We study some achievable rate regions for the vector Gaussian broadcast
channel (BC) with perfect channel state information at the receiver
(CSIR) but imperfect channel state information at the transmitter
(CSIT). We compare Cover - van der Meulen
- Hajek - Pursley (CMHP) scheme and dirty paper coding (DPC) and show when each scheme outperforms the other.
We also analyze the rate gap between CMHP and time-division multiple-access (TDMA) at 
asymptotically high signal-to-noise ratio (SNR). 
We develop algorithms for optimizing power allocation and beamforming 
for these schemes using multiple-access channel (MAC)-BC duality.