  Multimode precoding, where the number of independent data-streams is adapted
optimally, can be used to maximize the achievable throughput in multi-antenna
communication systems. Motivated by standardization efforts embraced by the
industry, the focus of this work is on systematic precoder design with
realistic assumptions on the spatial correlation, channel state information
(CSI) at the transmitter and the receiver, and implementation complexity. For
spatial correlation of the channel matrix, we assume a general channel model,
based on physical principles, that has been verified by many recent measurement
campaigns. We also assume a coherent receiver and knowledge of the spatial
statistics at the transmitter along with the presence of an ideal, low-rate
feedback link from the receiver to the transmitter. The reverse link is used
for codebook-index feedback and the goal of this work is to construct precoder
codebooks, adaptable in response to the statistical information, such that the
achievable throughput is significantly enhanced over that of a fixed,
non-adaptive, i.i.d. codebook design. We illustrate how a codebook of
semiunitary precoder matrices localized around some fixed center on the
Grassmann manifold can be skewed in response to the spatial correlation via
low-complexity maps that can rotate and scale submanifolds on the Grassmann
manifold. The skewed codebook in combination with a lowcomplexity statistical
power allocation scheme is then shown to bridge the gap in performance between
a perfect CSI benchmark and an i.i.d. codebook design.
