# Cross Sensor Simulation of Tomographic SAR Stacks
## 1 Introduction  
The design of any spaceborne synthetic aperture radar (SAR) mission poses several challenges, among others the definition of the orbital path or the amount of propellent on board. The vast majority of the system parameters cannot be adjusted after the launch, so their tuning cannot take advantage of the feedback provided by the first acquisitions. This issue, together with the great investment of resources, drives the attention on the reduction of hazards, namely on _derisking_. Usually, both technological choices and image formation can be properly modeled or simulated. End-to-end descriptions of the acquisition system are developed and can provide the expected output given any input target. Recently, several algorithms have been recently developed for this purpose. Efforts have been made to reduce the computational burden of the simulator especially whenever non-straight orbits are considered [1; 2].The electromagnetic features of the structures to be simulated have been studied too, geometrical optics, physical optics and full wave approaches have been proposed [3; 4]. Furthermore, ground topography and interferometric processing have been explored [3; 5]. These approaches are particularly effective whenever the reference targets are simple (their response is almost known) and the processing chain, up to parameters retrieval, is consolidated. These two conditions are not met in the case of complex natural media and tomographic [6; 7] measurements. Targets such as snowpacks [8], glaciers [9] and unmanaged forests [10; 11; 12] are currently under investigation andany model takes the risk of masking meaningful features. In particular, the analysis of dense forests is the main driver of the forthcoming ESA BIOMASS mission [13] whose launch is expected in 2022. The penetration capability of its P-band signal is expected to provide an insight of many environments as deserts and glaciers in addition to any forests (refer to [14] for further details). Acquisitions on vegetated areas, most importantly on tropical regions, will be processed to generate a map of Above Ground Biomass (AGB) at global scale. Tropical forests are very hard to reduce to a small number of significant elements, moreover the relationship between AGB and radar backscatter is not yet fully understood [15; 16]. As a consequence, assessing the impact of any change in BIOMASS system parameters on its capability to retrieve the AGB amount is not trivial and requires a specific strategy. The method here proposed relies on the exploitation of real tomographic SAR images gathered on forests by airborne systems for obtaining a description of the scene; this latter being recovered by means of the back-projection [17] algorithm. Then, the 3D reconstruction of the forest is projected into a tomographic stack in accordance with the geometry of acquisition and radar parameters of the spaceborne system to be simulated. This simple approach requires special care due to the different wavenumbers that gave rise to the airborne radar echo and that are illuminated by the simulated spaceborne system. Also, the three dimensional resolution cells of the two tomographic systems differ as regards their size (dependent on the bandwidth) but also their orientation because of the different acquisition geometry. This latter issue in particular cannot be accounted for by simply filtering the real airborne data stack. The simulator here proposed has been used to estimate the spaceborne tomographic reconstruction provided by the BIOMASS system. Particular attention has been paid to the power fluctuations due to inaccurate orbital control, that is to irregular baseline sampling. This fluctuations impact on the capability of the BIOMASS system of producing measurements to be used as proxy for AGB estimates. The deterioration of the correlation with AGB of tomographic derived quantities could be observed as a function of orbital inaccuracies.