In multiple-antenna wireless communication systems

when the trinsrrtitter obtains the quantized channel direction by a limited feedback link fiom the receiver

benefits of improving throughput and reducing bit error rate can be realized.This paper presents an overview of codebook design for limited feedback

which is the most important problem in the system.The codebook design can mainly classified as two schemes:one based on subspace packing in Grassmann manifold and another based on vector quantization in source coding.We highlight the principles and related algorithms of both schemes

which involve various modes about channels and data

and then compare the key characteristics of them.