This paper jointly optimizes the precoding matrices and the set of active remote radio heads (RRHs) to minimize the network power consumption for a cloud radio access network (C-RAN) where both the RRHs and users all have multiple antennas. Both users’ rate requirements and per-RRH power constraints are considered. Due to these conflicting constraints, this optimization problem may be infeasible. We propose to solve this problem with two phases. In Phase I, a new approach is proposed to check the feasibility of the original problem. If the feasibility is guaranteed, in Phase II, a low-complexity algorithm is proposed to solve the original optimization problem. Simulation results demonstrate the rapid convergence of the proposed algorithms and the benefits of equipping multiple antennas at the user side.