Joint Fiber Nonlinearity Mitigation and Compensation in Digital Sub-Carrier Multiplexing Systems

Introduction

As global information exchange continues to grow exponentially, optical fiber communication systems face increasing demands for higher capacity. Over the past decades, techniques like wavelength division multiplexing (WDM), polarization multiplexing (PM), coherent detection, and advanced modulation formats have enabled significant capacity increases. More recently, digital sub-carrier multiplexing (DSCM) has emerged as a promising solution to overcome bandwidth limitations of optical devices by processing multiple parallel signals in the radio frequency domain before multiplexing them into a single-wavelength optical signal.

However, nonlinear effects in optical fibers fundamentally limit the capacity of these systems. As optical power increases, changes in the fiber's refractive index lead to nonlinear distortions known as Kerr effects. In WDM systems, these manifest as self-phase modulation (SPM) within a channel, and cross-phase modulation (XPM) and four-wave mixing (FWM) between channels. DSCM systems face additional nonlinear interactions between closely-spaced sub-carriers.

This article explores an approach that combines nonlinearity mitigation and compensation techniques to address these challenges in polarization-multiplexed DSCM-WDM (PM-DSCM-WDM) systems. Specifically, we examine the joint use of symbol rate optimization (SRO) for nonlinearity mitigation and perturbation-based nonlinearity compensation (PB-NLC) in systems with pre-compensation of chromatic dispersion (pre-CDC). We also introduce a novel split PB-NLC technique that distributes compensation between transmitter and receiver.

System Model

Figure 1 illustrates the PM-DSCM-WDM system model considered:

Figure 1

At the transmitter, data is modulated onto multiple DSCM sub-carriers for each polarization of each WDM channel. The signals undergo pulse shaping, pre-CDC, and multiplexing before optical transmission. The fiber channel introduces linear and nonlinear impairments during propagation. At the receiver, the signal is filtered, undergoes chromatic dispersion compensation and matched filtering, and polarization mode dispersion is compensated. Carrier phase recovery is performed before nonlinearity compensation and demodulation.

Nonlinearity Mitigation and Compensation Techniques

1. Symbol Rate Optimization (SRO)

SRO exploits the fact that different nonlinear effects in DSCM systems exhibit distinct behaviors as the sub-carrier symbol rate changes. At higher symbol rates, SPM dominates. As the symbol rate decreases and the number of sub-carriers increases, inter-sub-carrier XPM (iXPM) and eventually inter-sub-carrier FWM (iFWM) become significant. This leads to an optimal symbol rate that minimizes overall nonlinear distortions.

2. Perturbation-Based Nonlinearity Compensation (PB-NLC)

PB-NLC estimates and compensates for nonlinear distortions using a first-order perturbation approximation of the signal propagation. It can be applied at the transmitter (pre-compensation) or receiver (post-compensation). The technique allows for selective compensation of different nonlinear effects (e.g. SPM only, or SPM + iXPM) and adjustment of computational complexity.

For a PM-DSCM-WDM system with pre-CDC, the received signal after post-PB-NLC can be approximated as:

b''(0)[h] ≈ (b'(0)[h] - Δ'(0)[h]) ⊙ exp(-jΦ'(0)[h])

Where b'(0)[h] is the received signal after SPM compensation, and Δ'(0)[h] and Φ'(0)[h] are additive and multiplicative correction terms for iXPM compensation.

3. Joint SRO and PB-NLC

Combining SRO and PB-NLC offers several advantages:

1. SRO reduces overall nonlinear effects, allowing PB-NLC to focus on residual distortions.

2. The optimal symbol rate depends on which nonlinear effects are compensated by PB-NLC.

3. The approach provides flexibility in balancing performance and computational complexity.

Figure 2 illustrates how performance and complexity vary with symbol rate for different PB-NLC schemes:

Figure 2

We observe that:

1. The optimal symbol rate shifts to higher values as more nonlinear effects are compensated (e.g. SPM only vs SPM + iXPM).

