Low-complexity subcarrier-merged digital back-propagation for high-symbol-rate subcarrier-multiplexing optical transmissions.

In this paper, we propose a subcarrier-merged digital back-propagation (SM-DBP) scheme to compensate for fiber nonlinearity in subcarrier-multiplexing (SCM) systems. By merging the intensities of interfering subcarriers, SM-DBP significantly reduces the complexity of nonlinear compensation. For high-symbol-rate SCM systems that require more subcarriers to mitigate fiber nonlinearity and equalization-enhanced phase noise, SM-DBP offers a more prominent advantage in complexity, as its complexity is independent of the number of subcarriers. The proposed method is numerically and experimentally evaluated in single-channel dual-polarization 16-ary quadrature amplitude modulation (16-QAM) SCM transmission systems over a distance of 480 km. For 8-subcarrier and 16-subcarrier 240-GBaud simulation systems, 6-step SM-DBP achieves a complexity reduction of 78% and 85%, respectively, while maintaining performance comparable to that of SCM-DBP. In 16-subcarrier systems, 6-step SM-DBP also reduces the complexity by 50% while achieving an additional compensation gain of 0.42 dB, compared with CB-ESSFM. We have also verified the performance of SM-DBP in a 4-subcarrier SCM experimental system. The results indicate that SM-DBP reduces complexity by 74% while achieving the same performance as SCM-DBP. Compared with CB-ESSFM, SM-DBP achieves an additional compensation gain of 0.12 dB while reducing the number of CMs by 20%. The proposed algorithm is also validated in distributed Raman amplifier (DRA)-amplified systems through simulations and experiments. In a 320-km 8-subcarrier 240-GBaud DRA-amplified simulation system and a 185-km 4-subcarrier 40-GBaud DRA-amplified experimental system, SM-DBP reduces complexity by 80% and 61%, respectively, while maintaining performance comparable to that of SCM-DBP.