Multi-Cell MIMO User Rate Balancing with Partial CSIT

In this paper, we consider the problem of user rate balancing in the downlink of multi-cell multi-user (MU) Multiple-Input-Multiple-Output (MIMO) systems with partial Channel State Information at the Transmitter (CSIT). With MIMO leading to multiple streams per user, user rate balancing involves both aspects of balancing and sum rate optimization. We linearize the problem by introducing a rate minorizer and by formulating the balancing operation as constraints leading to a Lagrangian, allowing to transform rate balancing into weighted sum minimization with Perron Frobenius theory. We provide original analytical expressions for the Lagrange multipliers for the multiple power constraints which can also handle the case in which some power constraints are satisfied with inequality, as can arise in a multi-cell scenario. We introduce two partial CSIT formulations. One is based on the ergodic rate Mean Squared Error (EMSE) relation, the other involves an original rate minorizer in terms of the received interference plus noise covariance matrix, in the partial CSIT case applied to the Expected Signal and Interference Power (ESIP) rate. The simulation results exhibit the improved performance of the proposed techniques over naive partial CSIT beamforming based on perfect CSIT algorithms, and in particular illustrate the close to optimal performance of the ESIP approach.