Quasi-Concavity for Gaussian Multicast Relay Channels

TL;DR

This paper demonstrates that key capacity bounds for Gaussian multicast relay channels exhibit quasi-concavity properties in various parameters, aiding in optimal relay positioning and understanding channel behavior.

Contribution

It establishes the quasi-concavity of upper and lower bounds on capacity in Gaussian multicast relay channels, providing insights into optimal relay placement.

Findings

Bounds are quasi-concave in receiver SNRs and source-relay correlation.

Cut-set rates are quasi-concave in relay position for fixed correlation.

Decode-forward rates are quasi-concave in relay position, aiding optimal relay placement.

Abstract

Standard upper and lower bounds on the capacity of relay channels are cut-set (CS), decode-forward (DF), and quantize-forward (QF) rates. For real additive white Gaussian noise (AWGN) multicast relay channels with one source node and one relay node, these bounds are shown to be quasi-concave in the receiver signal-to-noise ratios and the squared source-relay correlation coefficient. Furthermore, the CS rates are shown to be quasi-concave in the relay position for a fixed correlation coefficient, and the DF rates are shown to be quasi-concave in the relay position. The latter property characterizes the optimal relay position when using DF.