Entropy-driven optimization dynamics for Gaussian vector multiple access channels

We develop a distributed optimization method for finding optimum input signal covariance matrices in Gaussian vector multiple access channels (solving also an equivalent game-theoretic formulation of the problem). Since ordinary gradient ascent violates the problem´s semidefiniteness constraints, we introduce an entropic barrier term whose Hessian allows us to write a gradient-like flow which behaves well with respect to the problem´s constraints, and which allows users to achieve the channel´s capacity. The algorithm´s convergence speed can be tuned by adjusting the underlying entropy function (and thus changing the spectral geometry of the cone of semidefinite matrices), so, in practice, users are able to achieve capacity within a few iterations, even for large numbers of users and/or antennas per user.