Multiuser precoders for fixed receivers

We consider the problem of designing precoders for multiuser systems using fixed receivers. We first derive a precoder that minimizes the transmitted power subject to signal to interference plus noise ratio (SINK) constraints, and then derive a precoder that maximizes the worst case SINK subject to a power constraint. We show that both problems can be solved using standard optimization packages. In contrast to most of the existing precoders, our precoder design is not limited to full rank systems, and is applicable to systems in which the number of users is smaller, equal or larger than the processing gain. Simulation results in a multiuser system show that the proposed precoders can significantly outperform existing linear precoders.