Energy-Efficient Multicast Precoding for Massive MIMO Transmission with Statistical CSI

In this paper, we investigate energy-efficient multicast precoding for massive multiple-input multiple-output (MIMO) transmission. In contrast with most previous work, where instantaneous channel state information (CSI) is exploited to facilitate energy-efficient wireless transmission design, we assume that the base station can only exploit statistical CSI of the user terminals for downlink multicast precoding. First, in terms of maximizing the system energy efficiency, the eigenvectors of the optimal energy-efficient multicast transmit covariance matrix are identified in closed form, which indicates that optimal energy-efficient multicast precoding should be performed in the beam domain in massive MIMO. Then, the large-dimensional matrix-valued precoding design is simplified into an energy-efficient power allocation problem in the beam domain with significantly reduced optimization variables. Using Dinkelbach's transform, we further propose a sequential beam domain power allocation algorithm which is guaranteed to converge to the global optimum. In addition, we use the large-dimensional random matrix theory to derive the deterministic equivalent of the objective to reduce the computational complexity involved in sample averaging. We present numerical results to illustrate the near-optimal performance of our proposed energy-efficient multicast precoding for massive MIMO.