Massive MIMO Multicasting with Finite Blocklength

Massive multiple-input multiple-output (MIMO) multicasting is a promising approach for simultaneously delivering common messages to multiple users in next-generation wireless networks. However, existing studies have exclusively focused on multicast beamforming designs based on the Shannon capacity, assuming the infinite blocklength (IBL) for transmission. This assumption may lead to strictly suboptimal designs for practical multicast transmissions with finite blocklength (FBL), especially in ultra-reliable low-latency communications. In this paper, we explore the beamforming design for massive MIMO multi-group multicasting in the FBL regime. Our study considers both the max-min fairness and the weighted sum rate criteria for a comprehensive treatment. Due to the non-concave FBL rate function, the resulting optimization problems are known to be notoriously hard. We characterize the necessary and sufficient condition for the non-negative FBL rate to be a concave function of the received signal-to-interference-plus-noise ratio (SINR). Considering a finite number of transmit antennas, we propose low-complexity majorization-minimization (MM) type algorithms, which update variables in either closed or semi-closed form, to achieve locally optimal solutions of the formulated optimization problems. We further show that, as the number of transmit antennas becomes large, the optimal beamformer of each group aligns asymptotically with a linear combination of the channel vectors of that group of users, where the optimal normalized combining coefficients are derived in closed form. Subsequently, we obtain the globally optimal multicast beamformers by optimizing the power allocation using low-complexity iterative algorithms. Simulation results show that the proposed schemes outperform several existing methods, especially those employing the Shannon capacity as the performance metric. Moreover, the proposed algorithms exhibit complexities that only slightly grow with the number of transmit antennas and they can notably reduce the computation time by up to two orders of magnitude over the benchmarks, making them highly beneficial for massive MIMO applications.