Distributed optimization in multi-user MIMO systems with imperfect and delayed information

In this paper, we analyze the problem of signal covariance optimization in Gaussian multiple-input, multiple-output (MIMO) channels under imperfect (and possibly delayed) channel state information. Starting from the continuous-time dynamics of matrix exponential learning, we develop a distributed optimization algorithm driven by a damping term which ensures the method´s stability under stochastic perturbations and asynchronicities of arbitrary magnitude. As opposed to traditional water-filling methods, the algorithm´s convergence properties (speed and accuracy) can be controlled by tuning the users´ learning rate and/or the damping parameter. Accordingly, the algorithm converges arbitrarily close to an optimum signal covariance profile within a few iterations, even for large numbers of users and/or antennas per user; furthermore, the quality of the solution obtained remains robust in the presence of imperfect (or delayed) measurements and asynchronous user updates.