Wireless Network Simplification : Beyond Diamond Networks

TL;DR

This paper investigates how to select smaller subnetworks within layered Gaussian relay networks to retain a significant fraction of the overall capacity, providing theoretical guarantees and specific examples.

Contribution

It establishes capacity approximation ratios for subnetworks with fewer relays, extending understanding beyond diamond networks and deriving new results on MIMO antenna selection.

Findings

Existence of subnetworks achieving specific capacity fractions for various network configurations

Capacity bounds for subnetworks with K relays per layer

Examples demonstrating exact capacity fractions achieved by subnetworks

Abstract

We consider an arbitrary layered Gaussian relay network with $L$ layers of $N$ relays each, from which we select subnetworks with $K$ relays per layer. We prove that: (i) For arbitrary $L, N$ and $K = 1$, there always exists a subnetwork that approximately achieves $\frac{2}{(L-1)N + 4}$ $\left(\mbox{resp.}\frac{2}{LN+2}\right)$ of the network capacity for odd $L$ (resp. even $L$), (ii) For $L = 2, N = 3, K = 2$, there always exists a subnetwork that approximately achieves $\frac{1}{2}$ of the network capacity. We also provide example networks where even the best subnetworks achieve exactly these fractions (up to additive gaps). Along the way, we derive some results on MIMO antenna selection and capacity decomposition that may also be of independent interest.