Improved and Extended Sum-Capacity Computation for the Gaussian Vector Broadcast Channel via Dual Decomposition

An improved and extended algorithm is proposed to efficiently compute the sum capacity for the Gaussian vector broadcast channel. The sum capacity computation relies on the duality between the Gaussian broadcast channel and the sum-power constrained Gaussian dual multiple-access channel. Compared with the well-known iterative algorithm that computes the sum capacity of the Gaussian vector broadcast channel via dual decomposition, not only does the proposed algorithm extend into the field of complex numbers, which is more compatible with the way in which the communication systems are constructed in practice, but it also provides faster convergence.