OFC2025|A Modulation-Agnostic Pilot-Aided Fiber Length Estimator for High-Speed Coherent Links

Introduction

In modern high-speed optical communication systems, accurately estimating the fiber length within an optical links is critical for compensating chromatic dispersion (CD). This compensation occurs within the digital signal processing (DSP) chain at the receiver and represents a critical initial step required before subsequent processes such as polarization mode dispersion (PMD) equalization, carrier recovery, and timing recovery can effectively operate. This paper discusses a novel pilot-aided fiber length estimator (PA-FLE) developed by researchers from Marvell Technology, which addresses multiple challenges present in existing fiber length estimation techniques [1].

Challenges in Fiber Length Estimation

Traditional fiber length estimation methods typically employ brute-force searching, utilizing various cost functions such as autocorrelation of the input data or calculating timing tones. However, these methods perform inadequately with signals having low bandwidth redundancy or when the channel experiences severe bandwidth limitation caused by wavelength-selective switches. Alternative methods based on peak-to-average power ratio (PAPR) minimization degrade performance when handling signals using probabilistic constellation shaping (PCS).

Other existing pilot-sequence methods require excessively long sequences at high symbol rates, making efficient implementation challenging. The PA-FLE resolves these issues through a modulation-agnostic approach, requiring minimal pilot overhead (as low as 0.1%) while maintaining accuracy and robustness.

PA-FLE Method

PA-FLE employs customized pilot symbol sequences periodically inserted into the transmitted signal. The sequence consists of two identical QPSK patterns, each having short duration W, akin to the "cyclic prefix" method used in orthogonal frequency-division multiplexing (OFDM).

Figure 1: Structure of transmitted pilot sequence for two polarizations, with W representing the length of the pilot sequence.

At the receiver, the algorithm scans the CD equalizer coefficients over a range of potential CD values (e.g., from 0 ns/nm to 20 ns/nm with increments of 0.25 ns/nm). For each tested CD value, the algorithm computes a cost function using symbols output from the CD equalizer, selecting the CD value that maximizes this metric.

Cost function computation involves two steps:

1. Calculating a differential version of the input symbols to provide immunity against carrier frequency offset and phase noise.

2. Computing correlation between two non-contiguous signal segments.

Figure 2: Description of cost function. Metric peaks when two correlation windows align with the pilot sequence positions.

This design yields a robust metric immune to impairments such as bandwidth limitation, skew, PMD, sampling phase errors, and clock frequency offset. By averaging cost functions across two polarizations, the metric is also robust against variations in the state of polarization (SOP).

Experimental Validation

The research team performed extensive validation using a coherent DSP implemented in a 5 nm ASIC. The optical setup included a digital transmitter and receiver with drivers, optical modulators, integrated coherent receivers, and bias controllers.

Figure 3: Experimental setup illustrating transmitter optical sub-assembly (TOSA) and receiver optical sub-assembly (ROSA).

Experiments employed DP-QAM16 with PCS modulation running at 90 GBd—a configuration designed for high-performance 400 Gbps applications. The optical link consisted of up to three segments of 125 km single-mode fiber, configured to create four channel conditions: back-to-back (B2B), 125 km, 250 km, and 375 km.

To rigorously test the algorithm, several challenging conditions were introduced:

• Wide range of PMD with differential group delay up to 70 ps.

• Second-order PMD up to 1800 ps².

• Rapid polarization rotation up to 400 krad/s.

• Laser linewidth of 50 kHz.

• OSNR set at 17 dB.

• Imperfect digital pre-emphasis.

• Residual I/Q skew around 1 ps.

The pilot sequence length W was set to 128 symbols, configured to match the energy of data symbols. The pilot overhead was kept at 0.1%, resulting in negligible OSNR penalty, while maintaining the search time below 1 ms.

Results and Performance Comparison

The researchers conducted 2000 experiments, randomly varying channel conditions to cover extreme scenarios. PA-FLE performance was compared with a blind FLE based on PAPR.

Figure 4 here: Histogram of estimation errors comparing the proposed PA-FLE and PAPR-based blind FLE.

Results indicated that the blind FLE exhibited substantial residual CD, potentially compromising robustness of subsequent DSP stages. Some experiments using blind FLE showed errors greater than 1000 ps/nm. In contrast, PA-FLE consistently provided reliable and accurate estimations, maintaining errors below 250 ps/nm.

Advantages Over Alternative Methods

Unlike other pilot-aided FLE methods attempting to estimate the complete frequency response of multi-output optical channels, PA-FLE focuses solely on CD estimation. This method requires shorter pilot bursts and simpler computations within the receiver.

Furthermore, PA-FLE effectively synchronizes input pilot symbols from unequilibrated signals, addressing a challenge inadequately resolved by other pilot-based algorithms.

Conclusion

The Pilot-Aided Fiber Length Estimator (PA-FLE) introduced in this paper provides a robust solution for CD estimation in high-speed coherent optical links. By adopting a modulation-agnostic approach, it overcomes the limitations of traditional methods and remains effective even with complex modulation formats such as probabilistic constellation shaping.

With low computational complexity and minimal pilot overhead of 0.1%, PA-FLE is highly suitable for efficient hardware implementations. Experimental validation using a 5 nm ASIC coherent DSP confirmed accurate estimations for 90 GBd DP-QAM16+PCS signals, consistently yielding errors below 250 ps/nm. This performance ensures reliable operation of subsequent DSP stages in the receiver chain, enhancing overall system robustness.

Reference

[1] N. Campos, M. Olmos, A. Martinez Balsa, and D. Morero, "A Modulation-agnostic Pilot-aided Fiber Length Estimator for High-Speed Coherent Links," in OFC 2025, OFC Publishing Group, 2025, Paper M1E.7.