The explosive development of virtual reality applications, ultra-high-definition videos, and intelligent internet of things (IoT) devices has brought new challenges to existing fiber access network solutions. As the main scheme of optical access networks, widely deployed passive optical networks based on time division multiplexing (TDM), wavelength division multiplexing (WDM), and polarization multiplexing (PDM) are currently limited by the communication capacity of single-mode fibers (SMFs) and the signal orthogonality of the traditional Nyquist transmission mode. To further improve system capacity and spectral efficiency, we proposed a faster-than-Nyquist mode-division multiplexing passive optical network (FTN-MDM-PON) that combines mode-division multiplexing (MDM) and faster-than-Nyquist (FTN) transmission technologies. However, PON based on the MDM channel and FTN transmission mode exhibits mode crosstalk caused by low-mode fiber transmission and intersymbol interference (ISI) caused by FTN transmission. Because the FTN-MDM-PON divides users by mode, the mode crosstalk in the low-mode fiber (FMF) causes the user signals loaded on different modes to interfere with each other. The ISI introduced by the FTN transmission causes adjacent symbols influence each other at the sampling decision time. To mitigate the two types of impairments in FTN-MDM-PONs, we proposed a joint damage compensation method based on matrix decomposition precoding and MIMO pre-equalization and built a simulation system in the VPI Transmission Maker for verification.

Because the PON downlink is a point-to-multipoint structure, it is impossible to simultaneously receive and eliminate mode crosstalk for all modes on the receivers of user-side optical network units (ONUs). In addition, the ISI introduced by FTN transmission technology is determined by the rolling-down factor of the pulse-forming filter and the time-domain compression factor, which is determined at the end of the transmitter. Therefore, we propose a joint damage compensation method based on matrix-decomposition precoding and MIMO pre-equalization. For matrix decomposition precoding techniques, we used singular value decomposition (SVD) precoding, singular value decomposition with power allocation (SVD PA) precoding, and Cholesky decomposition (Chol) precoding and combine them with the MIMO pre-equalizer. The matrix decomposition precoding technique can obtain the precoding matrix for the sending signal and the decoding matrix for the receiving signal through the matrix decomposition of the interference matrix to realize the diagonalization of the interference matrix to eliminate the ISI. After adding the frame header, the transmission symbol sequence was precoded using the matrix decomposition precoding method, and then transmitted by the FMF. We inserted a time-division training sequence into the frame header to obtain the channel-impulse response of the downlink. The time-division training sequence was divided into multiple time slots of the same number as the mode; each time slot corresponds to only one mode and contains the corresponding time-slot training symbol sequence. After separating the time-division training sequence of different user data frame headers at the receiver end, we adopted a training sequence-based least mean square (LMS) adaptive algorithm for channel estimation. The channel estimate was fed back to the transmitter for MIMO pre-equalization. The transmitter-side MIMO equalizer used in this study had a linear structure and used the feedback channel impulse response to calculate the tap coefficients based on the zero-forcing (ZF) criterion.

Based on the FTN-MDM-PON simulation system, we analyzed the performance of three combined damage compensation methods using different matrix decomposition precoding methods and a MIMO pre-equalizer. The curves of bit error rate relative to the received optical power when the time-domain compression factors of the mode signals were 0.8 and 0.9 are shown in (Figs.7 and 8). Simulation results show that in the FTN-MDM-PON system with four linear polarization (LP) modes, FTN signals with time-domain compression factors of 0.8 and 0.9 are transmitted through 5 km low-mode fiber (FMF), and the received optical power ranges from -40 dBm to -26 dBm. The combined damage compensation method of SVD PA precoding or Chol precoding combined with MIMO pre-equalizer reduces the bit error rate of each mode (LP₀₁, LP₁₁, LP₂₁, LP₃₁) below the 7% hard decision forward error correction (HD-FEC) threshold of 3.8×10^-3. Among the three combined damage compensation methods, Chol precoding and SVD-PA precoding combined with a MIMO pre-equalizer exhibit better improvement effects than SVD precoding combined with a MIMO pre-equalizer. When SVD PA precoding combined MIMO pre-equalizer is used for joint damage compensation, the four LP mode signals reach 7% HD-FEC decision threshold when the received optical power is greater than -36 dBm. The combined damage compensation method of Chol precoding combined with MIMO pre-equalizer, compared with the SVD PA precoding combined with MIMO pre-equalizer, when the time domain compression factor is 0.8, the sensitivity of the four mode signals increase by 3.0 dB, 2.4 dB, 2.0 dB, and 1.3 dB. When the time domain compression factor is 0.9, the increases are 1.1 dB, 2.1 dB, 2.5 dB, and 2.1 dB. With a decrease in the time-domain compression factor, the interval between adjacent symbols in the FTN signal becomes narrower after time-domain compression, and the intersymbol crosstalk becomes more severe. When the time domain compression factor of each mode signal ranges 0.3 to 0.9, the relationship curve between bit error rate and received optical power is shown in (Figs.9 and 10). The results show that when the received optical power is greater than -34 dBm and the time-domain compression factor of FTN signal is ≥0.6, the combined damage compensation method based on SVD PA precoding and Chol precoding combined with MIMO pre-equalizer effectively reduce the bit error rate, and the bit error rate of FTN signal in four LP modes is below the threshold. The abovementioned results show that the combined damage compensation method can effectively compensate for MDM channel damage and FTN transmission damage in the FTN-MDM-PON system, and the combined damage compensation method with Chol precoding and MIMO pre-equalizer exhibits the best performance among the three precoding methods.

We proposed a joint damage compensation method based on matrix decomposition precoding combined with a MIMO pre-equalizer and built an FTN-MDM-PON downlink simulation system to verify the performance of this method in reducing the bit error rate of the system. We used SVD precoding, SVD PA precoding, Chol precoding, and a MIMO pre-equalizer to explore the performance of the three combined damage compensation methods in reducing the bit error rate. Moreover, the bit error rate performance of the FTN-MDM-PON using the joint compensation method was compared with that of the MDM-PON using MIMO pre-equalization only. Results show when using 4 LP modes (LP₀₁, LP₁₁, LP₂₁, LP₃₁) for 4×25 Gbaud FTN QPSK signal transmission, when the time domain compression factor is 0.8, by using the combined damage compensation method of SVD PA precoding and Chol precoding combined with MIMO pre-equalizer, the optical power of four LP mode signals only requires -36 dBm and -39 dBm, respectively, to reach 7% HD-FEC. When the time-domain compression factor is 0.9, the bit error rate performance of the combined damage compensation method using Chol precoding and the MIMO pre-equalizer is close to that of the MDM-PON system using MIMO pre-equalization only. The abovementioned results show that the proposed combined damage compensation method can effectively mitigate mode crosstalk and ISI in FTN-MDM-PON systems.