On the Capacity of Fading Channels with Peak and Average Power Constraints at Low SNR

TL;DR

This paper analyzes the capacity of fading channels with peak and average power constraints at low SNR, revealing how capacity scales with PAPR and showing that simple On-Off schemes are asymptotically optimal.

Contribution

It derives the asymptotic capacity expression under peak and average power constraints and proves the sufficiency of On-Off power schemes in the low-SNR regime.

Findings

Capacity scales as A * SNR * integral of inverse CDF of fading

On-Off power scheme is asymptotically capacity-achieving

Generalizes capacity scaling for variable PAPR scenarios

Abstract

The capacity of fading channels under peak and average power constraints in the low-SNR regime is investigated. We show that the capacity scales essentially as ${C \approx A \ \text{SNR} \int_{1- \frac{1}{A}}^1 F^{-1}\left(t\right)dt}$, where $A$ is the peak to average power ratio (PAPR), and $F(\cdot)$ is the cumulative distribution function of the fading channel. We also prove that an On-Off power scheme is sufficient to asymptotically achieve the capacity. Furthermore, by considering the variable PAPR scenario, we generalize the scalability of the capacity and derive the asymptotic expression for the capacity in the low-SNR regime.