  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.
