On the Capacity of the Half-Duplex MIMO Gaussian Diamond Channel

TL;DR

This paper analyzes the capacity of the 2-relay MIMO Gaussian diamond channel, demonstrating that a multihopping decode-and-forward protocol approaches capacity within a constant gap for certain channel conditions.

Contribution

It extends capacity analysis to MIMO channels and identifies optimal transmit covariance matrices for the relays in the protocol.

Findings

MDF-MAC protocol achieves near-capacity rates when $\Delta > 0$

Explicit transmit covariance matrices are derived for relays

Capacity gap is bounded by a constant under specified conditions

Abstract

In this paper, we analyze the 2-relay multiple-input multiple-output (MIMO) Gaussian diamond channel. We show that a multihopping decode-and-forward with multiple access (MDF-MAC) protocol achieves rates within a constant gap from capacity when a channel parameter $\Delta$ is greater than zero. We also identify the transmit covariance matrices to be used by each relay in the multiple-access (MAC) state of the MDF-MAC protocol. As done for the single-antenna 2-relay Gaussian diamond channel, the channel parameter $\Delta$ is defined to be the difference between the product of the capacities of the links from the source to the two relays and the product of the capacities of the links from the two relays to the destination.