Capacity per Unit Energy of Fading Channels with a Peak Constraint
<|reference_start|>Capacity per Unit Energy of Fading Channels with a Peak Constraint: 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.<|reference_end|>
@article{sethuraman2005capacity,
    title={Capacity per Unit Energy of Fading Channels with a Peak Constraint},
    author={Vignesh Sethuraman and Bruce Hajek},
    journal={arXiv preprint arXiv:cs/0504085},
    year={2005},
    doi={10.1109/TIT.2005.853329},
    archivePrefix={arXiv},
    eprint={cs/0504085},
    primaryClass={cs.IT math.IT}
}