  This work addresses the design of optimal linear transmit filters for the
Multiple Input-Multiple Output (MIMO) Broadcast Channel (BC) when several
spatial streams are allocated to each user.We also consider that the Channel
State Information (CSI) is perfect at the receivers but is only partial at the
transmitter. A statistical model for the partial CSI is assumed and exploited
for the filter design. Similarly to the single-stream per user case, the
problem is solved via Mean Square Error (MSE) dualities and interference
functions. However, including more streams per user involves an additional
complexity level since we must determine how to distribute the per-user rates
among the streams. Such problem is solved using a projected gradient algorithm.
