# Near-Nyquist-Limit Optical Communication and Ranging Method Based on Waveform Matched PPM
## 2 Deep-Space Optical Communication and Ranging Method Based on PPM  
### System Structure  
The integrated system for deep-space optical measurement and control contains the ground terminal and the space terminal, as shown in Figure 2. The electronic control unit controls the entire terminal: it sends and receives the communication data. The modern module processes electrical signals, including sampling, modulation/demodulation, etc. The optical module processes optical signals, realizing the mutual conversions between electrical and optical signals.  
The downlink refers to the transmission direction of the space terminal to the ground terminal. The modulation module operates framing, encoding, scrambling, modulating, and PPM symbol mapping of the control instructions and communication data issued by the electronic control unit in the space terminal. The laser diode transmitter converts electrical signals into optical signals. Then optical signals are transmitted through an optical antenna, i.e., an optical telescope. The optical antenna on the ground terminal receives downlink optical signals transmitted through free space. As downlink optical signals are extremely weak, a superconducting nanowire single-photon detector (SNSPD) [23; 24] is used to detect a single photon. The demodulation module conducts sampling, demodulation, and decoding of baseband signals. The field programmable gate array (FPGA) processes and transmits ranging information and communication data to the electronic control unit in the modern module.  
The uplink refers to the transmission direction of the ground terminal to the space terminal. The difference between an uplink and a downlink is that the space terminal uses a lightweight single-photon avalanche diode (SPAD) [25; 26; 27] for photon detection, limited by the volume and weight of the payload.  
The \(L\)-ary pulse position modulation (\(L\)-PPM) symbol [28] can be expressed as:  
\[s_{n}(t)=\frac{1}{\sqrt{T/N}}\text{rect}\bigg{[}\frac{t-nT/L}{T/N}\bigg{]},N \leq L, \tag{1}\]  
where \(T\) is the symbol period and \(L\) indicates the length of slots within a symbol. \(n=0,...,N-1\) indicates the location of the pulse. The \(\text{rect}(t)\) is defined as:  
\[\text{rect}(t)=\left\{\begin{array}{ll}1,&\quad 0\leq t<1,\\ 0,&\quad\text{otherwise}.\end{array}\right. \tag{2}\]  
Figure 2: Structure of the integrated system for deep-space optical measurement and control.  
As SPAD and SNSPD cannot detect the signal within their dead time [29; 30; 31], inserting the guard time slot into the signal and receiving it by the detector array are applied to solve the problem [32; 33]. The former can be realized by programming but reduces communication efficiency, whereas the latter increases hardware complexity and power consumption. Therefore, the method of inserting guard slots is applied to solve this problem of SPAD. Hence, there is \(N<L\) in (1) for the uplink signal, and the length of the guard slots is \(L-N\). An array comprising multiple SNSPDs is employed for the downlink signal; hence, there is no need to insert guard slots, \(N=L\), for the downlink signal.