Best Relay Selection in Gaussian Half-Duplex Diamond Networks

TL;DR

This paper establishes a fundamental bound on how much a single relay can contribute to the approximate capacity of Gaussian half-duplex diamond networks, revealing a sinusoidal relationship with the number of relays.

Contribution

It provides a tight, fundamental bound on the maximum contribution of the best relay to the network's approximate capacity, depending on the number of relays.

Findings

The ratio guarantee is a sinusoidal function of the number of relays.

The ratio guarantee decreases as the number of relays increases.

The bound is shown to be tight with existing network examples.

Abstract

This paper considers Gaussian half-duplex diamond $n$-relay networks, where a source communicates with a destination by hopping information through one layer of $n$ non-communicating relays that operate in half-duplex. The main focus consists of investigating the following question: What is the contribution of a single relay on the approximate capacity of the entire network? In particular, approximate capacity refers to a quantity that approximates the Shannon capacity within an additive gap which only depends on $n$, and is independent of the channel parameters. This paper answers the above question by providing a fundamental bound on the ratio between the approximate capacity of the highest-performing single relay and the approximate capacity of the entire network, for any number $n$. Surprisingly, it is shown that such a ratio guarantee is $f = 1/(2+2\cos(2\pi/(n+2)))$, that is a sinusoidal function of $n$, which decreases as $n$ increases. It is also shown that the aforementioned ratio guarantee is tight, i.e., there exist Gaussian half-duplex diamond $n$-relay networks, where the highest-performing relay has an approximate capacity equal to an $f$ fraction of the approximate capacity of the entire network.