This letter reveals that whole link reciprocity does not exist in general amplify-and-forward (AF) time division duplex (TDD) relay systems due to the gain matrix. To resolve this problem, a novel gain matrix design method is proposed. Any existing gain matrix design criterion can be adopted in the downlink (uplink) to ensure optimal performance, and the proposed scheme is used in the uplink (downlink), with small adjustment, to keep whole link reciprocity. Simulation results show that, the proposed method can maintain whole link reciprocity without performance loss.

In a codebook based precoding MIMO system, the precoding codebook significantly determines the system performance. Consequently, it is crucial to design the precoding codebook, which is related to the channel fading, antenna number, spatial correlation etc. So specific channel conditions correspond to respective optimum codebooks. In this paper, in order to obtain the optimum codebooks, a universal unitary space vector quantization (USVQ) codebook design criterion is provided, which can design the optimum codebooks for various fading and spatial correlated channels with arbitrary antenna configurations. Furthermore, the unitary space K-mean (USK) algorithm is also proposed to generate the USVQ codebook, which is iterative and convergent. Simulations show that the capacities of the precoding MIMO schemes using the USVQ codebooks are very close to those of the ideal precoding cases and outperform those of the schemes using the traditional Grassmannian codebooks and the 3GPP LTE DFT (discrete Fourier transform) codebooks.