Effects of Transmit Beamforming on the Capacity of Multi-Hop MIMO Relay Channels

In this paper we investigate multi-hop fading relay channels where the source, the destination and the multiple relay nodes are all equipped with multiple antennas. We study the ergodic capacities of multiple relay networks based on Amplify-and- Forward (AF) and Decode-and-Forward (DF) relaying modes. We examine multi-user beamforming (MU-BF), where each data stream is assumed to be matched to a specified relay node, based on the conventional eigen-mode transmission for both modes, and derive ergodic capacity expressions. We also examine the impact of the number of selected relay nodes on the network capacity both for modes of relaying. We show that by using MU-BF at the source node and a maximum number of relay nodes selected for cooperation, the network gains from multiplexing, while beyond that number of cooperating relay nodes, it only gains from relay selection.