Objective Because of the extremely long communication link in deep space, the detection signal is easily affected by channel characteristics such as background light noise and delay jitter, and the output signal-to-noise ratio (SNR) is very low, which leads to the poor synchronization performance of a receiver. Therefore, it is very important to achieve precise synchronization at low SNR. In general, pulse position modulation (PPM) slot synchronization is mainly in the form of closed-loop tracking, such as phase-locked loop and early-late gate, and the system design is complex. According to the estimation of timing error of the training sequence inserted periodically, the open-loop synchronization is realized, which will waste certain transmitting power. Using the maximum likelihood synchronization method of the guard slot, this method can reduce the computational complexity effectively, however, the bit error rate (BER) will be obvious when the signal power is high. The slot synchronization method of a photon detector array based on photon arrival time measurement requires complexity that is still high. The clock synchronization method based on the fast Fourier transform (FFT) has fast computing speed and the support of underlying hardware. It is suitable for real-time signal processing and has been widely used in wireless communication and optical fiber communication. However, the error of the signal parameters obtained directly from the FFT line spectrum is sometimes very large, which requires frequency correction. However, the single frequency correction method is not robust. We will apply the classical FFT algorithm to the photon-detected PPM communication system in slot synchronization. A method of PPM open-loop synchronization is proposed by selecting the optimal value from the Quinn, Jacobsen, and MacLeod algorithms. To solve the problem that the existing data recovery methods are inaccurate, a data recovery method based on correlation detection is proposed.
Methods The optical PPM signal is sampled asynchronously more than twofold and passed through the FFT, but the error of the signal parameters obtained directly from the FFT line spectrum is sometimes very large, which requires refinement of the frequency estimation. The common frequency correction methods are Rife, Quinn, MacLeod, and Jacobsen. However, the robustness of a single frequency correction method is poor. In this paper, we estimate the initial frequency deviation of the PPM signal using Quinn, Jacobsen, and MacLeod algorithms, and then obtain the time delay deviation. According to the frequency deviation and time delay deviation estimators, the photon number of the PPM signal is recovered through a correlation operation, and then three sets of slot logarithmic likelihood ratio sequences are obtained. Finally, the sequence with the largest standard deviation is selected from these three sets of time slot logarithmic likelihood ratio sequences as the input of the error correction decoder.
Results and Discussions The classical FFT method is applied to slot synchronization of a photon detection PPM communication system. Compared with existing PPM slot synchronization methods, the slot synchronization method proposed in this paper does not need to insert training series, is not limited by the number of guard slots, the system structure is simple, easy to implement by hardware, and the operation speed is fast, PPM slot synchronization can be achieved at very low optical power. The method estimates the initial frequency offset of the signal using the Quinn, Jacobsen, and MacLeod algorithms, and then obtains the time delay deviation of the signal, PPM open-loop synchronization is realized by selecting the optimal value from three ratio methods according to the maximum standard deviation criterion of logarithmic likelihood ratio of slots. Compared with the single ratio method, this method is more robust, and the calculation time is only 1.13 times that of the single ratio method. In this paper, the photon number recovery method based on correlation detection is proposed to verify the high-performance optical PPM experiment based on a multipixel photon counter (MPPC). For 64PPM and fourfold PPM slot frequency asynchronous sampling, the method in this paper only needs to detect 1.33 photons per signal pulse on average, which can make BER less than 10 -5.
Conclusions In this paper, an experimental optical PPM communication system based on MPPC is established, and the classical FFT method is applied to the photon detection PPM communication system. Through the maximum standard deviation criterion of the logarithmic likelihood ratio of the slot, the optimal value is selected from the three ratio methods to realize the open-loop synchronization of the PPM slot. Compared with the existing PPM slot synchronization method, the PPM open-loop synchronization method proposed in this paper does not require the insertion of training series and is not limited by the number of guard slots. The system is simple in structure, easy to implement by hardware, and fast in operation speed. PPM slot synchronization can be achieved at extremely low optical power. Compared with the single ratio method, the slot synchronization method is more robust, and the operation time is only 1.13 times that of the single ratio method. In this paper, a photon number recovery method based on correlation detection is proposed to verify the high-performance optical PPM experiment based on MPPC. The experimental results show that the BER performance of the proposed correlation detection algorithm is 0.65 dB and 0.50 dB compared with the ideal simulation data, for the asynchronous sampling signals with twofold and fourfold PPM slot frequency, respectively. For 64PPM and fourfold PPM slot frequency asynchronous sampling, the proposed method in this paper only needs to detect 1.33 photons per signal pulse on average, which can make BER less than 10 -5.
