# Free Space Optical Communication Networking Technology Based on a Laser Relay Station
## 2 Theory and System Design
The system implemented in this paper uses a repeater to complete point-to-multipoint free-space optical communication, and its implementation requires the ADC in the repeater to sample the received signal in all directions in a serial manner; if the pulse signal is narrow, a certain direction may not be able to sample the received signal, and then the wider pulse signal can increase the stability of the system. From Figure 1, it can be seen that under the condition of fixed time slot width, the PWM mode pulse width can be wider, compared with other modulation methods. PWM mode can make it easier for repeaters to sample the received signal, so PWM is more suitable for the research on networking technology of spatial optical communication than other modulation methods. Figure 3 shows the PWM modulation and demodulation schematic, which is implemented through an FPGA. First, the binary data are discriminated; for datum 1, a pulse signal with a pulse width of T\({}_{1}\) is generated by the FPGA, and for datum 0, a pulse signal with a pulse width of T\({}_{2}\) is generated by the FPGA, and the pulse signal period is fixed to T. The demodulation process is implemented by the ADC, which has a sampling interval of \(\tau\) in each direction during the fixed pulse signal period T time, and if there are N directions that need to probe the signal, the sampling rate of the ADC in the repeater is N\(\tau\). In Figure 3, H represents when the sampled level signal is logic level 1, L represents when the sampled level signal is logic level 0, and the number of instances of H is counted in T time. N1 represents the number of times the ADC samples to logic level 1 when the pulse width is T\({}_{1}\) in a pulse period T, and N2 shows the number of times the ADC samples to logic level 1 when the pulse width is T\({}_{2}\) in a pulse period T, and the data can be judged according to the size of the Count value. This paper focuses on the design of a point-to-multipoint free-space optical communication system, which aims to provide an effective solution for free-space optical communication networking technology, and the experiment is carried out in a relatively ideal environment, so this paper does not consider the influence of atmospheric turbulence on the performance of a free-space optical communication system and the suppression of the atmospheric turbulence effect by adaptive optical technology. Assuming that only Gaussian white noise is added to the communication system, and the error caused by other factors is not considered, under the condition that the matching filter is an ideal linear filter, the input signal of the matching filter can be expressed as: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Modulation Mode** & **OOK** & **PIM** & **LPPM** & **DPPM** & **PAM** & **PWM** \\ \hline Average symbol length & \(M\) & \(\frac{2^{M}+3}{2}\) & \(2^{M}\) & \(\frac{2^{M}+1}{2}\) & \(1\) & \(2^{M}+1\) \\ \hline Average Power & \(\frac{1}{2}P_{S}\) & \(\frac{2}{2^{M}+3}P_{S}\) & \(\frac{1}{2^{M}}P_{S}\) & \(\frac{2}{2^{M}+1}P_{S}\) & \(\frac{2^{M}+1}{2^{M}+1}P_{S}\) & \(\frac{1}{2}P_{S}\) \\ \hline Transmission Bandwidth & \(R_{b}\) & \(\frac{2^{M}+3}{2M}R_{b}\) & \(\frac{2^{M}}{M}R_{b}\) & \(\frac{2^{M}+1}{2M}R_{b}\) & \(MR_{b}\) & \(\frac{2^{M}+1}{M}R_{b}\) \\ \hline Channel Capacity & \(C_{b}\) & \(\frac{2M}{2^{M}+3}C_{b}\) & \(\frac{2M}{2^{M}}C_{b}\) & \(\frac{2M}{2^{M}+1}C_{b}\) & \(MC_{b}\) & \(\frac{M}{2^{M}+1}C_{b}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance index of several modulation modes in optical communication. \[x(t)=\sqrt{P}+n(t) \tag{1}\]  
where \(P\) represents the peak optical power of the emitted light pulse, while \(n(t)\) represents white Gaussian noise with a mean of 0 and a variance of \(\sigma_{n}{}^{2}\).