Limited feedback precoding based on hierarchical codebook and linear receiver

The analysis shows that the conventional codebook construction of Grassmannian subspace packing can not control the performance loss caused by a linear receiver, while a proper unitary perturbation to the codebook is capable of compensating for this performance loss. This paper therefore proposes a novel hierarchical codebook to exploit the gain of unitary perturbation. The hierarchical codebook consists of a Grassmannian subcodebook and a proposed perturbation subcodebook. To implement precoding, this paper also presents a successive codeword selection scheme, thus the receiver would successively selects two preferred codewords from Grassmannian an perturbation subcodebooks. With the feedback binary indices of these selections, the transmitter uses the product of two preferred codewords as the precoder. The theoretical analysis of the proposed precoding technique shows that the usage of the perturbation subcodebook can improve to a certain degree the system performance in terms of throughput as well as BER, with a small additional feedback overhead, and the proposed codebook would reduce the computational and storage requirements in contrast to the conventional codebook. It is also shown via computer simulations that the proposed technique gives a better BER performance than the single Grassmannian codebook based precoding technique does, even if the feedback overhead remains the same.