Limited Feedback Precoding System Based on Hierarchical Codebook with Linear Receiver

The performance loss of conventional Grassmannian codebook is analyzed. According to the analysis of unitary perturbations effects on channel capacity as well as the BER, a novel hierarchical codebook consisting of a Grassmannian main-codebook and a perturbation subcodebook proposed for multi-antenna systems with linear receivers is established, and corresponds with the two-step codeword selection scheme that uses the product of two codewords respectively selected from the main-codebook and the sub one as the ultimate precoder. Specifically to the design of subcodebook, two schemes is brought forward: rotation-based and householder transformation-based, and the superiority of the proposed codebook in terms of both the channel capacity and BER is further confirmed by computer simulations.