With the rapid development of technologies, such as the Internet and artificial intelligence, there has been an exponential increase in the demand for data from all areas of life. However, the capacity of traditional single-mode fiber (SMF) networks is approaching the Shannon limit. Consequently, several multiplexing technologies, including wavelength division multiplexing (WDM), polarization division multiplexing (PDM), and mode division multiplexing (MDM), have been explored to meet the growing data demand. In MDM, using few-mode fiber (FMF) for long-distance transmission is more cost effective than using multimode fiber (MMF) because of the lower nonlinear impairment. Moreover, MDM introduces severe crosstalk between different modes, which must be compensated for by advanced DSP algorithms on the receiver side. In China, most ongoing studies on MDM transmission employ the intensity modulation direct detection (IMDD) method, which is suitable for only short-distance transmissions. The number of modes that can be effectively exploited is also too small, making it difficult to achieve "ultrahigh-capacity" communication. In this study, we developed a high-capacity long-distance FMF transmission system that combines WDM, PDM, and MDM technologies. Eighty channels that satisfy the ITU-T standard are generated, and 32-GBaud 16QAM signals are transmitted up to 1000-km FMF on dual polarization and two modes (LP11a and LP11b). Multiple input multiple output(MIMO) equalization demultiplexing algorithms based on time domain (TD) and frequency domain (FD) are adopted, which can greatly improve system performance. For a transmission distance of 1000 km, the net data rate reaches 32.768 Tbit/s, which is the highest recorded rate in China.

In this experiment, we used strong coupling graded-index FMF that can support the transmission of six modes and we chose two degenerate modes, including LP11a and LP11b. At the transmitter side, 80 external cavity lasers generate 1530-1562 nm light waves with a 50-GHz frequency spacing. The digital baseband signal is generated with Matlab and then loaded into an arbitrary waveform generator to modulate the optical carriers through an IQ modulator. Polarization-beam splitters and combiners are used to conduct PDM so that the signal can be divided into two parts with orthogonal polarization of X and Y. After being boosted by an erbium-doped optical fiber amplifier (EDFA), two independent dual polarization signals are modulated into LP11a and LP11b modes through a mode multiplexer and then transmitted over a reel of 50-km FMF. Thereafter, mode demultiplexing is performed so that single-mode EDFAs can compensate for the transmission loss for each mode. Wavelength selective switches (WSS) are employed to solve the problem of the uneven gain of EDFAs. We adopted a loop structure to realize long-distance transmission. Thus, the output of WSS is sent back into the mode multiplexer to perform MDM and 50-km FMF transmission again until the total transmission distance meets our requirement. At the Rx side, the coherent optical receiver conducts homodyne detection on the selected signal after wavelength division demultiplexing. In the offline DSP, the captured electrical signal is mainly processed by dispersion compensation, clock recovery, MIMO equalization demultiplexing based on the least mean square (LMS) algorithm, carrier recovery, detection-directed least mean square algorithm, and, finally, BER calculation. Among them, MIMO-TDLMS and MIMO-FDLMS are the core parts. MIMO equalization creates a filter between each input and output. Since our proposed system uses three multiplexing technologies, every path of the received signal can contain information from other paths due to the crosstalk between different polarizations and modes, which well fits the characteristics of the MIMO model. The coefficients of the filters are trained using the LMS algorithm. For MIMO-FDLMS, fast Fourier transform is applied to the TD signal so that the algorithm can perform block processing in the FD, which is more efficient.

Fig.5 shows the optical spectrum of the received signal in BTB circumstance. It shows that 80 channels with a 50-GHz frequency spacing were successfully generated, and the optical signal-to-noise ratio (OSNR) difference between the adjacent channels is below 1 dB. The BER performance of the LP11a and LP11b modes under different OSNR values was evaluated, as shown in Fig.6. With an increase in OSNR, the crosstalk between different polarization and modes became the dominant factor of noise, and the performance of our system still differs from that of theoretical AWGN channels. Furthermore, we calculated the BER of the 80 WDM channels after 1000-km FMF transmission, and all of them are below 2×10^-2. Due to the uneven spectrum after several times of loop transmissions and EDFA amplification, the BER of different channels was unstable. Meanwhile, the BER values of different modes in the same channel were slightly different. This is because the refraction indices of LP11a and LP11b are comparable. Finally, Fig. 8 shows the BER performance under different FMF transmission distances. The BER increased with an increase in fiber length. After 500/1000-km FMF transmission, the BER of the LP11a and LP11b modes can meet the 7% HD-FEC threshold of 3.8×10^-3 and the 25% SD-FEC threshold of 4.2×10^-2, respectively.

In this study, we developed a WDM-PDM-MDM transmission system, in which 32-GBaud 16QAM signals can be transmitted over 1000-km FMF on dual polarization and LP11a and LP11b modes in 80 WDM channels. Using MIMO-TDLMS and MIMO-FDLMS algorithms in the offline DSP, the dispersion effect and the crosstalk between different polarizations and modes can be effectively compensated for. At an FMF transmission distance of 500 km, the BER can meet the 7% HD-FEC threshold of 3.8×10^-3, and the corresponding net data rate is 32×4×2×2×80/(1+0.07)=38.28 Tbit/s. At an FMF transmission distance of 1000 km, the BER can meet the 25% SD-FEC threshold of 4.2×10^-2, and the corresponding net data rate is 32×4×2×2×80/(1+0.25)=32.768 Tbit/s. This is a record-breaking result in China for both the net data rate and the transmission distance in an FMF MDM system. The proposed system is, thus, a promising candidate for future "ultrahigh-capacity, ultralong-distance" communication.