Beamforming Design for Multi-Hop Amplify-and-Forward MIMO Relay

This paper considers a multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. In the multi-hop AF MIMO relay network, the performance deteriorates as the number of hops increases because the effect of noise is enhanced. To suppress the effect of noise, this paper proposes the two beamforming schemes using channel state information (CSI) for the transmit beamforming at the source, relay beamforming at the relay, and receive beamforming at the destination. The forward-and-backward-CSI based beamforming and all-CSI based beamforming schemes are designed at each node based on the minimum mean square error criterion under the source and relay transmit power constraint. The forward-and-backward-CSI based beamforming scheme is designed by using the two matrices, forward channel, and backward channel. The two matrices are designed by using the beamforming matrices and channels from the previous nodes. Unlike the forward-and-backward-CSI based beamforming scheme, the all-CSI based beamforming scheme is designed by using all channels and an iterative algorithm. In terms of the complexity, the forward-and-backward-CSI based beamforming scheme is superior to the all-CSI based beamforming scheme. However, the all-CSI based beamforming scheme has advantage over the forward-and-backward-CSI based beamforming scheme in terms of the performance.