Linear precoding in MIMO broadcast channel with arbitrary rank constraints

We consider the problem of maximizing the weighted sum rate (WSR) in MIMO broadcast channel where the number of transmitted streams (ranks) is constrained. The problem is treated both with or without interference pre-compensation also known as dirty paper coding (DPC). The rank constrained problem is highly motivated by the practical consideration on the receiver complexity in current wireless systems such as LTE. We propose a unified algorithm based on fixed point iteration. The proposed approach has very fast convergence rate that usually converges to the minimal number of streams for each user and finds the corresponding optimal precoding matrix. Rank minimization is particularly desirable in practice. The order in which the users' streams are encoded is crucial when dirty paper coding is allowed. We prove that the optimal user ordering does not depend on the transmission rank constraints and is given only by the weight vector. Using simulations, we compare the performance of our proposed scheme with the best known algorithms in the literature and demonstrate the effect of rank constraints.