A Codebook-Based Precoding Method for MIMO Amplify-and-Forward Relaying System

This paper proposes a codebook-based precoding method for multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying system. The proposed codeword selection criterion is a distributed codeword selection criterion which allows base station and relay to choose optimal precoding matrix independently. Therefore the feedback delay is decreased. Based on the proposed criterion, we further develop a codebook design criterion. It is shown that the design criterion is equivalent to packing subspaces in the Grassmannian manifold using the Fubini-Study distance. Numerical simulations also show that the proposed scheme achieves elegant performance in terms of ergodic capacity.