## 1 Introduction
Aside form specific GNSS-R instruments, multiple research works have demonstrated that in some scenarios, it is possible to process the data provided by static ground-based GNSS receivers, such as the ones used for geodetic applications, to directly perform GNSS-R. Under the assumption of a strong enough specular reflection, such that the phase coherence is partially preserved, it is possible to observe the interference between the line-of-sight (LOS) signal and the reflected signal. This interference can provide information about the geometry of the scenario and the properties of the reflection surface. A GNSS-R technique that exploits this information is the interference pattern technique or GNSS multipath reflectometry (GNSS-MR) (The two terms are arguably interchangeable. Nonetheless, some authors differentiate them by associating GNSS-MR with the cases where most of the interfering signals are co-polar (right-hand circularly polarized (RHCP)), while they use IPT for dedicated experiments, with dedicated experiments and sometimes a different polarization basis [1]). Either received by the same antenna, or combined later, if the two signal components have a delay difference shorter than a single modulation's chip period, an interference pattern on the amplitude of the composite signal will be observed with the change of the GNSS satellite elevation with respect to the receiver. This interference pattern is mirrored into the receiver's signal-to-noise ratio (SNR) estimate for the receiver channel tracking that signal [55; 56; 7]. By applying the IPT to the SNR data provided by the already deployed GNSS receivers, belonging to geodetic networks, it is possible to scout the surface surrounding the sites where these receivers are installed in a very cost-effective manner. Several snow and soil moisture monitoring experiments have been conducted using these data and the IPT, as well as some calm water altimetry experiments. However, to the best of our knowledge, little work has been published trying to characterize the estimation precision of these GNSS-R scenarios/techniques, where long observation times are considered [57; 58]. The works previously mentioned, together with others such as [59; 60], have focused on GNSS (mostly GPS) ocean scattered signals, which are mostly incoherent, i.e., with significant speckle noise. In an attempt to fill this existing gap, in this paper, we make use of the CRB to provide the theoretical estimation bound for scenarios dominated by coherent reflection when the LOS and the reflected signals are received by the same antenna, both over short and long observation periods and for different GNSS signals: GPS L1 C/A and L5 and Galileo E1 and E5. In our previous work [57; 58], the CRB was computed considering the samples at the output of the receiver's prompt correlator during the tracking of the composite signal (i.e., LOS and the reflected component) as our measurements. In this paper, we assume no specific architecture for the GNSS-R receiver. The CRB is derived for the signal model corresponding to the samples obtained at the output of the receiver front-end. This implies that we are now considering all of the information contained in the received signal when computing the CRB, while in previous works, some information could be lost due to the processing of the received signal. Thus, the CRB expressions derived in this paper represent a more fundamental performance bound, independent of the GNSS receiver architecture considered. This paper is organized as follows. Section 2 describes the GNSS-R scenario under consideration, summarizing all of the relevant assumptions made and later introducing the corresponding signal model for this scenario. Section 3 contains the derivation of the CRB for the LOS and an arbitrary number of multipath components over short measurement intervals, which is further adapted to our specific scenario using the Fisher information matrix (FIM) transformation approach.