The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel

The Gaussian Multiple-Input Multiple-Output (MIMO) Broadcast Channel (BC) is considered. The Dirty-Paper Coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the non-degraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints.