Linear MIMO precoders for fixed receivers

We consider the problem of designing linear multiple input multiple output (MIMO) precoders for fixed receivers. We first derive a precoder that minimizes the average power subject to Signal to Interference plus Noise Ratio (SINR) constraints, and then derive a precoder that maximizes the worst case SINR subject to an average power constraint. We show that both problems can be solved using standard optimization packages. In addition, a more efficient solution based on Karush-Kuhn-Tucker (KKT) optimality conditions is presented which gives more insight into the problem. Our design promises equal SINRs and fairness among the multiple outputs. Simulation results in a multiuser system show that the proposed precoders can significantly outperform existing linear precoders.