  This paper jointly optimizes the precoding matrices and the set of active
remote radio heads (RRHs) to minimize the network power consumption (NPC) for a
user-centric cloud radio access network (C-RAN), where both the RRHs and users
have multiple antennas and each user is served by its nearby RRHs. Both users'
rate requirements and per-RRH power constraints are considered. Due to these
conflicting constraints, this optimization problem may be infeasible. In this
paper, we propose to solve this problem in two stages. In Stage I, a
low-complexity user selection algorithm is proposed to find the largest subset
of feasible users. In Stage II, a low-complexity algorithm is proposed to solve
the optimization problem with the users selected from Stage I. Specifically,
the re-weighted $l_1$-norm minimization method is used to transform the
original problem with non-smooth objective function into a series of weighted
power minimization (WPM) problems, each of which can be solved by the weighted
minimum mean square error (WMMSE) method. The solution obtained by the WMMSE
method is proved to satisfy the Karush-Kuhn-Tucker (KKT) conditions of the WPM
problem. Moreover, a low-complexity algorithm based on Newton's method and the
gradient descent method is developed to update the precoder matrices in each
iteration of the WMMSE method. Simulation results demonstrate the rapid
convergence of the proposed algorithms and the benefits of equipping multiple
antennas at the user side. Moreover, the proposed algorithm is shown to achieve
near-optimal performance in terms of NPC.
