## 4 Equivalent Block Diagrams for GNSS and Spoofing Signals
### Equivalent Transmitter Block Diagrams  
The equivalent block diagrams of a GNSS (e,g., Galileo) satellite transmitter and of a spoofer GNSS transmitter are depicted in Figure 7a,b, respectively. These summarizing block diagrams help in identifying at a glance the places where the different HW impairments discussed in Section 3 appear. For example, phase noises can appear in each of the transmitter blocks, such as the clock unit, Digital-to-Analog Converter (DAC), up-conversion unit/mixer units and power amplifier. I/Q imbalances are typically only present in the up-conversion unit/mixer units. Non-linearities can appear in the DAC and PA units. Different blocks have different noise levels: for example, the phase noise pn_s1 (s stands for satellite here) from the clock unit is not the same phase noise as in the up-conversion unit (phase noise pn_s2), etc. Moreover, the phase noise pn_s1 from the GNSS transmitter is different from the phase noise pn_i1 from spoofer (i stands for interferer, here), and the same is valid for all the different transmitter ((s1, s2, s3,...) and spoofer (i1, i2,...) features depicted in Figure 7a,b. The non-linearity _nl_s1_ effect in the Galileo clock unit (Figure 7a) appeared due to the additional DAC units employed in the Galileo clock unit [51]. Such additional DACs are, however, unlikely to be used in a spoofer, and thus the local oscillator (LO) of a spoofer ( Figure 7b) does not exhibit additional non-linearity effects.  
The GNSS power amplifier is typically an HPA, while the spoofer power amplifier is typically an LPA, as discussed in Section 3. The levels of various transmitter impairments are not known for GNSS transmitters and need to be learnt via the RFF feature extractors and classifiers discussed next, and based on training data. High-quality training data would need GNSS samples at various sampling rates (i.e., corresponding to both low-end and high-end receivers), for the duration of several milliseconds for each training sequence, and typically thousands of training sequences for robust RFF results. This may represent one of the main challenges or bottlenecks of RFF approaches at the pre-correlation level: for example, 2 ms of data sampled at a moderate sampling rate of 24 Mbps has 24,000 complex-valued samples per each sequence in the training data. Assuming 1000 sequences in the training database and data saved on 8-bit per real sample, this would require 0.48 GB of data in each training sequence. The 2 ms of data pieces per training sequence was shown as an example. We expect that several milliseconds of observations of I/Q raw data will be needed. As a rule of thumb, GNSS signal acquisition is usually performed using at least 10 ms. The needed size for the training databases increases with the increased processing time, with the increased sampling rate, and with the increased amount of sequences in the training database. Through some of the feature-extraction methods discussed in Section 5, one can reduce the dimensionality of the data, for example using images instead of matrices, or applying principal component analysis (PCA) methods to reduce the data dimensionality. More about PCA will be discussed in Section 6.