A Hybrid Codebook Design Algorithm for MIMO Amplify-and-Forward Relaying System with Power Allocation and Precoding

This paper proposes a hybrid codebook design algorithm and a distributed codeword selection criterion for multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying system with power allocation and precoding. The proposed codebook design algorithm exploits a modified LIoyd algorithm and converges to a locally optimal codebook. Closed form solution for power allocation problem is derived in order to maximize the channel capacity. Based on the codebook design algorithm, we further propose a codeword selection criterion which allows base station and relay to independently choose optimal codewords. The criterion effectively decreases the feedback delay in MIMO AF relaying system. Simulation results show that the proposed scheme achieves elegant performance in terms of ergodic capacity with very limited bits of feedback.