  In this paper, we consider a $n_t\times n_r$ multiple-input multiple-output
(MIMO) channel subjected to block fading. Reliability (in terms of achieved
diversity order) and rate (in number of symbols transmitted per channel use)
are of interest in such channels. We propose a new precoding scheme which
achieves both full diversity ($n_tn_r$th order diversity) as well as full rate
($n_t$ symbols per channel use) using partial channel state information at the
transmitter (CSIT), applicable in MIMO systems including $n_r<n_t$ asymmetric
MIMO. The proposed scheme achieves full diversity and improved coding gain
through an optimization over the choice of constellation sets. The optimization
maximizes $d_{min}^2$ for our precoding scheme subject to an energy constraint.
The scheme requires feedback of $n_t-1$ angle parameter values, compared to
$2n_tn_r$ real coefficients in case of full CSIT. Error rate performance
results for $3\times 1$, $3\times 2$, $4\times 1$, $8\times 1$ precoded MIMO
systems (with $n_t=3,3,4,8$ symbols per channel use, respectively) show that
the proposed precoding achieves 3rd, 6th, 4th and 8th order diversities,
respectively. These performances are shown to be better than other precoding
schemes in the literature; the better performance is due to the choice of the
signal sets and the feedback angles in the proposed scheme.
