On the Capacity of Fading MIMO Broadcast Channels with Imperfect   Transmitter Side-Information
  A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signal-to-noise (SNR) throughput is greatly reduced if, rather than knowing the fading realization \emph{precisely}, the trasmitter only knows the fading realization \emph{approximately}. The results are general and are not limited to memoryless Gaussian fading. 
Amos Lapidoth, Shlomo Shamai, Michele Wigger