⚡ electrical engineering

On the Bit Error Rate Fluctuation Induced by Multipath Interference in the Coherent Regime for Intra Data Center Applications

This paper theoretically explains for the first time how multipath interference resizes PAM-4 constellations in the coherent regime, thereby increasing bit error rate fluctuations in intra-data center applications.

Original authors: Wing-Chau Ng, Scott Yam

Published 2026-03-24

📖 5 min read🧠 Deep dive

CC0 1.0

Original authors: Wing-Chau Ng, Scott Yam

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Why Data Centers Are Getting "Nervous"

Imagine a massive data center as a super-fast highway where information (data) travels between servers. To move huge amounts of data quickly, engineers are using a new, high-speed language called PAM-4. Think of this like a traffic light system that doesn't just have Red, Yellow, and Green, but also Orange and Blue. This allows cars (data) to move much faster.

However, there's a problem. Sometimes, the road isn't perfectly smooth. There are tiny cracks in the fiber optic cables or dirty connectors that act like mirrors. When a beam of light hits these mirrors, a tiny bit of it bounces back and catches up to the main beam. This is called Multipath Interference (MPI).

Usually, engineers know how to handle these echoes. But recently, they found a weird glitch: in very short connections (less than 100 meters), the error rate (how many cars crash) fluctuates wildly and unpredictably. Sometimes it's great; sometimes it's terrible. No one knew why until this paper.

The Core Discovery: The "Dancing" Signal

The authors of this paper figured out that the culprit is a "ghost" effect caused by laser instability and distance.

The Analogy: The Echoing Choir

Imagine you are in a large hall singing a note.

The Main Singer: You are the main signal.
The Echo: A tiny bit of your voice bounces off a wall and comes back to your ears a split second later.

In the old days (the "decorrelation regime"), the echo was so delayed that it sounded like a completely different note. The main singer and the echo didn't really interact; they just made a bit of noise.

But in these short data center links (the "coherent regime"), the echo comes back almost instantly. It's like the echo is singing the exact same note as you, but slightly out of sync.

The "Phase Offset": The Secret Ingredient

Here is where the magic (and the math) happens. The laser light isn't perfectly steady; it wobbles slightly in frequency (like a singer who is slightly off-key). Because the echo travels a tiny extra distance, it arrives with a phase offset.

Think of this phase offset as the timing difference between you and your echo.

Scenario A (The Good Timing): The echo arrives exactly when you are at the peak of your voice. They combine forces, making the sound louder and clearer. In the paper, they call this "Constellation Dilation." It's like stretching a rubber band; the distance between your data points gets bigger, making it easier to tell them apart.
Scenario B (The Bad Timing): The echo arrives when you are at the bottom of your voice. They cancel each other out, making the sound weaker and muddy. This is "Constellation Contraction." The rubber band shrinks; your data points get squished together, making it hard to tell them apart.

Why Does This Cause "Fluctuation"?

The scary part is that the laser's frequency wobbles randomly. So, the "timing" of the echo changes constantly.

One millisecond, the echo helps you (Dilation = Low Errors).
The next millisecond, the echo hurts you (Contraction = High Errors).

This is why the Bit Error Rate (BER) fluctuates. It's not a steady problem; it's a random rollercoaster. The paper explains that if the laser drifts just enough to create a specific phase shift (like $\pi$ or 180 degrees), the data points get squished so tight that the system crashes.

The "Magic Distance" Rule

The paper also explains why this only happens in short links (under 100 meters):

Short Links: The echo returns so fast that the laser hasn't had time to change its "mood" (frequency). The echo and the main signal are still "in sync" enough to interfere dramatically.
Long Links: If the link is long, the echo takes so long to return that the laser has completely changed its frequency by the time the echo arrives. The echo and the main signal are now strangers; they don't interfere anymore. The problem disappears.

The Takeaway

What did they do?
They built a mathematical model that proved this "squishing and stretching" of data points is the reason for the random errors.

Why does it matter?
Data centers are building faster, shorter connections to handle AI and cloud computing. If they don't account for this "echo interference," their super-fast 1.6 Terabit modules might fail randomly.

The Solution?
Now that we know the cause (random phase offsets causing constellation squishing), engineers can design better software (DSP) to detect when the signal is getting "squished" and adjust accordingly, or use better lasers that don't wobble as much.

In a nutshell:
Imagine trying to hear a friend whisper in a room. If a mirror bounces their voice back at the exact right time, you hear them clearly. If it bounces back at the wrong time, you hear nothing. In data centers, the "mirror" is a dirty connector, and the "wrong time" is changing randomly, causing the data to vanish and reappear. This paper explains exactly why that happens.

1. Problem Statement

The rapid scaling of intra-data center connectivity (driving 1.6 Tbps PAM4 modules) faces significant performance margins due to optical impairments. While Multipath Interference (MPI) is a known issue, its behavior differs based on the relationship between the optical path-length difference ( $L$ ) and the laser coherence length ( $L_c$ ):

Decorrelation Regime ( $L \gg L_c$ ): MPI performance degradation is well-understood and analytically modeled.
Coherent Regime ( $L < L_c$ ): Recent experimental work [3] observed anomalously high and randomly fluctuating Bit Error Rates (BER) in short links (<100m), but the root cause remained unexplained.
The Gap: Existing models did not account for how laser frequency drift and path-length differences interact in the coherent regime to cause dynamic constellation distortion.

