The bandwidth requirement of the optical fiber communication network is increasing rapidly. To further enhance the transmission capacity of the optical fiber communication systems, we should adopt higher-order modulation formats or a higher single-wavelength transmission rate. However, higher-order modulation formats are more sensitive to channel impairment, which complicates the design of the receiver. The faster-than-Nyquist (FTN) system, one of the research hotspots of the next generation optical fiber communication systems, can transmit more bits than the Nyquist system within the same time period by introducing inter-symbol interference (ISI). The ISI and the transmission impairments of the FTN systems can be equalized and compensated by powerful digital signal processing (DSP) algorithms. In coherent digital optical communication systems, clock synchronization is a prerequisite for normal information transmission, so the clock recovery algorithm is crucial for the receiver. The clock recovery algorithm based on signal power, which is used to compensate for the sampling error induced by the ADC, is applicable to the FTN systems. The adaptive equalization algorithm is used to compensate for channel impairments, such as polarization mode dispersion (PMD). The ISI introduced by FTN systems and PMD introduced by the fiber will degrade the performance of the clock recovery module. Meanwhile, the adaptive equalization module and the clock recovery module, which are two key modules in the receiver DSP system, may mutually constrain each other. Thus, resolving the issue between the clock recovery and adaptive equalization modules is the key to ensuring the performance of the optical fiber communication systems. In this study, we intensively study the joint algorithm of adaptive equalization and power-based clock recovery (AE-PCR). Simulation results show that the AE-PCR algorithm can effectively achieve clock synchronization, equalization, and polarization demultiplexing in the FTN system with a smaller compression factor, and improve the convergence speed of the clock recovery algorithm.

In the proposed AE-PCR scheme, we embed the adaptive equalization module in the clock recovery module, which can effectively solve the mutual constraint between the adaptive equalization module and the clock recovery module. The data sampled by the ADC are fed forward to the interpolation filter in the loop of the clock recovery module. After interpolation, the data are fed forward to the butterfly filter of the adaptive equalization module to compensate for the PMD and part of the ISI. Then, the error function is calculated by the RDE algorithm based on the compensated data to update the tap coefficients of the butterfly filter. Meanwhile, the timing error is calculated based on signal power in the timing error detector to obtain more accurate timing information and improve the tracking accuracy of the clock synchronization loop, which can promote the performance of the clock recovery module. During the simulation, we successively analyze the performances of the conventional method (adaptive equalization and clock recovery non-joint algorithm) and the proposed AE-PCR method. The results show that the AE-PCR algorithm can effectively achieve clock synchronization, equalization, and polarization demultiplexing in the FTN system with a smaller compression factor and improve the convergence speed of the clock recovery algorithm. The AE-PCR algorithm can provide additional OSNR gain relative to the conventional scheme at the BER threshold of 2×10^-2.

In the PDM-FTN-16QAM system, the convergence cost increases with the increase in sampling error in back-to-back transmission (Table 2), which makes it more difficult to track the clock recovery module. The ISI becomes more serious with the decrease in the compression factor, which increases the convergence cost of the power-based clock recovery module in back-to-back (BTB) transmission (Fig. 4). The convergence cost of the clock recovery module further increases under the influence of the large PMD introduced by fiber transmission (Fig. 5). The convergence cost of the AE-PCR algorithm increases with the increase in sampling error and the decrease in the compression factor, which is the same as that of the power-based clock recovery algorithm. The proposed AE-PCR scheme can increase the convergence speed and reduce the convergence cost in both BTB and transmission scenarios, and achieve polarization demultiplexing function simultaneously (Figs. 7 and 8). Finally, we simulate and compare the BER performances of the conventional and proposed methods. The required OSNR at the BER threshold of 2×10^-2 of the AE-PCR is 0.9 dB and 1.5 dB lower than that of the conventional method in the BTB and transmission scenarios, respectively (Fig. 9).

In this study, we conduct an in-depth study of the non-data-aided AE-PCR algorithm, which embeds the adaptive equalization module into the clock recovery loop. The proposed method can simultaneously compensate for channel impairments and timing errors, effectively resolving the issue of mutual restraint between the adaptive equalization and clock recovery modules. Simulation results show that the AE-PCR scheme can compensate for the timing error, equalize the ISI, and realize polarization demultiplexing in the FTN system with a compression factor of 0.85, which can increase the convergence speed by at least 51% and effectively reduce the convergence cost of the clock recovery module. With the same simulation parameters, the required OSNR at the BER threshold of 2×10^-2 of the AE-PCR is lower than that of the conventional method in both BTB and transmission scenarios.