  In this work, we derive a lower bound on the training-based achievable
downlink (DL) sum rate (SR) of a multi-user multiple-input-single-output (MISO)
system operating in frequency-division-duplex (FDD) mode. Assuming linear
minimum mean square error (LMMSE) channel estimation is used, we establish a
connection of the derived lower bound on the signal-to-interference-noise-ratio
(SINR) to an average MSE that allows to reformulate the SR maximization problem
as the minimization of the augmented weighted average MSE (AWAMSE). We propose
an iterative precoder design with three alternating steps, all given in closed
form, drastically reducing the computation time. We show numerically the
effectiveness of the proposed approach in challenging scenarios with limited
channel knowledge, i.e., we consider scenarios with a very limited number of
pilots. We additionally propose a more efficient version of the well-known
stochastic iterative WMMSE (SIWMMSE) approach, where the precoder update is
given in closed form.
