  The focus of this paper is on spatial precoding in correlated multi-antenna
channels, where the number of independent data-streams is adapted to trade-off
the data-rate with the transmitter complexity. Towards the goal of a
low-complexity implementation, a structured precoder is proposed, where the
precoder matrix evolves fairly slowly at a rate comparable with the statistical
evolution of the channel. Here, the eigenvectors of the precoder matrix
correspond to the dominant eigenvectors of the transmit covariance matrix,
whereas the power allocation across the modes is fixed, known at both the ends,
and is of low-complexity. A particular case of the proposed scheme (semiunitary
precoding), where the spatial modes are excited with equal power, is shown to
be near-optimal in matched channels. A matched channel is one where the
dominant eigenvalues of the transmit covariance matrix are well-conditioned and
their number equals the number of independent data-streams, and the receive
covariance matrix is also well-conditioned. In mismatched channels, where the
above conditions are not met, it is shown that the loss in performance with
semiunitary precoding when compared with a perfect channel information
benchmark is substantial. This loss needs to be mitigated via limited feedback
techniques that provide partial channel information to the transmitter. More
importantly, we develop matching metrics that capture the degree of matching of
a channel to the precoder structure continuously, and allow ordering two matrix
channels in terms of their mutual information or error probability performance.
