On the capacity of multiple input multiple output broadcast channels

We consider a multi-user multiple input multiple output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO broadcast channel is in general a non-degraded broadcast channel, its capacity region remains an unsolved problem. In this paper, we establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai achievable region) for the MIMO broadcast channel and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. The duality also enables us to translate previously known results for the MIMO MAC to the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper-bound on the sum rate of the MIMO BC.