  In this paper, we investigate the design of linear precoders for the
multiple-input multiple-output (MIMO) multiple access channel (MAC). We assume
that statistical channel state information (CSI) is available at the
transmitters and consider the problem under the practical finite alphabet input
assumption. First, we derive an asymptotic (in the large system limit)
expression for the weighted sum rate (WSR) of the MIMO MAC with finite alphabet
inputs and Weichselberger's MIMO channel model. Subsequently, we obtain the
optimal structures of the linear precoders of the users maximizing the
asymptotic WSR and an iterative algorithm for determining the precoders. We
show that the complexity of the proposed precoder design is significantly lower
than that of MIMO MAC precoders designed for finite alphabet inputs and
instantaneous CSI. Simulation results for finite alphabet signalling indicate
that the proposed precoder achieves significant performance gains over existing
precoder designs.
