Optimal beamforming for non-regenerative MIMO relays with direct link

In this letter, we generalize the existing works on the design of the optimal relay amplifying matrix for nonregenerative multiple-input multiple-output (MIMO) relay communication systems by including the direct source-destination link. We show that for most commonly used objective functions, the optimal relay amplifying matrix has a general beamforming structure, that is, the relay first sets beams to the direction of the source-relay channel, then conducts a linear precoding, and finally beamforming towards the direction of the relay-destination channel.