration step, and _G(t)_ is the along track ripple pattern, in time domain, as the one shown in Figure 2 on the bottom panel. This second term is not stable in time, as it appears in Figure 2 on the middle panel, and it needs to be estimated from the data. The estimate is carried out by first compensating the range spectra, by the inverse profile 1/_H0(f)_, and then computing the spectral median for each time. The median is robust respect to the RFI that can be in the dataset, however, for further improving RFI rejection, a second order polynomial Savitzky-Golay filter [10] is applied to the along-track profile to derive the estimate of _G(t)_. An example of a data spectrogram prior and after compensating for the frequency and time-domain ripples is shown in Figure 5. The spectrogram has already been averaged in frequency by a multi-look factor of 100, to reduce noise fluctuation, then enhancing the detection of the slightest RFI. Detection is performed by a combination of the one tailed [PERSON]'s Z test [6]:  
\[Z=\frac{H_{f}-E\Big{[}H_{f}\Big{]}}{VAR\Big{[}H_{f}\Big{]}}, \tag{2}\]  
\(H_{f}\) being the power spectrum, and the use Kullback-Leibler (KL) divergence [11], proposed here:  
\[K=\int p\Big{(}H_{f}\Big{)}\log\Bigg{(}\frac{p\Big{(}H_{f}\Big{)}}{p_{fit} \Big{(}H_{f}\Big{)}}\Bigg{)}dH_{f} \tag{3}\]  
The first detector, (2), finds those extremal peaks, say isolated RFI with powers much stronger than noise one. The KL based detector, in (3), measures the mean distance between the logarithms of the actual power spectrum density distribution, _p(H)_, and the Normal one, _pfit_. This corresponds to the maximum-likelihood hypothesis testing for non-Normal distributed data [12], and is sensitive to maybe many RFI samples of very low power, that is the case of RLAN [13], distributed RFI, or other  
Figure 5: Example of a spectrogram of noise data before (**a**) and after (**b**) compensation for the ripples in frequency and time. The residual along-track ripple is less than 0.1 dB. factors affecting the raw data quality.