[en] This paper deals with the practical precoding design for a dual hop downlink with multiple-input multiple-output (MIMO) amplify-and-forward relaying. First, assuming that full channel state information (CSI) of the two hop channels is available, a suboptimal dual hop joint precoding scheme, i.e., precoding at both the base station and relay station, is investigated. Based on its structure, a scheme of limited feedback joint precoding using joint codebooks is then proposed, which uses a distributed codeword selection to concurrently choose two joint precoders such that the feedback delay is considerably decreased. Finally, the joint codebook design for the limited feedback joint precoding system is analyzed, and results reveal that independent codebook designs at the base station and relay station using the conventional Grassmannian subspace packing method is able to guarantee that the overall performance of the dual hop joint precoding scheme improves with the size of each of the two codebooks. Simulation results show that the proposed dual hop joint precoding system using distributed codeword selection scheme exhibits a rate or BER performance close to the one using the optimal centralized codeword selection scheme, while having lower computational complexity and shorter feedback delay.
