TY - JOUR

T1 - Gaussian Half-Duplex Diamond Networks

T2 - Ratio of Capacity the Best Relay can Achieve

AU - Jain, Sarthak

AU - Mohajer, Soheil

AU - Cardone, Martina

N1 - Publisher Copyright:
IEEE

PY - 2021

Y1 - 2021

N2 - 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+2cos(2π/(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.

AB - 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+2cos(2π/(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.

KW - Additives

KW - approximate capacity

KW - Diamond

KW - diamond network

KW - Half-duplex

KW - Next generation networking

KW - Relay networks (telecommunication)

KW - relay selection

KW - Relays

KW - Topology

KW - Wireless networks

UR - http://www.scopus.com/inward/record.url?scp=85103296851&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85103296851&partnerID=8YFLogxK

U2 - 10.1109/TWC.2021.3066527

DO - 10.1109/TWC.2021.3066527

M3 - Article

AN - SCOPUS:85103296851

JO - IEEE Transactions on Wireless Communications

JF - IEEE Transactions on Wireless Communications

SN - 1536-1276

ER -