Multi-Cell Multi-User MIMO Imperfect CSI Transceiver Design with Power Method Generalized Eigenvectors

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 imperfect Channel State Information at the Transmitter (CSIT). 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 Mean Squared Error (MSE) or Interference Plus Noise (IPN) power minimization with Perron Frobenius theory. We introduce two imperfect CSIT formulations. One is based on the expected rate vs. Expected MSE (EMSE) relation, the other involves an original rate minorizer in terms of the received IPN covariance matrix, in the imperfect CSIT case applied to the Expected Signal and Interference Power (ESIP) rate. The main contribution here is another minorization step via an extended Rayleigh quotient which leads to a principled approach for introducing power method iterations replacing explicit generalized eigenvector computations. This allows to bring down the complexity per iteration of the better ESIP approaches to that of the EMSE based approaches. But we further reduce complexity by introducing also a (large) matrix inverse free power method.