Hierarchical codebook design for fast search with Grassmannian codebook

It has been well known that channel aware systems (closed-loop) have better performance than channel unknown systems (open-loop). In order to know channel in the transmitter, receivers should send own channel information the transmitter through reverse channel. However, the channel information should be fed back in Frequency Division Duplexing (FDD) additionally since forward link channel and reverse link channel are different each other. In FDD, the channel information is usually quantized as a codebook and each receiver feedback the best codeword index within the codebook by any metric generally. The codebook has the characteristic that as codebook size is larger system performance increases but computational complexity to find the best codeword also increases exponentially in conventional codebook structure. In this paper, we propose some codebook design schemes which have hierarchical structure to overcome the complexity problem as well as achieves near-optimal performance.