Transmit power optimization for Gaussian vector broadcast channels

This paper proposes a transmit power optimization algorithm for a Gaussian vector broadcast channel. The optimal power allocation minimizes the sum trace of input covariance matrices of all the users in the Gaussian vector broadcast channel. By duality the transmit power optimization can be transformed into an equivalent convex optimization in a multiple access channel. Recursive equations are derived as sufficient conditions for the minimum transmit power and an iterative algorithm is proposed to solve the equations. Numerical examples show that the iterative algorithm converges very fast and efficiently determines the input covariance matrices for the optimum power allocation.