Iterative Waterfilling for Weighted Rate Sum Maximization in MIMO-OFDM Broadcast Channels

We study the maximization of the weighted sum rate in Gaussian multi-input multi-output OFDM broadcast channel under a total power constraint. This problem is motivated by adaptive resource allocation policies in a multi-carrier wireless system with multiple antennas at the base station. We propose a iterative waterfilling algorithm based on dual decomposition. Two decompositions are considered, one in subcarrier domain and another in both subcarrier and user domain. We show that both decompositions reduce to an identical problem that can be solved by multiuser waterfilling approach simultaneously for all subcarriers. A master problem is solved iteratively to achieve the total power constraint by a simple bisection method. Numerical examples show that our proposed algorithm converges much faster than steepest ascent algorithm and makes convergence almost independent of a number of subcarriers and antennas.