On the Bottleneck Users for Multiple-Antenna Physical-Layer Multicasting

Given the optimal transmit beamforming vector, the user who has the worst signal-to-noise ratio (SNR) is referred to as a bottleneck user for a single-group multicasting system with multiple antennas at the transmit side. In this paper, we present some interesting insights into the bottleneck users, such as the maximum number as well as the optimal beamformer when the transmitter has an arbitrary number of antenna elements. The max-min fair SNR problem is employed and the closed-form solutions are proposed from the weighted sum-SNR maximization perspective for different numbers of possible bottleneck users. A new heuristic beamforming algorithm based on the bottleneck users is also presented to improve the system performance in terms of the achievable rate for physical-layer multicasting.