Abstract: Abstract： Aimed at the feedback delay problem in the multipleantenna limited feedback precoding systems, and based on the full use of the time correlations of timevarying channel, the linear vector spaces spanned by the channel direction vector was modeled as points on a Grassmannian manifold, and the adjacent channel directions were assumed to move along the geodesic on a Grassmannian manifold, in order to compensate the effect of feedback delay on the performance of the system. Meanwhile, by exploiting the differential geometric properties of the Grassmannian manifold, the dynamic focused codebook with high resolution on the tangent space of Grassmannian manifold was proposed, which tracked the correlated channel and updated itself accordingly. The computer simulation results show that the system performance of the proposed Grassmannian predictive precoding is obviously superior to that of memoryless quantitation precoding which has a shortcoming of feedback delay. Moreover, compared with the channel prediction of fixed codebook, the proposed dynamic focused codebook with high resolution is equipped with the higher quality of keeping tracking with the timevarying channel.

Key words: Key words： multiple antenna systems, timevarying channel, limited feedback, Grassmannian manifold