  In this paper, a new optimization framework is presented for the joint design
of user selection, power allocation, and precoding in multi-cell multi-user
multiple-input multiple-output (MU-MIMO) systems when imperfect channel state
information at transmitter (CSIT) is available. By representing the joint
optimization variables in a higher-dimensional space, the weighted sum-spectral
efficiency maximization is formulated as the maximization of the product of
Rayleigh quotients. Although this is still a non-convex problem, a
computationally efficient algorithm, referred to as generalized power iteration
precoding (GPIP), is proposed. The algorithm converges to a stationary point
(local maximum) of the objective function and therefore it guarantees the
first-order optimality of the solution. By adjusting the weights in the
weighted sum-spectral efficiency, the GPIP yields a joint solution for user
selection, power allocation, and downlink precoding. The GPIP is also extended
to a multi-cell scenario, where cooperative base stations perform joint user
selection and design their precoding vectors by sharing global yet imperfect
CSIT within the cooperative BSs. System-level simulations show the gains of the
proposed approach with respect to conventional user selection and linear
downlink precoding.
