On the Capacity of Free-Space Optical Intensity Channels (0805.0521v1)

Abstract: New upper and lower bounds are presented on the capacity of the free-space optical intensity channel. This channel is characterized by inputs that are nonnegative (representing the transmitted optical intensity) and by outputs that are corrupted by additive white Gaussian noise (because in free space the disturbances arise from many independent sources). Due to battery and safety reasons the inputs are simultaneously constrained in both their average and peak power. For a fixed ratio of the average power to the peak power the difference between the upper and the lower bounds tends to zero as the average power tends to infinity, and the ratio of the upper and lower bounds tends to one as the average power tends to zero. The case where only an average-power constraint is imposed on the input is treated separately. In this case, the difference of the upper and lower bound tends to 0 as the average power tends to infinity, and their ratio tends to a constant as the power tends to zero.

• The paper presents tight upper and lower bounds on capacity under simultaneous average and peak-power constraints, with the gap under 1 nat when the average-to-peak power ratio exceeds 0.03.
• The paper models the channel using nonnegative inputs with AWGN, thoroughly analyzing behavior in both high and low power regimes.
• The paper highlights implications for optical system design and suggests future research directions including non-Gaussian noise and multipath effects.

Analyzing the Capacity Bounds of Free-Space Optical Intensity Channels

The paper "On the Capacity of Free-Space Optical Intensity Channels" by Amos Lapidoth, Stefan M. Moser, and Michèle A. Wigger explores the capacity limits of free-space optical channels modulated by intensity. Optical channels are regarded as a promising technology for short-distance communications, such as remote controls transmitting signals to televisions, where the primary modulation involves optical intensity. The focus is on the channel capacity influenced by both average and peak-power constraints, shaped by the non-negativity of inputs due to the proportional nature of channel input with the optical light intensity.

Channel Model and Constraints

The authors model the channel with nonnegative inputs corrupted by additive white Gaussian noise (AWGN), which stems from multiple independent noise sources—primarily significant due to ambient light-induced shot noise. The researchers address scenarios with simultaneous average and peak power constraints, a peak-power-only constraint, and an average-power-only constraint. This layered approach offers a detailed exploration of the channel behavior under varying power conditions. The model assumes a dominant line-of-sight component and omits effects from multipath propagation.

Capacities and Bounds

For channels affected by both an average- and peak-power constraint, the authors present upper and lower bounds on capacity. Importantly, these bounds converge asymptotically, zeroing the difference as average and peak power increase while keeping their ratio constant. Notably, the gap between bounds remains under 1 nat if the ratio of average power to peak power is above 0.03.

When a pure average-power constraint is considered, the channel capacity behaves differently. The difference between bounds vanishes as average power grows towards infinity, whereas the bounds themselves tend towards a constant ratio as power decreases.

Key Findings

1. Asymptotic Behavior: The capacity bounds coincidentally decrease to zero as power increases infinitely, holding the power ratio fixed. This suggests that at extremely high power levels, channel capacity stabilizes.
2. Capacity with Constraints: The provided theorems deliver meticulous capacity bounds when both average and peak powers are constrained, as well as specifics for inactive average-power constraints when sufficiently large peak powers dominate.
3. Low Power Asymptotics: In the low power regime, with peak-power constraints, asymptotic expressions for capacity are furnished. Interestingly, for average-power-only constraint scenarios, the bounds are defined up to a constant factor, revealing less precision than with peak power.

Implications and Future Research

This work advances the theoretical understanding of free-space optical channels, essential for designing future optical communication systems. The precise bounds offer benchmarks for evaluating optical system designs under specific power constraints, ensuring adherence to physical and regulatory limitations.

Future advancements could extend these analyses to incorporate non-Gaussian noise models or more complex channel environments, including multipath effects and adaptive strategies for power allocation. Additionally, experimental validation under realistic channel conditions would bridge the gap between theory and practical implementations, enhancing the robustness and applicability of these theoretical constructs.

In conclusion, this paper provides a comprehensive exploration of capacity limits for free-space optical intensity channels under varied constraints, offering essential insights for optical communication system design and optimization. The novel bounds and their implications pave the way for both theoretical enrichment and practical enhancements in optical communication technologies.