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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. [ABSTRACT FROM PUBLISHER]

Millimeter-wave (mmWave) and ultra-dense networks are two key technologies for the fifth-generation (5G) and beyond communication system. However, the ultra-dense deployment of small base stations (SBSs) might introduce severe interference to users that connect to SBSs. This paper analyzes the performance of 5G communication networks where the SBSs with coordinated beamforming, operating at mmWave frequency band and macro base stations (MBSs) operating at sub-6 GHz coexist. First, by utilizing a stochastic geometry approach, we obtain the cell association probability expressions in terms of different cell association biases, base station density ratios and probabilities of line of sight (LoS) link. Furthermore, we propose a clustering method to choose some SBSs to eliminate intra-cell interference. Then, we put forward an average distance from the Kth SBS to a user to obtain signal-to-interference-ratio (SINR) and rate coverage probability expressions. The simulation results validate the correctness of the expressions, and indicate that the optimal cardinality of coordinated SBSs increases with the density of SBSs. In addition, the relationship between the cluster size K and the average energy efficiency is obtained, which can be used to guide the coordination principle in 5G and beyond communication systems. [ABSTRACT FROM AUTHOR]