中文摘要：

针对MIMO时变信道下，有限反馈发射预编码存在反馈延迟的问题，提出将多数据流空间复用传输的MIMO信道的主右奇异矩阵的列空间建模于n维复欧氏空间上P维子空间的集合Grassmannian流形Gn,p上，利用Grassmannian流形的测地线对时变信道进行跟踪预测，以补偿反馈延迟对于系统性能的影响。在此基础上，从Grassmannian流形的几何特性人手，针对Grassmannian流形的切空间提出了一种高分辨率动态聚焦的多维切空间码本。计算机仿真表明，Grassmannian流形上基于高分辨率动态聚焦码本的有限反馈预测预编码的系统性能明显优于存在反馈延迟的无记忆有限反馈预编码和采用固定码本的有限反馈预测预编码。

英文摘要：

For the MIMO time-varying channel with memory, the feedback delay is inevitable in limited feedback precoding systems. To overcome this problem, the column spaces spanned by principal right singular matrix of the singular value decomposition of the channels are modeled as points on a Grassmannian manifold Gn,p ofp dimensional subspaces in the n di- mensional Euclidean space, so that the time-varying channel can be tracked and predicted by the geodesic of the Grassman- nian manifold. More specifically, by exploiting the differential geometric properties of the Grassmannian manifold, the multi-dimensional dynamic focused codebook with high resolution on the tangent space of Grassmannian manifold is pro- posed in this paper. The computer simulation results show that the system performance of the proposed Grassmannian pre- dictive precoding using the dynamic focused codebook with high resolution is obviously superior to memoryless limited feed- back precoding which has a shortcoming of feedback delay, as well as the limited feedback predictive precoding using the fixed codebook.