## 3 Sounding System
### Data Frame Design  
The correct definition of the data frame was essential for the experiment. We defined a level one frame of the Open Systems Interconnection model (OSI model), that consists of a physical structure of the transmitted data. We named this level one frame the \"data frame\". A poor definition of the data frame could imply intersymbol interference (ISI) and signal-to-noise ratio (SNR) fadings. Two different data frames were used to perform our tests, which were designed on the basis of earlier studies and the soundings of the ionospheric channel [27]. Figure 5 displays a graphical representation of the first type of signal sent (Frame number 1), which was composed by a total of 50 data groups (we named these structures \"packets\"), each formed by three different modulations: Phase-shift keying (PSK), frequency-shift keying (FSK), and quadrature amplitude modulation  
Figure 4: Block diagram of the phasing network. (QAM). All the packets added a preamble that aims to mitigate the negative effects of the ionospheric channel and the frequency deviation between the transmitter and the receiver (the preamble is used to analyze and compensate the received signal's phase and amplitude via software). This preamble consisted of a 600 Hz tone and a sixth-order PN sequence, and it was located at the beginning of each of the 50 transmitted packets. The sampling speed of the system was 100 kS/s. Figure 5 exhibits the data frame's duration at both the sample and time levels. Analyzing all the packet segments and their respective lengths, it can be observed that the 600 Hz tone's duration was 6000 samples, the PN's sequence duration was 512 samples, and the modulated data transmitted corresponded to 10,500 samples. Furthermore, every data block contained 250 symbols with a resample of 42 (10,500 samples divided by 250 symbols), resulting in a bandwidth of 2.38 kHz per data block. On the other hand, the bandwidth used in the PNs was 12 kHz. This is because our frame had to respect the coherence time of the ionospheric channel, and in the design of the data frame, we did not want the PN sequences to have a significant influence. Our team decided to make the pseudo-random sequences shorter in time, resulting in a bandwidth of 12 kHz. The data frame designed had a total duration of 510.36 ms, which was less than the most restrictive coherence time of the ionospheric channel (1.46 s) [28]. The total duration of the 50 packets sent was 25.518 s.  
The first tone of the data frame was preceded by an extra block made of a PN sequence, intended to synchronize the system sample-wise. All the data frames received were stored to be treated afterwards. The processing applied to each one of the data frames is explained as follows: First of all, the system identifies the data frame by correlating the signal received with the value of the PN sequence transmitted. If there are equispaced peaks in the result of this correlation, a data frame is identified. Once the system identifies the data frame, the first block encountered is the 600 Hz tone. This tone of a duration of 60 ms is key to identify and correct the channel's Doppler shift. In our system, the Doppler shift could not be studied as a frequency offset, as the Red Pitaya platform clocks have a low stability and create a relative frequency-drift effect that is higher than the ionospheric channel. Measures of the platform show that the maximum value of the frequency offset received, due to the low stability clocks, is about  
Figure 5: Data frame design [27]. \(\pm\)20 Hz [29]. The 600 Hz tone added to the data frame helps in identifying the frequency instability inserted by its variations between 580 and 620 Hz, approximately. Once the frequency offset is calculated, the received signal is corrected and this frequency offset is compensated for a correct demodulation of the signal. The second block included in the data frame's preamble is the sixth-order PN sequence, whose function is to identify the start of the modulated data.