# Near-Nyquist-Limit Optical Communication and Ranging Method Based on Waveform Matched PPM
## 5 Experimental Results  
In order to verify the feasibility of the proposed method, we have built a hardware platform for real world tests. A diagram and a photograph of the hardware platform are given in Figure 8.2 is the initiator of the system. The uplink PPM electrical signal sent by the ground terminal is converted into a 1550 nm laser signal by the laser diode transmitter placed in the laser source modulation module. The laser signal is transmitted in the optical fiber and detected into an electrical signal by SPAD. The electrical signal is sent to the space terminal, which samples the uplink signal and performs digital signal processing to receive communication and ranging information. The frequency reference provides a GPS timing clock and time information for the ground terminal and the space terminal. Similarly, the downlink PPM signal sent by the space terminal is converted into the laser signal, which is transmitted in optical fiber and detected by SNSPD array. The ground terminal collects the downlink PPM signal with ADC and processes the sampled digital signal to obtain communication and ranging information.  
The variable optical attenuator FVA-600 is applied to simulate the atmospheric attenuation. The atmospheric attenuation [34] can be calculated using  
\[A_{atm}=\alpha_{10}(V)\times l\quad[\mathrm{dB}], \tag{13}\]  
where \(\alpha_{10}(V)\) is an atmospheric attenuation coefficient, \(V\) is visibility in kilometers, and \(l\) is the transmission distance in kilometers. In the experiment, the emission power of the laser was 10 dBm. We set the attenuation value to 100 dB. The equivalent transmission distance exceeds 100,654 km when \(V\) is greater than 750 km.  
A small number of control commands were transmitted through the uplink, for deep-space exploration spacecraft, and a large amount of research data obtained by the probe were transmitted through the downlink. Therefore, the demand for downlink communication speed was much higher than that for uplink communication speed. The hardware system depicted in Figure 8 applied \(R_{s}=311.04\) Mslot/s for the uplink and \(R_{s}=4.97664\) Gslot/s for the downlink, respectively, with an oversampling factor near the Nyquist limit.  
Figure 7: BER simulation results (\(F_{s}=2.5\) Gsps).  
The video transmission results are given in Figure 9, which displays the local video (left) and the received video (right). Real-time video transmission can be carried out between the two terminals to visually demonstrate the communication quality.  
The ranging performances of the system at different distances were tested. Four distance scenarios were selected for statistics, 0.5, 1.5, 3, and 5 m, respectively. The ranging results are presented in Figure 10. As shown, a blue dot resulted from a single ranging, and the red line is the average of total single ranging results. The statistics for the ranging results are displayed in Table 1. The RMSE(\(\sigma_{R}\)) was calculated with the total data observed. It can be seen that the RMSE(\(\sigma_{R}\)) was less than 0.4 mm at each set distance. Some experimental data show low frequency variation due to instability of the frequency reference module.  
\begin{table}
\begin{tabular}{c c c c c} \hline True Distance/cm & 50 & 150 & 300 & 500 \\ \hline Mean of ranging value/cm & 49.995 & 150.021 & 300.013 & 500.011 \\ RMSE/mm & 0.23 & 0.37 & 0.27 & 0.38 \\ \hline \end{tabular}
\end{table}
Table 1: RMSE(\(\sigma_{R}\)) results at different distances.  
Figure 8: Structure of the hardware platform: (**a**) Topology of the hardware platform. (**b**) Photograph of the hardware platform.  
Figure 10: Ranging results at different distances. (**a**) True distance is 50 cm. (**b**) True distance is 150 cm. (**c**) True distance is 300 cm. (**d**) True distance is 500 cm.  
Figure 9: Video transmission experiment results: (**a**) Experimental results at the ground terminal. (**b**) Experimental results at the space terminal. The local video is on the left and the received video is on the right in each subplot.