A Semi-Closed Form Solution to MIMO Relaying Optimization With Source-Destination Link

We study transceiver optimization in the context of amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying with source-destination link. In particular, by applying the known results of the optimal destination receiver and relay precoder, we mainly focus on the source beamformer optimization which manifests itself as a difficult non-convex problem. To find a globally optimal solution to this problem, we first transform it into an equivalent solvable convex problem via semidefinite relaxation (SDR). Inspired by the SDR based approach, we conduct a further analysis and successfully derive a novel semi-closed form solution to the optimal source beamformer. It is interesting to observe that the solution possesses a generalized eigenmode transmission structure depending on a weighted sum of the Gram matrices of both source-relay and source-destination channels.