Physical Layer Multicasting in Massive MIMO Systems With Statistical CSIT

We present a transmit design for physical layer multicasting in single-cell massive multiple-input-multiple-output (MIMO) systems using statistical channel state information at the base station (BS). We first establish the relationship between the transmit design problems under the quality of service (QoS) and max-min fair (MMF) criteria. According to the relationship between the QoS and MMF problems, we only focus on the transmit covariance optimizations under the latter criterion. We show that when the uniform linear array is equipped at the BS, the eigenvectors of the optimal transmit covariance are given by columns of the discrete Fourier transform matrix, which reveals the optimality of the beam domain transmission in massive MIMO multicasting. A dual algorithm together with stochastic programming is proposed to specify the eigenvalues of the transmit covariance. To reduce the complexity involved in stochastic programming, we further formulate two simplified MMF problems by using the deterministic equivalents and upper bound to approximate the ergodic achievable rate, respectively. We show that the optimality of the beam domain transmission still holds for the two simplified MMF problems. Then we present two low-complexity transmit designs. Simulation results demonstrate the performances of the proposed algorithms.