With the advancement of ultra-wideband amplifiers, multi-band transmission has emerged as one of the most effective strategies to enhance the capacity of standard single-mode fiber systems. Currently, optical transmission across the C+L band has already been commercially implemented. Among potential candidates for further spectral extension, the S-band appears to be the most promising. However, the incorporation of the S-band into the transmission system introduces pronounced power tilt from higher to lower frequencies due to the influence of stimulated Raman scattering (SRS), which results in significantly degraded performance in the S-band compared to the C-band. Consequently, the expected linear capacity growth with increased bandwidth cannot be fully realized. To address this challenge, techniques such as power pre-emphasis, advanced digital signal processing (DSP) algorithms, and the deployment of Raman amplifiers have been introduced into S+C+L band transmission systems, achieving substantial performance improvements. Nevertheless, the introduction of Raman amplification also brings increased system complexity and power consumption. In this study, we propose a joint optimization approach combining power pre-emphasis and entropy minimization, aiming to explore the performance enhancement potential of these two techniques within a lumped amplification transmission link.

In this study, a joint optimization scheme combining power pre-emphasis and group-wise entropy minimization is proposed. Initially, system performance is enhanced through optimized power pre-emphasis. Based on the resulting performance distribution, transmission channels are grouped, and for each group, the worst-performing channel is selected as the representative target for entropy optimization, ensuring error-free transmission within the entire group. During the power pre-emphasis stage, we investigate both uniform and non-uniform power allocation strategies. The non-uniform optimization is guided by a 3 dB criterion accounting for both linear and nonlinear noise, while the uniform and non-uniform schemes targeting maximum capacity are also explored. All optimization processes are conducted using a particle swarm optimization algorithm. In the entropy optimization stage, a look-up table is first established using generalized mutual information, signal-to-noise ratio, and entropy values under probabilistic shaping 256 quadrature amplitude modulation (PS-256-QAM) to determine initial values. These are then fine-tuned within the transmission system to minimize entropy. The proposed optimization framework is validated through numerical simulations, demonstrating clear improvements in overall system performance.

In the power optimization phase, the average power levels and spectral tilts across different frequency bands are first optimized using three distinct strategies: non-uniform channel power optimization, uniform channel power optimization, and a criterion-guided power control strategy referred to as ASENLI. The comparative performance of these approaches is systematically illustrated in Fig. 5. Specifically, the corresponding signal-to-noise ratio (SNR), amplified spontaneous emission (ASE), and nonlinear interference (NLI) ratios achieved under the non-uniform and ASENLI strategies are shown in Figs. 5(a)?(c), respectively. For the uniform strategy, the optimal launch power is determined to be 0.967 dBm, and the associated SNR values are also presented in Fig. 5(a).

Fig. 5(b) shows the optimized launch power profiles obtained using both the non-uniform and ASENLI methods, revealing that these two strategies yield closely matched power distributions. As demonstrated in Fig. 5(d), the system capacity achieved by the ASENLI strategy is only 0.06% lower than that obtained by maximizing SNR, indicating that the criterion-based strategy is well-suited for power optimization in multi-band transmission systems. Furthermore, comparison with the flat-optimal launch power scheme reveals that the non-uniform strategy delivers a 3.4% enhancement in total system capacity, confirming its effectiveness in improving the performance of S+C+L band optical fiber transmission. Following power optimization, a rapid multi-channel grouping mechanism is established to enable the implementation of entropy loading, thus validating the proposed joint active-passive optimization framework. To achieve this, edge and center channels within each band are evaluated via a sliding-window simulation method, and these results are compared with full-band predictions obtained through a closed-form analytical model, as shown in Fig. 6. Although a degree of discrepancy in SNR values exists between the simulation and theoretical model, the overall trend alignment validates the feasibility of rapid grouping based on the modeled full-spectrum SNR distribution. The wavelength division multiplexing (WDM) system channels are subsequently grouped in sets of 30. According to the look-up table provided in Fig. 3, the channel with the lowest SNR in each group—specifically, channels indexed at 30, 60, 90, 120, 150, and 180—is selected for initial entropy assignment, with corresponding initial entropy values of 7.6, 7.4, 7.3, 7.2, 7.0, and 6.8 bit/symbol. These values are further refined via the proposed entropy-loading method, which performs fine adjustments based on the weakest channel within each group to ensure the normalized generalized mutual information (NGMI) meets the 0.833 threshold. Resulting adjusted entropy values are 7.4657, 7.4657, 7.3056, 7.0703, 6.7134, and 6.5854 bit/symbol, respectively. To evaluate the capacity enhancement offered by the joint optimization strategy, three transmission scenarios are simulated and compared in terms of system generalized mutual information (GMI): 1) uniform launch power with 128-QAM, 2) ASENLI-based power control with 128-QAM, and 3) ASENLI-based power control with PS-256-QAM. These simulation results are shown in Fig. 7. Across the L, C, and S bands, launch power optimization contributes GMI improvements of 1.53%, 7.12%, and 15.22%, respectively. On top of this, entropy loading further enhances GMI by 11.71%, 7.03%, and 7.66% in each corresponding band. These findings indicate that while benefits of power optimization are most prominent in the S band, entropy loading delivers consistent and substantial capacity gains across all spectral bands.

In this study, a joint active-passive optimization strategy, integrating criterion-guided power control and grouped entropy loading, is proposed to enhance the transmission capacity of S+C+L band optical systems. This strategy is designed to simultaneously mitigate the impact of stimulated Raman scattering (SRS) and maximize spectral channel utilization. The proposed framework begins with the application of particle swarm optimization to jointly optimize the average launch power and spectral tilt across the S, C, and L bands. Building upon these optimized power profiles, entropy is then loaded group-wise based on system performance, aiming to further elevate the total system capacity. A simulation platform incorporating 180 channels across the S+C+L band, based on the mean-field theory, is constructed to evaluate and compare the system capacities under different power allocation strategies, including non-uniform channel power optimization, uniform power optimization, and the proposed criterion-guided power control approach. Results demonstrate that non-uniform power optimization yields the highest system capacity. However, the proposed criterion-guided strategy, despite employing a sub-optimal power allocation from an engineering perspective, achieves 99.4% of the optimal capacity while exhibiting significantly faster convergence, making it more practical for real-world deployment. Following entropy loading, the GMI sees further improvement when compared to the uniform power optimization baseline, with GMI increases of 1.53%, 7.12%, and 15.22% observed in the L, C, and S bands, respectively. When combined with group-wise entropy refinement, additional GMI enhancements of 11.71%, 7.03%, and 7.66% are attained. These findings confirm the effectiveness of the proposed joint optimization strategy in delivering comprehensive capacity gains across all spectral bands.