  Channel estimation and data transmission constitute the most fundamental
functional modules of multiple-input multiple-output (MIMO) communication
systems. The underlying key tasks corresponding to these modules are training
sequence optimization and transceiver optimization. Hence, we jointly optimize
the linear transmit precoder and the training sequence of MIMO systems using
the metrics of their effective mutual information (MI), effective mean squared
error (MSE), effective weighted MI, effective weighted MSE, as well as their
effective generic Schur-convex and Schur-concave functions. Both statistical
channel state information (CSI) and estimated CSI are considered at the
transmitter in the joint optimization. A unified framework termed as joint
matrix-monotonic optimization is proposed. Based on this, the optimal precoder
matrix and training matrix structures can be derived for both CSI scenarios.
Then, based on the optimal matrix structures, our linear transceivers and their
training sequences can be jointly optimized. Compared to state-of-the-art
benchmark algorithms, the proposed algorithms visualize the bold explicit
relationships between the attainable system performance of our linear
transceivers conceived and their training sequences, leading to implementation
ready recipes. Finally, several numerical results are provided, which
corroborate our theoretical results and demonstrate the compelling benefits of
our proposed pilot-aided MIMO solutions.
