## 7 Conclusions and Future Work  
In this work, we have derived a theoretical precision bound for the GNSS-R coherent reflection scenario, for ground-based static receivers. The CRB has been derived first for observation times of up to 1 s (short observation intervals), and later on, we have extended this bound for long observation intervals of up to hundreds of seconds, where the satellite elevation angle was changing during the observation time. The CRB was computed for GPS and Galileo signals with different bandwidths and different modulations, i.e., BPSK, CBOC (6,1,1/11) and AltBOC (15,10). For short observation times and \(\Delta\rho>\rho_{chip}\), we obtained simple analytic expressions of the CRB for the parameters of interest. Later on, the CRB was extended for long observation times by using the FIM transformation approach. The approach followed can easily accommodate different models for the surface's reflection coefficient \(\Gamma\). In this paper, we selected the Z-L model to describe \(\Gamma\), and then, we have computed the CRB as a function of satellite elevation spans of different sizes covered during the observation time. The impact of the antenna radiation pattern was considered within the modeling of \(\Gamma\). The specific case that we have studied (receiver height, antenna pattern and surface properties) is an example selected to understand the dependency of the CRB on the signal properties and the scenario parameters. For short observation times of up to 1 s, the results obtained have shown that even for antennas designed to mitigate multipath and these antennas being installed with their boresight perpendicular to the ground, it is still theoretically possible to obtain meter precision (or even decimeter in the case of using the full Galileo E5) given a front-end with a large enough bandwidth. In the case of long observation intervals, the CRB computed confirms the link between the variation of the satellite elevation and the achievable precision. Moreover, the CRB evaluation presented confirms the cm level precision that has been reported by many works, e.g., [29; 32; 38; 41; 77; 78; 79], among others, some of them using standard GNSS geodetic stations [80]. Reasonable accuracy was obtained in the estimation (joint) of \(\varepsilon_{r}\) and \(\sigma\) over observation times covering satellite elevation variations above \(10^{\circ}\). According to the CRB results computed, the modernized GNSS signals considered in this work, i.e., GPS L5, Galileo E1 and Galileo E5, can potentially provide better estimation precision for all of the parameters when compared to the GPS L1. In this work, the CRB results presented have been mainly focused on the \(h\) estimation. Using the approach described in this paper, further study of the CRB for the parameters related to the reflection surface's properties is planned, in order to characterize the precision achievable in other GNSS-R applications, such as soil moisture determination. In addition, two main future activities are planned to continue with the work described in this paper: first, to further explore the CRB for similar scenarios with different models for the \(\Gamma\) and, second, to compute the CRB for the scenarios where experimental campaigns were carried out, as a way to fully validate the bound obtained and assess the performance of the techniques used. As a final remark, we want to point out that a practical limitation of the precision bounds provided in this paper is the fact that our signal model (for coherent reflection) might not accurately match the true reflected signal. In many practical scenarios, the reflected signal will be better described as a combination of the coherent and incoherent components. The importance of each component will depend on the considered scenario. In any case, the CRB results provided in this paper will lower bound those obtained with a signal model considering also the presence of incoherent reflections.