# Multiplexing Gain of Amplify-Forward Relaying in Wireless Multi-Antenna Relay Networks

## TL;DR

This paper analyzes the multiplexing gain in multi-antenna relay networks, proving that amplify-forward relaying achieves maximum multiplexing gain equal to the network's minimum vertex cut-set, with extensions to multicast and multi-access scenarios.

## Contribution

It establishes the maximum multiplexing gain for multi-antenna relay networks and links it to the network's graph-theoretic minimum cut-set, extending the analysis to multicast and multi-access cases.

## Key findings

- Amplify-forward relaying achieves maximum multiplexing gain.
- Maximum multiplexing gain equals the minimum vertex cut-set.
- The results extend to multicast and multi-access scenarios.

## Abstract

This paper studies the general multi-antenna multiple-relay network. Every two nodes of the network are either connected together through a Rayleigh fading channel or disconnected. We study the ergodic capacity of the network in the high SNR regime. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.