Polite water-filling for the boundary of the capacity/achievable regions of MIMO MAC/BC/interference networks

We found a network version of water-filling, named polite water-filling, that is optimal for all boundary points of the capacity regions of MAC and BC and for all boundary points of a set of achievable regions of a general class of interference networks, named MIMO B-MAC networks that include BC, MAC, interference channels, X networks, and most practical networks as special cases. It is polite because it strikes an optimal balance between reducing interference to others and maximizing a link´s own rate. Unlike in single-user MIMO channels, where the optimal input covariance can be solved by the water-filling, the traditional water-filling is far from optimal in networks. Thus, general purpose optimization algorithms have been used for networks but have high complexity and do not work well for non-convex cases. Together with our duality result, the polite water-filling can be used to design highly efficient low-complexity iterative centralized/distributed algorithms for the optimization of input covariance matrices, including both power and beamforming matrices, because it takes the advantage of the structure of the problems. References to the resulting algorithms that outperform the state-of-the-art by a wide margin are provided.