2. Methodology

The authors developed a theoretical framework and performed numerical simulations to analyze MPI in the coherent regime.

Theoretical Formulation

Signal Model: The received signal $y(t)$ is modeled as the sum of the direct signal and a reflected interferer. The interferer travels an extra round-trip distance $L$ , introducing a time delay $\tau = nL/c$ .
Key Variables:
- PAM4 Symbols: $d(t) \in \{-1.5, -0.5, 0.5, 1.5\}$ with bias $V_b$ .
- Phase Offset ( $\Phi$ ): Defined as $\Phi = \omega_o\tau - \Delta\omega t + \Delta\omega\tau$ . This captures the phase shift caused by laser frequency instability ( $\Delta\omega$ ) and the path difference over time $\tau$ .
- MPI Power Ratio: $\rho^2$ .
Mechanism: The paper posits that the term $B(\Phi, t)$ in the received signal equation represents a bias fluctuation shaped by the phase offset. Crucially, because the delay $\tau$ is unknown to the receiver, the time-shifted copy of the signal acts as high-frequency interference that Digital Signal Processing (DSP) cannot track. However, the slowly varying bias caused by $\Phi$ can be tracked but leads to constellation distortion.

Simulation Setup

Parameters: 200 Gbps/lane (2 $\times$ DR4/FR4), 106.25 GBaud PAM4, 4 dB extinction ratio.
Noise/Impairments:
- Wiener laser phase noise added in the field domain.
- MPI modeled as an attenuated, delayed replica of the signal with specific power ratio $\rho$ .
- Phase Offset ( $\Phi$ ): Systematically varied from $0$ to $\pi$ to cover the principal range of cosine.
- DSP: A 15-tap Feedforward Equalizer (FFE) using Least-Mean-Square (LMS) to track bias shifts. No Decision Feedback Equalizer (DFE) was used to isolate MPI effects.
Metrics: BER measured against Signal-to-Interference Ratio (SIR) at a fixed Signal-to-Noise Ratio (SNR) of 18 dB.

3. Key Contributions

The paper provides the first theoretical explanation for BER fluctuations in the coherent regime:

Constellation Dilation and Contraction: The authors demonstrate that the random phase offset $\Phi$ $Φ$ causes the PAM4 constellation to dynamically dilate (expand) or contract (shrink).
- $\Phi \approx 0$ : Results in a positive DC shift and "constellation dilation," increasing the Euclidean distance between symbols and lowering the BER.
- $\Phi \approx \pi$ : Results in a negative DC shift and "constellation contraction," reducing the Euclidean distance and increasing the BER.
Source of Fluctuation: The random nature of laser frequency drift causes $\Phi$ to vary over time. Consequently, the BER is not static but fluctuates randomly between the upper bound (worst case, $\Phi=\pi$ ) and lower bound (best case, $\Phi=0$ ).
Regime Transition: The study clarifies the transition from the coherent regime (where $\Phi$ dominates and causes fluctuation) to the decorrelation regime (where phase noise decorrelates the signal and reflection, averaging out the $\Phi$ effect).

4. Results

Coherent Regime ( $L = 0.1L_c$ ):
- Significant BER fluctuation was observed depending on $\Phi$ .
- The curve for $\Phi = \pi$ (black square) consistently represented the worst-case BER (upper bound).
- The curve for $\Phi = 0$ (red line) represented the best-case BER (lower bound).
- This matches the "anomalously high BER" observed in previous experiments, explaining that the system occasionally hits the $\Phi = \pi$ worst-case scenario.
Transition Regime ( $L = 1L_c$ ):
- The difference between the best and worst-case BER curves diminished as signal and reflection phase noises began to decorrelate.
Decorrelation Regime ( $L = 10L_c$ ):
- All curves for different $\Phi$ values converged to a single BER result. The initial phase offset no longer impacted performance because the phase noise randomized the interference completely.
Statistical Validation: Simulations with varying symbol counts (230k to 900k) confirmed that the observed trends are statistically robust and not artifacts of short simulation times.

5. Significance

Theoretical Breakthrough: This work resolves the mystery of random BER spikes in short-reach data center links, attributing them to the interaction between laser frequency drift and multipath interference in the coherent regime.
Design Implications:
- Laser Linewidth: Since the effect is driven by frequency drift ( $\Delta\omega$ ), data center laser sources with wider linewidths (common in cost-sensitive modules) are more susceptible to these fluctuations.
- DSP Limitations: Standard LMS algorithms can track the average bias shift but cannot compensate for the rapid, random constellation contraction caused by the unknown phase offset $\Phi$ .
- System Margin: Network designers must account for the "worst-case" BER (when $\Phi \approx \pi$ ) rather than the average BER when planning link budgets for short-reach coherent PAM4 systems.
Validation: The theoretical model successfully reproduces the unexplained experimental trends found in prior literature, providing a solid foundation for future mitigation strategies.