Capacity Results for Block-Stationary Gaussian Fading Channels with a Peak Power Constraint

TL;DR

This paper analyzes the capacity of block-stationary Gaussian fading channels with peak power limits, revealing how capacity scales with SNR and the importance of codeword length and signaling schemes.

Contribution

It provides the first asymptotic capacity characterization for peak-power-limited block-stationary Gaussian channels and explores the interplay between codeword length, rate, and error probability.

Findings

Capacity depends on the channel model in high SNR

Codeword length must scale with SNR for logarithmic rate growth

Capacity per unit energy is achievable with ON-OFF signaling

Abstract

We consider a peak-power-limited single-antenna block-stationary Gaussian fading channel where neither the transmitter nor the receiver knows the channel state information, but both know the channel statistics. This model subsumes most previously studied Gaussian fading models. We first compute the asymptotic channel capacity in the high SNR regime and show that the behavior of channel capacity depends critically on the channel model. For the special case where the fading process is symbol-by-symbol stationary, we also reveal a fundamental interplay between the codeword length, communication rate, and decoding error probability. Specifically, we show that the codeword length must scale with SNR in order to guarantee that the communication rate can grow logarithmically with SNR with bounded decoding error probability, and we find a necessary condition for the growth rate of the codeword length. We also derive an expression for the capacity per unit energy. Furthermore, we show that the capacity per unit energy is achievable using temporal ON-OFF signaling with optimally allocated ON symbols, where the optimal ON-symbol allocation scheme may depend on the peak power constraint.