  Signal-to-leakage-and-noise ratio (SLNR) is a promising criterion for linear
precoder design in multi-user (MU) multiple-input multiple-output (MIMO)
systems. It decouples the precoder design problem and makes closed-form
solution available. In this letter, we present a new linear precoding scheme by
slightly relaxing the SLNR maximization for MU-MIMO systems with multiple data
streams per user. The precoding matrices are obtained by a general form of
simultaneous diagonalization of two Hermitian matrices. The new scheme reduces
the gap between the per-stream effective channel gains, an inherent limitation
in the original SLNR precoding scheme. Simulation results demonstrate that the
proposed precoding achieves considerable gains in error performance over the
original one for multi-stream transmission while maintaining almost the same
achievable sum-rate.
