## 3 The Receiver Acquisition Chain and the Ad Hoc Back-End of the BIRALET Radar
### Transmitter Architecture of the TRF Antenna Based on the USRP-2954R Board  
As mentioned above, the new back-end of the BIRALET radar, funded and developed under the European Space Surveillance and Tracking (EUSST) program [12], is based on a National Instrument USRP-2954R board. The same USRP-2954R board has been installed on both the TRF and SRT antennas in order to transmit a well-known signal (that will be explained in more detail below) which permits slant-range and Doppler shift measurements, simultaneously, according to the EUSST program requirements. In detail, the USRP-2954R board is part of the transmitter architecture, which is shown in Figure 4, with the aim of generating the I/Q samples of the waveform to send out. The waveform is chosen by the operator, using the Operator workstation with a dedicated Graphical User Interface (GUI) and a waveform generator (see Figure 4), on the basis of the specifications required by the observation scenario. The I/Q samples are then converted into an analogue signal by two 16-bit DACs and up-converted by the I/Q up-converter chip, in order to have a signal in the frequency range 410-415 MHz, indicated as ultra-high frequency (UHF) signal in the block diagram of Figure 4. This UHF signal is then amplified thanks to the up to 10 kW power amplifier of TRF, described in Section 2.1 (see Figure 1b). Finally, the UHF signal is transmitted towards the expected target position (considering the antenna pointing coordinates predicted propagating the TLE with the SGP4 software [9]). The overall performances of the radar are also determined by the synchronization accuracy of the TRF and SRT systems. The receiver and the transmitter are synchronized in time and frequency using the GPS one pulse per second (1 PPS) and the 10 MHz reference signals of the GPSDO module of the USRP-2954R board. In particular, the 10 MHz signal is used as reference for all down-conversions and sampling frequency generation (ensuring no drift between transmitter and receiver). On the other hand, the 1 PPS signal is used to start the acquisition/generation between receiver/transmitter, simultaneously. The GPSDO module of the USRP-2954R board guarantees a maximum error of \(10^{-7}\) s, that means 30 m in distance, according to the EUSST program specifications. The system has been developed with the aim to detect debris at a maximum range of 3000 km with an accuracy of about 30 m (as explained in the previous lines) and to perform also Doppler shift measurements with an accuracy of few Hertz. For this reason, the waveform transmitted by TRF is a mixed signal composed of a frequency modulation continuous wave (FMCW) signal, known better as chirp, plus a CW tone, with an overall bandwidth of 5 MHz, as shown in Figure 5.  
In particular, the transmitted signal is set to a central frequency of 412.23 MHz, with the CW tone generated with an offset frequency of \(-2.145\) MHz from the central one. Regarding the chirp, it is a down-chirp in the range between 410.43 MHz and 414.03 MHz, with a pulse repetition interval (PRI) of 20 ms and a pulse repetition frequency (PRF) of 50 Hz. This guarantees a slant-range measurement of objects at distances up to 3000 km, as shown by the following formula [32]:  
\[\mathrm{PRF}\ =\ \frac{c}{2d}\ \approx\ 50\ \mathrm{Hz} \tag{1}\]  
Figure 4: Transmitter architecture of the TRF antenna based on the USRP-2954R board. Figure 5: Transmitter architecture of the TRF antenna based on the USRP-2954R board. where \(c\) is the speed of light and d is the maximum range, in this case equal to 3000 km. This value of PRF prevents the possibility of Doppler measurements using only a pulsed signal, because typical space debris Doppler shift values in LEO are in the range of a few kilohertz (in P-band), values greater than our PRF. For this reason, the system transmits a mixed signal based on the chirp plus the CW tone, in order to work as a pulsed radar (for slant-range measurements) and as a CW radar (for Doppler shift measurements).