## 4 Data Set Generation and Processing
### GNSS Signal and Playback with Specific Bit-Depth  
The data set is created using recorded GNSS signals from an amplified roof antenna (to ensure adequate reception strength) installed in the JRC premises. Then, real-world signal and not simulated signals are used for the study. A 25 dB Low Noise Amplifier (LNA), which includes a GPS L1 band RF filter as well, is introduced to further bolster the signal level, mitigating potential noise issues. We consider the GPS L1 band even if the data set includes Galileo E1. To power this external LNA, a bias-tee and a 5V Direct Current (DC) power supply are incorporated, ensuring its functionality while simultaneously DC blocking the RF to the output. This step prevents any unwanted DC components from reaching the subsequent component in the signal processing chain (e.g., X410's RF input), maintaining signal integrity. In the X410 SDR, the RF analog signal undergoes conversion to the digital domain with a sampling rate of 10 MSamples/Sec using a bandwidth of 10 MHz and bit-depth of 16 bits. This sampling rate and bit-depth provide sufficient resolution to capture the relevant information within the chosen GPS L1 and Galileo E1 bands and keep the recorded files small enough. See [18; 19] for an analysis of the bit-depth impact in GNSS recording and playback. The center frequency is set to 1.57542 GHz, encompassing both the L1 and E1 bands and the maximum gain of 59 dB was used in the LNA of the X410 (to ensure adequate signal strength for optimal recording). An extended recording duration of 30 min was employed. This timeframe allows for the observation of signal variations arising from environmental fluctuations, satellite movements, and potential interference events. The next step is to create a representation of the GNSS signal for playback with different bit-depths, which is one of the main objectives of the study presented in this paper. This was achieved with a custom LabVIEW application designed specifically for this purpose to synthesize signal files at various bit-depths: 8, 4, 2, and 1 bit-depths starting from the original 30 min file recorded at 16 bits. The algorithm implemented with LabVIEW discards less significant bits to achieve the desired bit-depth. For example, transitioning from 16 to 8 bits involves eliminating the 8 least significant bits while retaining the most significant 8 bits in the output file. The algorithm was designed to preserve negative numbers with two's complement: the bit reduction may impact negative values, essential for In-phase and Quadrature component (IQ) signals. By using this representation, discarding the Least Significant Bits (LSBs) preserves the sign bit and, consequently, the negative values embedded within the signal. This ensures accurate representation of both positive and negative components, which is crucial for faithful signal reconstruction. On the other hand, discarding LSBs effectively reduces the signal's dynamic range. To maintain accurate representation after this reduction, the original signal must possess sufficient power in its Most Significant Bits (MSBs), which is the reason why the maximum gain of 59 dB was used. Some background information on the USRP digital representation and the two's complement is provided here because it is a core part of the bit-depth aspect of this study. USRPs handle numbers in integer binary format, using 16-bit sequences of 0 s and 1 s. An I16 integer (signed 16-bit integer) can represent values from \(-\)32,768 to 32,767. Each bit has a specific weight based on its position, starting with 2\({}^{0}\) for the least significant bit (LSB) and increasing by a power of 2 for each bit to the left. The positive numbers are directly represented by their binary equivalent (e.g., the decimal number 10 in 16-bit binary is 0000 0000 1010 with \(0\times 2^{0}+1\times 2^{1}+0\times 2^{2}+1\times 2^{3}+0\times 2^{4}+0 \times 2^{5}+0\times 2^{6}+0\times 2^{7}\) + 0 \(\times\)\(2^{8}+0\times 2^{9}+0\times 2^{10}+0\times 2^{11}+0\times 2^{12}+0\times 2^{13}+0 \times 2^{14}+0\times 2^{15}=10\) dec).