Power optimization in fading Gaussian MIMO broadcast channels

In this paper, we consider the problem of minimizing long-term sum power under the constraint of an average sum rate in fading multiple input multiple output (MIMO) broadcast channels (BC) with additive Gaussian noise. This problem arises frequently in dynamic power allocation and power efficiency optimization for wireless communication systems. It is complementary to sum capacity maximization with a sum power constraint for a fading MIMO downlink. We first formulate the equivalent convex optimization problem using the duality between the MIMO multi-access channel (MAC) and the MIMO BC. Then we derive a simple and fast iterative water-filling algorithm based on the subgradient and bisection methods that computes the long-term sum power of the transmitter. Theoretical analysis and numerical simulations show that the proposed algorithm converges to the minimum sum power globally and efficiently.