On the Fraction of Capacity One Relay can Achieve in Gaussian Half-Duplex Diamond Networks

This paper considers the Gaussian half-duplex diamond n-relay network, which consists of a broadcast hop between the source and n relays, and of a multiple access hop between the relays and the destination. The n relays do not communicate with each other and operate in half-duplex mode. The main focus of the paper is on answering the following question: What fraction of the approximate capacity of the entire network can be retained by only operating the highest-performing single relay? It is shown that a fraction f = 1/2 + 22π {n + 2} of the approximate capacity of the entire network can always be guaranteed. This fraction is also shown to be tight, that is, there exist Gaussian half-duplex diamond n-relay networks for which exactly an f fraction of the approximate capacity of the entire network can be achieved by using only the highest-performing relay.