Low Complexity Kolmogorov-Arnold Network-based DPD for Analog RoF Fronthaul

Technical Summary: Low Complexity Kolmogorov-Arnold Network-based DPD for Analog RoF Fronthaul

Problem Statement
The transition to 6G mobile wireless systems necessitates the use of higher frequency bands (mmW and Terahertz) to meet demands for high data rates and seamless connectivity. However, these frequencies suffer from significant atmospheric attenuation, limiting transmission reach. Analog Radio-over-Fiber (A-RoF) systems offer a solution by leveraging optical fiber's high bandwidth and low attenuation to transport wireless signals over long distances. Despite this advantage, A-RoF links are susceptible to signal quality degradation caused by both linear and nonlinear impairments. Key sources of nonlinearity include the electro-optic modulators (specifically Mach-Zehnder Modulators or MZMs), the fiber channel (Kerr effects and dispersion), and, most critically, the Power Amplifiers (PAs) used to boost radio signals.

Nonlinear distortions are particularly detrimental as they depend on signal power levels, creating a trade-off between power efficiency and Quality of Transmission (QoT). While PAs are most efficient in saturation, this regime enhances nonlinear effects. Digital Predistortion (DPD) is a standard technique to mitigate these distortions by estimating and applying the inverse of the channel's nonlinear response. While Memory Polynomials (MP) are well-established for this purpose, recent research has explored Neural Networks (NNs) for their ability to model complex multidimensional mappings. However, NN-based DPD models often suffer from high computational complexity and lack interpretability compared to traditional models.

Methodology
This paper proposes and experimentally validates a novel DPD model named Envelope Time-Delay Kolmogorov-Arnold Network (ETDKAN). The approach integrates physical constraints of RF nonlinear devices into the network architecture.

1. Theoretical Foundation: The model is based on the Kolmogorov-Arnold Representation Theorem, which represents multivariable functions as compositions of univariate functions. Unlike Multilayer Perceptrons (MLPs) that optimize weights and biases, KANs optimize parameterizable activation functions (represented as a sum of a fixed nonlinear function and a B-spline).
2. Model Architecture: The ETDKAN adapts the Envelope Time-Delay Neural Network (ETDNN) architecture by replacing the MLP component with a KAN. The input consists of time-delayed magnitudes of the input signal, ensuring the output is an odd function of the input, a physical constraint required for accurate PA modeling.
3. Symbolic Reduction: To address the high computational cost of KANs (specifically the B-spline calculations), the authors employ a symbolization process. After initial training, the learned activation functions are approximated by analytical expressions (e.g., affine transformations of standard functions) using symbolic regression. This results in a symbolic ETDKAN (symbETDKAN) model.
4. System Simulation and Experimentation:
   • Simulation: An A-RoF system model was implemented including OFDM waveform generation, MZM modeling (push-pull configuration), fiber channel effects (loss and chromatic dispersion), photodiode detection, and a 3GPP-specified memoryless PA model.
   • Training: Models were trained using the Indirect Learning Architecture (ILA) with 50,000 signal samples. Hyperparameters were optimized using the Optuna framework.
   • Experiment: A back-to-back A-RoF experimental setup was constructed using an external cavity laser, an MZM, a photodetector, and a PA. The system utilized 64QAM OFDM signals with a 100 MHz bandwidth.

Key Contributions

• First Experimental Demonstration: This work presents the first experimental demonstration of a KAN-based DPD model for A-RoF systems.
• ETDKAN Proposal: The introduction of the ETDKAN model, which incorporates envelope time-delay inputs to satisfy PA physical constraints while leveraging the KAN framework.
• Complexity Reduction via Symbolization: The successful application of the symbolization process to the ETDKAN, creating the symbETDKAN variant. This variant retains the interpretability and performance of the neural network while drastically reducing computational complexity.
• Comparative Analysis: A comprehensive comparison against established models: Memory Polynomials (MP), ARVTDNN, ETDNN, and the non-symbolic ETDKAN.

Results

• Numerical Simulation:
  • The non-symbolic ETDKAN achieved the best Adjacent Channel Leakage Ratio (ACLR) at -36.54 dB and an Error Vector Magnitude (EVM) of 3.16%, outperforming MLP-based models (ETDNN and ARVTDNN). However, it required a high computational cost of 5,804 Floating-Point Operations (NFLOP).
  • The symbETDKAN achieved comparable performance to the neural network models (ACLR: -35.71 dB, EVM: 3.46%) but with a computational complexity (53–143 NFLOP) close to that of the Memory Polynomial model (60 NFLOP).
  • Compared to the ARVTDNN, the symbETDKAN required approximately 8 times fewer NFLOPs for similar performance.
• Experimental Validation:
  • In the physical A-RoF testbed, the proposed models successfully mitigated nonlinear distortions.
  • The ETDKAN achieved an ACLR of -34.49 dB, while the symbETDKAN achieved -33.12 dB.
  • The experimental results confirmed a 4–5 dB reduction in ACLR for the proposed models compared to the system without DPD.
  • The relative performance ranking remained consistent with simulations: the symbETDKAN offered a favorable balance between the high performance of NNs and the low complexity of MP models.

Significance and Claims
The paper claims that the proposed symbETDKAN approach offers a practical solution for linearizing A-RoF links in future 6G networks. By combining the superior modeling capabilities of KANs with a symbolization process, the authors demonstrate that it is possible to achieve performance comparable to complex neural networks while maintaining a computational complexity similar to traditional, low-complexity polynomial models.

The authors emphasize that the KAN framework's ability to derive analytical expressions makes it a promising candidate for the equalization and modeling of nonlinearities in modern communication systems. The study concludes that the ETDKAN-based DPD is a viable candidate for A-RoF fronthauls, particularly where the interpretability and reduced complexity of the symbolic model are advantageous for implementation. Future work suggested by the authors includes investigating KAN performance under different nonlinear regimes and assessing the impact of frequency-selective optical channel responses in direct-detection systems.