Analog Network Coding in General SNR Regime

TL;DR

This paper analyzes the maximum achievable rate of analog network coding in layered wireless relay networks, revealing that optimal scaling can be computed layer-by-layer and that previous assumptions may lead to suboptimal performance.

Contribution

It introduces a lemma for layer-wise computation of optimal scaling factors, enabling performance analysis beyond high-SNR assumptions and improving understanding of analog network coding.

Findings

Optimal scaling factors can be computed layer-by-layer.

Assumption of maximum power scaling is generally suboptimal.

Performance characterized in symmetric layered networks.

Abstract

The problem of maximum rate achievable with analog network coding for a unicast communication over a layered wireless relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under two assumptions: (A) each relay node scales its received signal to the upper bound of its transmit power constraint, (B) the relay nodes in specific subsets of the network operate in the high-SNR regime. We establish that assumption (A), in general, leads to suboptimal end-to-end rate. We also characterize the performance of analog network coding in class of symmetric layered networks without assumption (B). The key contribution of this work is a lemma that states that a globally optimal set of scaling factors for the nodes in a layered relay network that maximizes the end-to-end rate can be computed layer-by-layer. Specifically, a rate-optimal set of scaling factors for the nodes in a layer is the one that maximizes the sum-rate of the nodes in the next layer. This critical insight allows us to characterize analog network coding performance in network scenarios beyond those that can be analyzed using the existing approaches. We illustrate this by computing the maximum rate achievable with analog network coding in one particular layered network, in various communication scenarios.