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 lowcomplexity 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.find the optimal solution. Although these two approaches yield the optimal solution, they have an exponential complexity. The third approach is the smooth function method, where the l 0norm was approximated as Gaussian-like function in [19], the exponential function in [20], and arctangent function in [21]. However, the smooth function cannot produce sparse solutions in general. The last approach was inspired by the compression sensing, named re-weighted l 1 -norm minimization method [27]. This method has been widely adopted in the literature [22]-[26], [28] due to its low computational complexity and sparsity guarantee, which will also be applied in this paper.All of the above papers only considered the single-antenna user (SAU) case. With the increasing development in antenna technology [29], [30], it is possible to equip the wireless devices with multiple antennas. When both the transmitter and the receiver are equipped with multiple antennas, multiple streams can be transmitted simultaneously, rather than only one stream in the SAU case. Simulation results show that with the increasing number of receive antennas, more users can be admitted. Therefore, in this paper, we consider the multiple-antenna user (MAU) case and jointly optimize the precoding matrices and the set of active RRHs to minimize the NPC subject to users' rate requirements and per-RRH power constraints.Unfortunately, the techniques in [16]-[26] dealing with the SAU case cannot be extended d...
