A fast converging algorithm for sum power minimization in MIMO uplink

The sum power minimization with per MS rate constraint problem in multiple-input multiple-output (MIMO) multiple access channels (MACs) is considered in this paper. The problem can be transformed into a series of convex weighted sum rate problems and iteratively solved by standard solvers. However, even with the efficient interior-point method in the latest solver, the computational effort to solve the convex problem in each iteration is still prohibitively high. We propose an efficient algorithm that utilizes the convexity of the rate region to reduce number of iterations. It consists of power bisection and optimal user weights search. The algorithm avoids the full search for the optimal user weights. By continuously constructing a convex rate polyhedron, it determines the feasibility of the current rate target at a early phase and immediately goes to the power bisection without knowing the optimal user weights. The proposed algorithm is compared with the existing methods and is shown to be significantly more efficient than the existing methods in terms of computational complexities.