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