⚡ electrical engineering

Modeling and Modulation Optimization for OWC Limited by Electronic and Photonic Bandwidth

This paper addresses the bandwidth limitations of optical wireless communication (OWC) components by modeling their frequency response as a low-pass pole-zero transfer function and optimizing the signal power spectral density of DCO-OFDM using a novel Newton-based algorithm and an accelerated Hughes-Hartogs method to maximize throughput beyond the 3-dB bandwidth.

Original authors: Xiaochen Liu, Jean-Paul M. G. Linnartz, Thiago E. B. Cunha

Published 2026-05-06

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CC BY 4.0

Original authors: Xiaochen Liu, Jean-Paul M. G. Linnartz, Thiago E. B. Cunha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ 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

Imagine you are trying to shout a message across a crowded room. In a radio system (like Wi-Fi), the government tells you, "You can only shout at this specific volume and pitch to avoid disturbing your neighbors." But in Optical Wireless Communication (OWC)—which is like sending messages using light instead of radio waves—there are no government rules stopping you from shouting as loud or as fast as you want.

The problem isn't the rules; it's the hardware.

The Problem: The "Old Speaker" and the "Bad Microphone"

Think of your light source (like an LED bulb) as a speaker and your receiver (a camera or sensor) as a microphone.

The Speaker (LED): If you try to make the LED blink incredibly fast to send data, it gets tired. It can't change its brightness fast enough. It's like an old speaker that gets muffled when you try to play high-pitched notes.
The Microphone (Receiver): Similarly, the sensor trying to catch the light has its own limits. It might be too heavy (large) to react quickly, or its electronics might get "noisy" when the signal gets too fast.

When you combine a tired speaker and a slow microphone, the whole system acts like a low-pass filter. This is a fancy way of saying: "Low frequencies (slow blinks) come through clearly, but high frequencies (fast blinks) get squashed and distorted."

The Solution: The "Smart Water Filler"

The paper proposes a clever way to send more data through this "tired" system without changing the hardware. They use a technique called DCO-OFDM.

Imagine you have a bucket of water (your total power budget) and a landscape of holes (the different frequencies your system can use).

The Old Way (Uniform Loading): You just pour the water evenly across the whole landscape. But if some holes are deep (bad frequencies) and some are shallow (good frequencies), you waste water on the deep holes where it doesn't do much good, and you don't have enough water for the shallow ones.
The New Way (Waterfilling Optimization): The authors suggest pouring the water intelligently. You fill the shallow holes (the frequencies where the system works well) first. If you have extra water, you let it spill over into the deeper holes (the high frequencies where the system is weak), but you only put enough there to make it useful. You stop pouring when the water level is even across the whole landscape.

This "water level" represents the maximum frequency you can use. The paper shows that by doing this, you can actually use frequencies beyond the point where the system usually starts to fail, squeezing out extra data speed that was previously ignored.

The "Recipe" for Speed

The authors created a mathematical "recipe" (a closed-form expression) that tells you exactly how much data you can send based on:

How many "poles" and "zeros" your system has (think of these as the specific ways your speaker and microphone get tired or get noisy).
How much power you are willing to use.

They found that if you only look at the speaker (the transmitter) or only the microphone (the receiver), you get the wrong answer. You have to look at the whole chain (speaker + wire + light + air + sensor + amplifier) to get the right speed. If you ignore part of the chain, you might think you can go faster than you actually can, leading to errors.

The "Smart Algorithms"

To make this work in real life, you need a computer to calculate the perfect water-filling pattern. The paper compares two ways to do this math:

Newton's Method: Like a hiker using a map and a compass to find the peak of a mountain quickly. It's very fast if the mountain isn't too jagged (simple system).
Accelerated Hughes-Hartogs (HH): Like a hiker who only checks the next few steps instead of looking at the whole mountain. This is great if you have a lot of steps to take (complex system) but you are moving slowly (low power).

They found that their new "accelerated" version of the second method is much faster at finding the best path, saving computer power.

The Bottom Line

The paper proves that by understanding exactly how every part of the light-sending system slows down, and by using a "smart water-filling" strategy to distribute power, you can send significantly more data than before. They showed this using real experiments and computer simulations, proving that ignoring the "tired" parts of the system leads to bad predictions, but fixing the strategy leads to big speed gains.

Technical Summary: Modeling and Modulation Optimization for OWC Limited by Electronic and Photonic Bandwidth

Problem Statement
Unlike radio frequency (RF) communications, where modulation bandwidth is often restricted by regulatory spectral masks, Optical Wireless Communication (OWC) systems are primarily constrained by the frequency response of their physical components. In OWC, the overall Gain-to-Noise Ratio (GNR) typically exhibits a low-pass characteristic due to the cascaded limitations of electronic components (e.g., op-amps, driver circuits) and photonic components (e.g., LEDs, lasers, photodiodes). While existing literature has addressed bandwidth limitations in specific components (such as LEDs or photodetectors) or specific modulation schemes, there is a lack of comprehensive modeling that accounts for the cumulative bandwidth constraints of the entire link. Furthermore, many optimization strategies assume a flat frequency response or consider only the most limiting component, leading to inaccurate throughput estimations. The paper addresses the need for accurate, end-to-end channel modeling and the subsequent optimization of the signal Power Spectral Density (PSD) to maximize throughput beyond the standard 3-dB bandwidth.

