Capacity per Unit Energy of Fading Channels with a Peak Constraint

TL;DR

This paper derives a simple expression for the capacity per unit energy of fading channels with a peak constraint, analyzing the impact of fading correlation and side information on channel capacity.

Contribution

It extends Verdu's capacity per unit cost formula to channels with memory and provides insights into how fading correlation affects capacity, including continuous-time models.

Findings

Capacity per unit energy is one nat per Joule with side information, regardless of peak power.

Derived explicit formulas for Gauss-Markov and Clarke fading channels.

Established bounds and relationships between fading correlation and channel capacity.

Abstract

A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of Verdu for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are extended to a channel with side information, showing that the capacity per unit energy is one nat per Joule, independently of the peak power constraint. A continuous-time version of the model is also considered. The capacity per unit energy subject to a peak constraint (but no bandwidth constraint) is given by an expression similar to that for discrete time, and is evaluated for Gauss-Markov and Clarke fading channels.