2. PB-NLC complexity generally decreases with symbol rate before sharply increasing at very high rates.

3. Joint optimization can achieve significant gains. For example, iXPM-Full compensation at 6 GBd provides a 0.25 dB Q2-factor improvement with 6x lower complexity compared to a conventional 48 GBd WDM system.

Split PB-NLC Technique

The proposed split PB-NLC technique leverages a unique property of iXPM in pre-CDC systems to distribute compensation between transmitter and receiver. For 50% pre-CDC, distinct sets of symbol triplets contribute to iXPM distortions in the first and second halves of propagation.

This allows:

1. Pre-compensation of first-half iXPM effects at the transmitter

2. Post-compensation of second-half iXPM and full SPM effects at the receiver

The technique offers several advantages:

• Reduced approximation and decision errors compared to full post-compensation

• Even distribution of iXPM computational complexity between transmitter and receiver

• Slight performance improvement at no additional overall complexity

Figure 3 compares the performance of split PB-NLC to conventional post-PB-NLC:

Figure 3

We observe that split PB-NLC provides a modest performance gain while significantly reducing receiver-side complexity.

Implementation Considerations

Several factors influence the performance-complexity trade-offs of joint SRO and PB-NLC:

1. Perturbation Coefficient Selection

PB-NLC performance and complexity depend on the number of perturbation coefficients used. A truncation threshold can be applied to select the most significant coefficients. Figure 4 illustrates this trade-off:

Figure 4

We see diminishing returns below a -30 dB threshold relative to the strongest SPM coefficient.

2. Adjacent Sub-Carrier Selection

For iXPM compensation, considering more adjacent sub-carriers improves performance but increases complexity. Figure 4(b) shows this relationship. The nearest sub-carriers have the most significant impact, with diminishing returns for distant sub-carriers.

3. Quantization

Perturbation coefficients can be quantized to reduce complexity with minimal performance impact. Figure 4(c) demonstrates the effect of quantization. Significant complexity reduction is possible with a large number of quantization levels before performance degrades.

Practical Recommendations

Based on the insights from joint SRO and PB-NLC analysis, we offer the following recommendations for practical implementation:

1. Select the DSCM symbol rate based on the specific nonlinear effects compensated by PB-NLC. Higher rates are generally optimal as more effects are compensated.

2. Use a -30 dB truncation threshold for perturbation coefficient selection as a good starting point for balancing performance and complexity.

3. Focus iXPM compensation on the nearest 2-3 adjacent sub-carriers for most efficient performance improvement.

4. Apply quantization to reduce computational complexity, starting with a large number of levels (e.g. 64 or 128) and reducing until performance degradation becomes noticeable.

5. Consider split PB-NLC for systems where receiver complexity is a major constraint, as it can significantly reduce receiver-side processing while maintaining overall performance.

6. When very low complexity is required, optimize the symbol rate for SPM-only compensation, as this provides the largest complexity reduction with still meaningful performance gains.

Conclusion

Joint symbol rate optimization and perturbation-based nonlinearity compensation offer a flexible and efficient approach to addressing fiber nonlinearities in PM-DSCM-WDM systems. By carefully balancing mitigation and compensation techniques, significant performance gains can be achieved with manageable computational complexity. The proposed split PB-NLC technique further enhances this approach by distributing processing between transmitter and receiver.

As optical communication systems continue to evolve, these joint optimization strategies will play an important role in maximizing capacity while managing the ever-present challenge of fiber nonlinearities. Future research directions may include integrating these techniques with machine learning approaches for adaptive optimization and exploring their application in emerging optical network architectures.

Reference

[1] S. Tharranetharan, S. K. Orappanpara Soman and L. Lampe, "Joint Fiber Nonlinearity Mitigation and Compensation for Digital Sub-Carrier Multiplexing System," in IEEE Photonics Journal, vol. 16, no. 4, pp. 1-15, Aug. 2024, Art no. 7201517, doi: 10.1109/JPHOT.2024.3429381.