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.