Optimal Cooperative Beamforming Design for MIMO Decode-and-Forward Relay Channels

In this paper, we consider a transmit beamforming design for multiple-input-multiple-output (MIMO) decode-and-forward (DF) half-duplex two-hop relay channels with a direct source-destination link. For the scenario where source and relay nodes are equipped with multiple antennas and the destination node is deployed with single antenna, we formulate and solve the optimal beamforming vectors for source and relay nodes jointly. Specifically, we identify several unique properties of the optimal solutions through mathematical derivation, based on which we develop a systematic approach to arrive at the optimal beamforming vectors for the source and relay nodes for different system configurations. We derive a low-complexity explicit expression for the optimal beamforming vectors for some specific scenarios. Numerical results show that our proposed beamforming design scheme can achieve the ε-optimal solution with low computational complexity for MIMO DF relay networks.