# Near-Nyquist-Limit Optical Communication and Ranging Method Based on Waveform Matched PPM
###### Abstract  
Deep-space optical communication and ranging technologies have attracted much attention for satellite-to-earth and moon-to-earth exploration. In integrated communication and ranging scenarios, non-integer oversampling factors are employed to improve the ranging performance, which can cause accumulated timing errors. We propose a novel pulse position modulation (PPM) symbol decision method based on waveform matching to reduce the impact of accumulated timing errors near the Nyquist sampling limit. Simulation results demonstrate that the ranging accuracy can reach 2.6 and 0.52 mm at sampling rates of 625 Mps and 2.5 Gsps, respectively. The proposed symbol decision method has a gain of over 1.1 dB compared with the traditional method at the bit error rate (BER) of less than \(10^{-6}\). The experimental results verify that this method can achieve high-precision measurements of distance and reliable transmission of information. optical communication; ranging method; time-of-flight (TOF); pulse position modulation (PPM); photon detection +
Footnote †: journal: 2022, 11, 565. [[https://doi.org/10.3390/electronics11040565](https://doi.org/10.3390/electronics11040565)]([https://doi.org/10.3390/electronics11040565](https://doi.org/10.3390/electronics11040565))
multiple satellites for the European Data Relay System, realizing a 1.8 Gbps laser link between LEO-GEO devices [15; 16; 17]. It will launch Engineering Test Satellite 9 by NICT in 2022 to study deep-space optical communication between GEO and GND at 10 Gbps [18]. The research trend of deep space laser communication is shown in Figure 1.  
In the pulse position modulation (PPM) scheme, a symbol period is divided into several time slots, i.e., the information is transmitted by the position of a single pulse slot within the symbol [19]. The modulation methods of deep-space optical communication include on-off keying (OOK) control modulation, PPM, binary phase shift keying (BPSK) modulation, and differential phase shift keying (DPSK) modulation [14]. Taking advantage of its eminent power efficiency [20] and weak inter-symbol interference [21], PPM is suitable for future deep-space communication and ranging demands. The theoretical ranging accuracy depends on the slot rate, and higher ranging accuracy can be achieved at a higher slot rate. Restricted by the analog-to-digital converter (ADC) device sampling technology, it is necessary to process signals close to the Nyquist sampling limit to realize high-speed communication and high-precision ranging. The signal, meanwhile, needs to be operated on non-integer oversampling factors to improve the ranging performance. This process causes accumulated timing errors, so the pulse energy leaks to the adjacent slots. The bit error rate (BER) performance is degraded because of the leaked energy. [PERSON] proposed a method for simultaneous communication and ranging using dual-pulse interval modulation (DPIM) [22]. The method improves the reliability of system communication and has a simple hardware structure. However, it does not address the relationship between \(E_{b}/N_{0}\) and ranging accuracy. The communication rate was extremely low: 6.25 kbps was realized. The ranging accuracy was only about 2 cm in a laboratory environment, which is not enough for deep space exploration. The performance of this method is degraded near the Nyquist sampling limit. An integrated method of optical communication and ranging is described, and a PPM symbol decision method based on waveform matching is proposed to reduce the impact of PPM signal energy leakage near the Nyquist sampling limit. A technical approach to high-precision ranging and reliable communication is presented for the integrated task for deep-space optical measurement and control. The rest of this paper is organized as follows. In Section 2, the system structure and ranging method are described. In Section 3, the waveform matching algorithm is proposed. In Section 4, simulation results are, presented and discussed.