Oblivious Fronthaul-Constrained Relay for a Gaussian Channel

TL;DR

This paper analyzes the maximum reliable data rate in a Gaussian channel with a frequency-selective relay constrained by capacity, considering oblivious relay operation and spectrum shaping, with implications for MIMO systems.

Contribution

It introduces a new analysis of oblivious, capacity-limited relays with spectrum shaping, deriving achievable rates and bounds, including the impact of discontinuous spectrum allocation.

Findings

Gaussian signaling achieves reliable rates under the constraints.

Optimal spectrum allocation can be discontinuous, unlike classical water-pouring.

Bounds and approximations for entropy-limited relay performance.

Abstract

We consider systems in which the transmitter conveys messages to the receiver through a capacity-limited relay station. The channel between the transmitter and the relay-station is assumed to be a frequency selective additive Gaussian noise channel. It is assumed that the transmitter can shape the spectrum and adapt the coding technique so as to optimize performance. The relay operation is oblivious (nomadic transmitters), that is, the specific codebooks used are unknown. We find the reliable information rate that can be achieved with Gaussian signaling in this setting, and to that end, employ Gaussian bottleneck results combined with Shannon's incremental frequency approach. We also prove that, unlike classical water-pouring, the allocated spectrum (power and bit-rate) of the optimal solution could frequently be discontinuous. These results can be applied to a MIMO transmission scheme. We also investigate the case of an entropy limited relay. We present lower and upper bounds on the optimal performance (in terms of mutual information), and derive an analytical approximation.