  This paper investigates the linear precoder design that maximizes the average
mutual information of multiple-input multiple-output channels with
finite-alphabet inputs and statistical channel state information known at the
transmitter. This linear precoder design is an important open problem and is
extremely difficult to solve: First, average mutual information lacks
closed-form expression and involves complicated computations; Second, the
optimization problem over precoder is nonconcave. This study explores the
solution to this problem and provides the following contributions: 1) A
closed-form lower bound of average mutual information is derived. It achieves
asymptotic optimality at low and high signal-to-noise ratio regions and, with a
constant shift, offers an accurate approximation to the average mutual
information; 2) The optimal structure of the precoder is revealed, and a
unified two-step iterative algorithm is proposed to solve this problem.
Numerical examples show the convergence and the efficacy of the proposed
algorithm. Compared to its conventional counterparts, the proposed linear
precoding method provides a significant performance gain.
