Iterative waterfilling for weighted rate sum maximization in MIMO-MAC

We consider the weighted sum rate maximization in Gaussian MIMO multiple access channel (MAC) under individual power constraints. This problem arises in the stability-wise optimal scheduling policy that allocates the resource as a function of the buffer queue states and the channel matrices in each time slot. The straightforward generalization of Yu et al.'s well-known iterative waterfilling algorithm for the sum rate maximization is non-trivial because the problem cannot reduce to decoupled single-user waterfilling-type solutions with arbitrary weights. Therefore, we propose a simple alternative treating multiple antennas at each transmitter as virtual single-antenna transmitters, which enables a iterative waterfilling-type algorithm. For a special case such as a OFDM-MAC, the proposed algorithm converges to the optimal solution faster than a steepest ascent algorithm and makes the convergence speed independent of the number of subcarriers.