OFC2025| Low-Complexity Digital Twinning of Optical I/Q Modulators Using Direct Detection and Phase Retrieval Techniques

Introduction

In today's rapidly evolving optical communications field, network digital twins have become essential tools for optimization, decision-making, and testing. These digital twins provide virtual replicas of physical network components, enabling engineers to accurately simulate and predict behaviors. This paper explores an innovative method for creating a digital twin of an optical in-phase/quadrature (I/Q) modulator using direct detection and widely nonlinear phase retrieval (WNL-PR) technology [1].

Overview of Digital Twins in Optical Networks

Network digital twins are virtual representations of physical entities that simulate real-world behavior. In optical networks, these twins help operators optimize performance, make informed decisions, and test configurations without disrupting actual services. Creating accurate digital twins requires comprehensive monitoring solutions that can capture the complex behaviors of optical components.

Traditional methods for monitoring optical I/Q modulators rely on coherent optical modulation analyzers (Coh-OMA), which employ expensive coherent receivers. However, these methods suffer from inaccuracies caused by receiver-side I/Q imbalance and carrier frequency offset (CFO).

Single-Pixel Optical Modulation Analyzer (SP-OMA)

The single-pixel optical modulation analyzer (SP-OMA) offers a direct detection-based alternative. Unlike coherent detection methods, SP-OMA employs simple photodetectors to monitor optical signals and uses phase retrieval algorithms to recover phase information from intensity-only measurements. Advantages of this method include:

1. Lower hardware complexity and cost

2. Immunity to receiver-side impairments affecting traditional methods

3. Accurate capture of frequency-dependent characteristics

Recent advances have extended SP-OMA to incorporate widely nonlinear phase retrieval (WNL-PR), accounting for nonlinearities. This technique facilitates estimating complex Volterra-type nonlinearities affecting modulator performance.

Widely Nonlinear Phase Retrieval Framework

The WNL-PR framework utilizes a generalized Volterra model to represent I/Q-correlated and frequency-selective behaviors in optical modulators.

Figure 1: Mathematical representation of the M-order generalized Volterra model (Equation 1), illustrating system output as a function of input and Volterra kernels, along with a schematic comparison of single-stage and multi-stage WNL-PR algorithms.

In this model, different components represent specific physical phenomena:

• w₀,₀: Residual carrier/DC component

• w₁,₀: Impulse response

• w₀,₁: Frequency-selective I/Q imbalance

• Higher-order terms (w₁,₁, w₂,₀, w₀,₂): Nonlinear behaviors such as gain compression

WNL system identification becomes a phase retrieval task, recovering complex coefficients from intensity-only measurements.

Multi-Stage WNL-PR Algorithm

Although WNL-PR holds significant potential, traditional single-stage methods struggle with convergence for higher-order nonlinear terms. To address this, a multi-stage WNL-PR algorithm is proposed.

As illustrated in Figure 1, the multi-stage approach estimates parameters sequentially:

1. Initially estimates first-order widely linear (WL) model

2. Use this estimate as the initial value for the next stage

3. Gradually incorporates higher-order nonlinearities

4. Refine estimates at each stage

This incremental refinement helps avoid "poor" local minima, offering stable convergence, particularly for higher-order nonlinearities significantly impacting model fidelity.

Experimental Setup and Implementation

The method was validated experimentally using a 10-Gbaud 128-QAM system.

Figure 2: Experimental setup comprising an optical transmitter, EDFA, coupler, coherent receiver, and direct detection components.

Experimental configuration includes:

• 1551.06 nm fiber laser

• Two-channel, 92-GSa/s arbitrary waveform generator

• Lithium niobate Mach-Zehnder I/Q modulator

• Signal processing with SP-OMA (direct detection) and Coh-OMA (reference)

To induce I/Q-related nonlinearities, automatic bias controllers were disabled, and peak-to-peak RF voltage levels in the I and Q branches were intentionally mismatched.

Figure 3: Offline processing workflow for Coh-OMA and SP-OMA methods, showing various signal processing steps.

Received signals underwent offline processing, with both OMAs employing 8000 symbols as pilot data to estimate a third-order WNL model. SP-OMA used a hybrid phase retrieval algorithm combining reweighted Wirtinger Flow (RWF) and Alternating Direction Method of Multipliers (ADMM).

Performance Evaluation and Results

Performance of the proposed multi-stage WNL-PR was compared to traditional single-stage methods, using Coh-OMA results as reference.

Figure 4: Normalized mean square error (MSE) and error vector magnitude (EVM) performance of estimated WNL models versus modulator driving voltage difference.

Results demonstrated:

• Multi-stage method improved MSE performance by approximately 3 dB across all test cases

• Digital twin output accuracy improved by 2.5% to 4.5% at practical nonlinear levels

• At ΔV = 300 mV, improvements corresponded to a 6.7 dB increase in SNR

Figure 5: Estimated WNL model tap amplitudes at ΔV = 300 mV, highlighting the accuracy of wide linear taps and slight errors in higher-order taps.

Visualizations indicated minor mismatches in higher-order coefficients, impacting digital twin fidelity slightly but maintaining overall strong performance.

Figure 6: Constellation diagrams of original received signals and outputs from various digital twins under different nonlinear conditions.

Constellation diagrams further illustrated method effectiveness. At practical nonlinear levels (ΔV ≤ 400 mV), differences in EVM between SP-OMA and Coh-OMA remained below 5%, with negligible visual discrepancy.

Conclusion

This paper discusses an innovative method using direct detection and widely nonlinear phase retrieval to digitally twin optical I/Q modulators. The proposed multi-stage WNL-PR algorithm effectively overcomes convergence challenges of traditional methods, accurately estimating complex, frequency-selective distortions.

Experimental results confirm that SP-OMA combined with multi-stage WNL-PR produces digital twins nearly as accurate as coherent detection-based approaches, providing significant cost advantages. This advancement offers an economical, distributed, and online optical monitoring solution for constructing high-fidelity digital twins of optical network components.

As optical networks continue to grow in complexity and scale, efficient digital twinning technologies will be crucial for ensuring optimal performance, reliability, and adaptability in next-generation optical communication systems.

Reference

[1] Y. Yoshida, S. Oda, N. Yamamoto, T. Hoshida, and K. Akahane, "Low-Complexity Digital Twinning of Optical I/Q Modulator by Direct-Detection with Widely Non-Linear Phase Retrieval," in OFC 2025, 2025, pp. M1E.3.