Tradeoff between Grassmannian and Orthogonalizing Precoding

In this paper, we study unitary precoding for multistream MIMO systems with partial channel state information at the transmitter. We consider the full space of non-equivalent unitary precoding matrices which can be divided into two parts, Grassmmannian precoding and orthogonalizing precoding. The parts have different role and relevance depending on the scenario. In case of limited feedback, the design problem is to find an optimal assignment of the feedback bits into these two parts. It is shown that when spatial correlation increases, more bits should be allocated into the orthogonalizing part. Moreover, when the correlation between antenna elements is large, the combined codebook is able to outperform Grassmannian codebook even when the combined codebook has less codewords than the Grassmannian one.