Characterizing the Low-Signal-to-Noise Ratio Asymptotic Capacity of Gaussian and Poisson Optical Wireless Channels under Average-Intensity Constraints

Core Concepts

The low-signal-to-noise ratio asymptotic capacity of Gaussian and Poisson optical wireless channels under average-intensity constraints scales as E√log(1/E) and E log log(1/E), respectively.

Abstract

This paper studies the low-signal-to-noise ratio (SNR) asymptotic capacity of two types of optical wireless channels under average-intensity constraints. The first channel considered is the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by additive white Gaussian noise. The second channel is the Poisson optical intensity channel, where the channel output models the number of received photons corrupted by positive dark current. The key highlights and insights are: For the Gaussian optical intensity channel, the low-SNR asymptotic capacity is shown to scale as E√log(1/E), where E is the average input intensity constraint. This exactly characterizes the scaling order derived in prior work. For the Poisson optical intensity channel, the low-SNR asymptotic capacity is shown to scale as E log log(1/E). This also exactly characterizes the scaling order derived in prior work. The results are proved from two directions - the direct direction uses the duality capacity expression by carefully choosing the auxiliary distribution, while the reverse direction leverages tools from the data processing inequality, Fano's inequality, and the maximum a posteriori probability (MAP) decision rule. The techniques used in this paper may be extended to analyze the low-SNR asymptotic capacity of multiple-antenna optical wireless channels.

Stats

E√log(1/E) E log log(1/E)

Quotes

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Key Insights Distilled From

On the Low-SNR Asymptotic Capacity of Two Types of Optical Wireless Channels under Average-Intensity Constraints

by Longguang Li at arxiv.org 04-09-2024

https://arxiv.org/pdf/2310.15756.pdf

Deeper Inquiries

How can the insights from this work be extended to analyze the capacity of optical wireless channels with more general channel models, such as those incorporating fading or atmospheric turbulence effects

The insights from this work can be extended to analyze the capacity of optical wireless channels with more general channel models by incorporating fading or atmospheric turbulence effects. Fading in optical wireless channels can be modeled using techniques from wireless communication theory, such as Rayleigh or Rician fading models. By considering the impact of fading on the channel, the capacity of the optical wireless channel can be analyzed under different fading conditions. Similarly, atmospheric turbulence effects can be incorporated into the channel model to study the capacity of optical wireless channels in realistic environmental conditions. Techniques from free-space optical communication can be adapted to model the effects of turbulence on the channel and analyze its impact on capacity.

What are the practical implications of the low-SNR asymptotic capacity results, and how can they guide the design of energy-efficient optical wireless communication systems

The practical implications of the low-SNR asymptotic capacity results are significant for the design of energy-efficient optical wireless communication systems. By understanding the capacity scaling behavior at low SNR, system designers can optimize the energy efficiency of optical wireless systems by operating in regimes where the capacity scales favorably with the average input intensity. This knowledge can guide the design of power-efficient modulation schemes, transmission strategies, and receiver architectures to achieve higher data rates with lower energy consumption. Additionally, the results can inform the development of adaptive power control algorithms that adjust the transmission power based on the channel conditions to maximize capacity while minimizing energy usage.

The paper focuses on the low-SNR regime - what can be said about the capacity characterization in the high-SNR regime for these optical wireless channels

While the paper primarily focuses on the low-SNR regime, insights can also be drawn for the high-SNR regime in optical wireless channels. In the high-SNR regime, where the signal power dominates over noise, the capacity behavior of optical wireless channels can exhibit different characteristics compared to the low-SNR regime. By analyzing the capacity scaling at high SNR, system designers can gain insights into the achievable data rates and spectral efficiency of optical wireless systems under favorable signal conditions. Understanding the capacity behavior at both low and high SNR regimes provides a comprehensive view of the performance limits of optical wireless communication systems across a wide range of operating conditions.