Methodology
The authors propose a systematic approach involving three main stages:

Comprehensive Channel Modeling: The paper reviews the frequency characteristics of all major OWC link stages, including transmitters (LEDs, lasers, phosphors, modulators), propagation channels (diffuse reflection, plastic optical fiber, beam squint in RIS/OPAs), and receivers (photodiodes, Transimpedance Amplifiers). These components are modeled as cascaded transfer functions characterized by poles and zeros. The resulting spectral GNR is formulated as a rational function (a zero-pole transfer function), capturing the low-pass decay and potential non-monotonic behaviors (e.g., resonant peaks or DC blocking).
Throughput Optimization via Waterfilling: The authors formulate the throughput maximization problem for DC-biased Optical Orthogonal Frequency-Division Multiplexing (DCO-OFDM) under a total power constraint. Using Lagrangian optimization, they derive a closed-form expression for the optimal signal PSD.
- For monotonically decreasing GNR (typical low-pass behavior), the optimal PSD follows a "waterfilling" solution where the signal spectrum is shaped to counteract the channel decay, allowing modulation beyond the 3-dB bandwidth.
- The authors derive a closed-form expression for the optimized throughput as a function of the maximum modulation frequency ( $f_{max}$ ), incorporating the specific number of poles ( $N$ ) and zeros ( $M$ ) in the channel model.
- Special attention is given to non-monotonic GNR scenarios (e.g., due to resonant peaks), where the complementary slackness condition of the Karush–Kuhn–Tucker (KKT) conditions is applied to ensure the PSD remains non-negative, effectively creating "island" regions where no power is allocated.
Algorithmic Implementation: To implement the optimization in practical systems, two algorithms are developed and compared:
- Newton-based Method (NT): An iterative algorithm that efficiently searches for the optimal $f_{max}$ given a specific signal variance (power budget) by utilizing the derivative of the power constraint.
- Accelerated Hughes-Hartogs Algorithm (HHA): A discrete bit-loading algorithm optimized for low-pass channels. The authors introduce a novel acceleration technique using a lookup table to track the lowest-frequency subcarrier for each bit level, significantly reducing the search space per iteration compared to the standard HH algorithm.

Key Contributions

Holistic GNR Modeling: The paper presents the first expression for the optimized throughput of DCO-OFDM over a low-pass channel that explicitly captures the bandwidth constraints imposed by the concatenation of various OWC system components (TX, propagation, RX), rather than isolating a single bottleneck.
Closed-Form Throughput Expression: A closed-form analytical expression for the optimized throughput is derived as a function of the maximum modulation frequency and the channel's pole-zero configuration. This provides a more accurate estimation than uniform power loading assumptions.
Novel Optimization Algorithms: The paper introduces a Newton-based method for continuous rate optimization and an accelerated version of the Hughes-Hartogs algorithm for discrete bit loading. The accelerated HHA leverages the monotonic nature of low-pass channels to reduce computational complexity.
Validation of Modeling Accuracy: The study demonstrates that neglecting the cumulative bandwidth limitations of the entire link (considering only TX or RX) leads to significant errors in throughput estimation, either underestimating or overestimating performance depending on the power budget.

Results
The proposed models and algorithms were validated using experimental data from a yellow phosphor-coated blue LED system and circuit simulations (LTspice) of a large-area PIN photodiode with a TIA.

Model Accuracy: The pole-zero GNR model derived from the full link (TX + Propagation + RX) closely matched the simulated and experimental GNR responses. In contrast, models considering only the transmitter or receiver showed significant deviations, particularly in the high-frequency roll-off region.
Throughput Gains: Numerical results confirmed that employing the proposed waterfilling optimization significantly improves throughput compared to baseline schemes that restrict modulation to the flat region of the GNR. The optimized signal spectrum effectively utilizes frequencies beyond the 3-dB bandwidth.
Algorithm Performance: The Newton-based method was found to be computationally efficient for low-order GNR models (simpler pole-zero counts), while the accelerated HHA demonstrated superior efficiency for low power budgets and low data rates. The lookup table acceleration in the HHA resulted in substantial reductions in floating-point operations (FLOPs) compared to non-accelerated bit-loading algorithms, especially as the number of subcarriers increased.

Significance
The paper claims that accurate, end-to-end modeling of the OWC channel is essential for real-time Channel State Information (CSI) estimation and effective modulation optimization. By moving beyond simplified models that focus on single components, the proposed framework enables a more realistic assessment of achievable data rates. The closed-form throughput expression and the efficient optimization algorithms provide practical tools for designing high-speed OWC systems. The results highlight that significant performance gains are achievable by adapting the signal spectrum to the specific frequency characteristics of the entire optical link, rather than being limited by the 3-dB bandwidth of the slowest individual component. The work underscores that while component limitations are inherent, their impact on system capacity can be mitigated through rigorous modeling and optimized signal design.

The Problem: The "Old Speaker" and the "Bad Microphone"

The Solution: The "Smart Water Filler"

The "Recipe" for Speed

The "Smart Algorithms"

The Bottom Line

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