With the rapid development of technologies such as the Internet and artificial intelligence, the demand for data in various fields of life is growing exponentially. However, the capacity of traditional single-mode fiber (SMF) networks is approaching the Shannon limit. Therefore, various multiplexing technologies including wavelength division multiplexing (WDM), polarization multiplexing (PDM), and mode division multiplexing (MDM) have been explored to meet the growing demand for data. In MDM, FMF fibers for long-distance transmission have lower nonlinear losses than multi-mode fibers, which makes it more cost-effective. Additionally, MDM introduces severe crosstalk among different modes, which should be compensated for by advanced DSP algorithms at the receiving end. We propose a crosstalk correlation ratio measurement method based on signal correlation peak extraction to address the channel crosstalk caused by mode coupling in MDM systems. The crosstalk correlation coefficient is applied to the correlation peak ratio multi-input-multi-output constant modulus algorithm (CPR-MIMO-CMA) to improve channel equalization performance. An SMF optic transmission experimental platform is built, and the CPR-MIMO-CMA is utilized to process the data from the receiving end to verify the algorithm superiority. The experimental results show that the proposed algorithm has a significant improvement in both convergence speed and balancing effect compared to traditional CMA, and is expected to be employed in future high-capacity FMF transmission scenarios.

Firstly, we model and calculate the coupling mode equation and coupling coefficient, and derive the expression of the coupling coefficient in FMF and also the relationship between the signal correlation peak and it. Then, the FMF transmission system is built using simulation software. The signal generation end of the system is responsible for generating repetitive and misaligned digital signals. Then, the mode laser generator generates LP01 mode and LP11 mode optical signals, which are modulated by 16QAM and enter the FMF link. The FMF adopts a segmented simulation structure, and the two signals at the receiving end are processed with digital signals to obtain XT-CPR. It performs multiple changes in fiber length and coupling strength, recording data to explore the relationship among XT-CPR, coupling strength, and propagation distance. To verify the performance of the CPR-MIMO-CMA, we also build a third mock examination transmission experimental platform. At the transmitting end of the experimental system, firstly the software generates a pseudo-random binary sequence with a code length of 2¹⁴, maps it into a 16QAM symbol every four bits, and realizes baseband shaping through root raised cosine (RRC) filter. Meanwhile, the signal is loaded after resampling to an arbitrary waveform generator (AWG) with a sampling rate of 64 GSa/s, and it is converted into two electrical signals to drive the IQ modulator to modulate two groups of optical carriers. The 3 dB bandwidth of the IQ modulator is 29 GHz. The working wavelength of the laser is 1550.1 nm, and the modulated optical signal is amplified by a low noise erbium-doped fiber amplifier (EDFA) before entering a 1×3 coupler. At the same time, to eliminate the correlation between modes, we add LP11 and LP21 optical fibers with delay lines of different lengths and employ a polarization controller to control the polarization state of the signal. The fiber adopts a step type four-mode fiber with a length of 5 km, model FM SI-4, which can transmit up to four modes of optical signals including LP01, LP11a, LP11b, and LP21. Additionally, we employ three channels of LP01, LP11a, and LP21 for experiments. At the receiving end, the multiplexed signal is divided into three channels by the mode demultiplexer and enters the coherent receiver. The relevant image and waveform data are observed and recorded for offline digital signal processing (DSP). In the DSP, the signal is sequentially processed by the RRC low-pass filter, resampling, timing recovery, and the proposed CPR-MIMO-CMA. Then, the blind phase search algorithm is adopted to enter the sampling decision with experimental results observed.

Fig. 6 shows a visual graph of the signal correlation peaks under three modes. According to Formula (11), when other conditions are constant, the larger crosstalk leads to smaller XT-CPR. The height comparison of the correlation peaks in Fig. 6 is basically consistent with the size relationship shown in the reference values of Table 1. Fig. 7 demonstrates a comparison of error rates between traditional equalization and equalization with CPR parameters. The figure indicates that the proposed CPR-MIMO-CMA has a performance improvement of 1.3 dB, 0.9 dB, and 1.0 dB compared to traditional CMA in LP01, LP11, and LP21 channels respectively under the threshold of forward error correction (FEC) of 3.8×10^-3. When the received optical power is low or the signal-to-noise ratio is high, there is not much difference in the effect between traditional equalization and equalization with CPR parameters. This is because the damage caused by noise is much greater than that caused by mode crosstalk. When the received optical power is high, the equalization effect with CPR parameters reaches the best. As the received optical power continues to increase, the equalization effect of the two tends to be similar. At this point, the signal already meets the FEC threshold of 3.8×10^-3. Fig. 8 shows a comparison of the average convergence speed of CPR-MIMO-CMA and the traditional CMA for processing the data at the receiving end of the third mock examination transmission system. This figure reveals that the proposed CPR-MIMO-CMA has a faster convergence speed, and the average convergence time under the three modes is reduced by about 50%.

We propose a crosstalk equalization method based on signal correlation peaks, which combines mode coupling theory and signal correlation peak theory to eliminate the randomness error of traditional crosstalk measurement, making the algorithm have a better mode equalization effect. A third mock examination transmission experimental platform is built, on which the feasibility and accuracy of the method are verified. The BER performance and convergence speed of CPR-MIMO-CMA based on signal correlation peak and traditional CMA equalization are compared. The results show that the method can effectively equalize mode crosstalk, and the performance of this method is improved by 1.3 dB, 0.9 dB, and 1.0 dB respectively compared with traditional equalization in LP01, LP11, and LP21 channels. Meanwhile, the average convergence time in the three modes is reduced by about 50%.