Sum-Capacity and MMSE for the MIMO Broadcast Channel without Eigenvalue Decompositions

In this paper, we present a novel algorithm for determining the sum-rate optimal transmit covariance matrices for the MIMO broadcast channel. Instead of optimizing the covariances directly, our algorithm operates on the preceding matrices, i.e., the square roots of the covariances. As a result, no eigenvalue decompositions are required in the iterations, and the complexity per iteration is significantly lower. A look at the convergence over the required number of computations shows a visible advantage over the state-of-the-art sum power iterative waterfilling algorithm. Also, our algorithm allows us to find the optimal sum-rate for an arbitrarily limited number of data streams per user. Finally, with a simple modification, our algorithm can also be used for sum-MSE minimization.