# Cross Sensor Simulation of Tomographic SAR Stacks
## 6 Conclusions  
In this paper, a new procedure for simulating a tomographic SAR stack was presented; the main free parameters of the system to be simulated are: sensors positions, central frequency and bandwidth. The target of interest comes from tomographic reconstruction based on actual data acquired by a real SAR system. The possibility of simulating SAR images based on real data is particularly convenient whenever the scene is complex and all physical phenomena must be respected rather than modeled. The two systems may be tuned on different central frequencies, have different bandwidths, cover different look angles and provide different vertical resolutions. Special attention was paid to account for all these differences resulting in a simple yet effective procedure. The algorithm here proposed relies on the identification of the spatial frequencies of the target made available by the real system and required by the simulated one. This analysis was made possible by interpreting SAR tomography in the wavenumber domain. The procedure here proposed allows for the desired geometry of acquisition to be properly simulated, in terms of both \(kz\) distribution and shape of the three-dimensional resolution cell. It must be observed that these properties cannot be imposed through a simple filtering of the original stack. The features of the resulting stack were discussed as well; in particular, it was shown that each image of simulated stack may be characterized by power fluctuations depending on the instability of the platform providing the original stack.  
The simulator here proposed was implemented and used to simulate the tomographic stack that will be provided by the forthcoming ESA BIOMASS mission; the input data coming from the TropiSAR  
Figure 12: Evolution of the sensitivity and correlation to the above ground biomass (AGB) of the tomographic power at 40 m above the ground level as the sampling of the baseline aperture drives away from the regular grid. The top panel shows the scatterplot relating tomographic power and AGB in case of perfectly regular sampling.  
airborne campaign. It was possible to evaluate the relationship between tomographic power and above ground biomass as a function of the baselines irregularities.  
Conceptualization, M.M.d. and S.T.; Methodology, M.M.d. and S.T.; Software, M.M.d. and S.T.; Validation, M.M.d. and S.T.; Formal Analysis, M.M.d. and S.T.; Investigation, M.M.d. and S.T.; Resources, S.T.; Data Curation, M.M.d.; Writing--Original Draft Preparation, M.M.d.; Writing--Review & Editing, M.M.d. and S.T.; Visualization, M.M.d.; Supervision, M.M.d. and S.T.; Project Administration, S.T.; Funding Acquisition, S.T.  
This research received no external funding.  
The authors wish to acknowledge the European Space Agency and the whole Level-2 team of the ESA BIOMASS mission for providing the framework in which this algorithm was developed.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} AGB & Above ground biomass \\ DBH & Diameter breast height \\ IRF & Impulse response function \\ SAR & Synthetic aperture radar \\ SLC & Single look complex \\ TomoSAR & Tomographic SAR \\ \end{tabular}