## 2 Overview of InSAR Methodology
### Noise Signals Corrupting SAR Interferograms  
This subsection shortly addresses the issue of characterizing the noise that corrupts the interferometric SAR signal. The focus is mostly on the noise signals that characterize the interferometric  
Figure 3: **(a)** Standard Deviation of the height measurement vs. the perpendicular baseline of the used interferometric data pairs for different values of the phase noise standard deviation (\(\pi/16\), \(\pi/8\), \(\pi/4\), \(\pi/2\) and \(\pi\)). **(b)** Standard Deviation of the height measurement vs. the phase noise standard deviation for different values of the InSAR perpendicular baseline (i.e., 125 m, 250 m, 500 m, 750 m and 1000 m). Plots refer to technical parameters of ENVISAT/ASAR radar sensor. phase. Accordingly, we neglect the effect of additional noise signals corrupting the complex-valued SAR signals that are ascribable to inaccurate pre-processing of SAR data. To this class belong the errors due to an incorrect focusing of SAR raw data [41; 46; 47; 48], the presence of uncompensated radio frequency interference (RFI) signatures in the focused SAR imagery [49; 50; 51], or other possible causes of disturbances in the complex SAR signal. These effects globally increase the level of noise in the generated interferograms but their full characterization is outside the aim of this review paper. Here, we only spend a few words about the effect of uncompensated RFI signals in the two interfering master and slave SAR acquisitions. RFI artefacts are due to electromagnetic interference signals emitted by civil and military communication systems at the operational radar frequency in many areas of the world [49; 50]. These artefacts are known to be more prominent at low frequency (L-band). For instance, SAR raw data collected by the Japanese L-band PALSAR systems are affected by such mistakes, which are mostly compensated during pre-processing and focusing of SAR data at ground stations before the delivering to users. At higher frequencies, RFI events have occurred but they are somewhat limited. ESA has reported some limited RFI events at C-band (although there is evidence they are increasing), whereas at X-band they have not been reported so frequently to represent a real problem [50]. Uncompensated RFI artefacts appear as various kinds of bright linear features in the azimuth-time range frequency domain [51]. Incoherent RFI is filtered out (at most) by the matched-filter used for focusing the SAR images. However, high-power RFI signals might be filtered during focusing step and they require proper RFI filters to be implemented [52; 53; 54]. Uncompensated RFI can increase the noise level in the phase signature of SAR images at L-band [55]. As said, however, the characterization of the RFI effects falls outside the limits of our investigation. Interested readers can find details on the RFI sources and the developed algorithms for their mitigation in SAR images, in [51] and the references listed therein. This subsection aims to get an estimate of the error-budget associated to the InSAR measurement of the terrain height topography. As said, the standard deviation of the height is linked to the standard deviation of the InSAR phase \(\sigma_{\varphi}\) by Equation (12). Our analysis moves from the basic observation that, in the interferometric processing, the conjugate multiplication of the two co-registered master and slave SAR images yields the complex interferogram:  
\[I=\hat{\gamma}_{1}\cdot\hat{\gamma}_{2}^{*}=|\hat{\gamma}_{1}\cdot\hat{\gamma}_ {2}^{*}|\exp[j\varphi] \tag{17}\]  
where \(\varphi\) is the interferometric phase. To further reduce the phase noise corrupting the interferometric phase, a multi-look operation [56] is usually carried out on the generated SAR interferograms, at the expenses of a worse spatial resolution of InSAR products. The multi-looking operation consists in the calculation, pixel-by-pixel, of the statistical expectation value of the complex interferogram, namely \(E[I]\).