  This paper characterizes the capacity region of Gaussian MIMO broadcast
channels (BCs) with per-antenna power constraint (PAPC). While the capacity
region of MIMO BCs with a sum power constraint (SPC) was extensively studied,
that under PAPC has received less attention. A reason is that efficient
solutions for this problem are hard to find. The goal of this paper is to
devise an efficient algorithm for determining the capacity region of Gaussian
MIMO BCs subject to PAPC, which is scalable to the problem size. To this end,
we first transform the weighted sum capacity maximization problem, which is
inherently nonconvex with the input covariance matrices, into a convex
formulation in the dual multiple access channel by minimax duality. Then we
derive a computationally efficient algorithm combining the concept of
alternating optimization and successive convex approximation. The proposed
algorithm achieves much lower complexity compared to an existing interiorpoint
method. Moreover, numerical results demonstrate that the proposed algorithm
converges very fast under various scenarios.
