A Physical Layer Multicast Precoding and Grouping Scheme for Bandwidth Minimization

Physical layer multicasting exploits multiple antennas at the transmitter side to deliver a common message to a group of
$K$
users. To this end, two formulations have been well addressed in the literature: i) the max-min-fair criterion, which maximizes the signal-to-noise ratio (SNR) of the worst user for a fixed transmit power; and ii) the quality of service (QoS) formulation, which minimizes the transmit power subject to a target SNR. Nevertheless, it is known that the performance and complexity of these approaches is severely degraded as the group size grows. In this paper, we propose a different formulation that aims at minimizing the required bandwidth needed to provide the multicast service. This is achieved by dividing the users into smaller groups and assigning the bandwidth required to provide a target rate to each group. Contrary to the common belief, it is shown that dividing the users into different groups that use orthogonal bandwidth allocations can lead to a smaller aggregated bandwidth than the single-group with single bandwidth allocation counterpart, if an intelligent grouping scheme is used. An iterative algorithm to derive the optimal number of groups is presented with an stopping criterion to reduce the numerical complexity. It is shown through simulation that our proposed approach greatly reduces the required bandwidth compared to existing schemes that rely on single bandwidth allocation. Interestingly, results reveal that our proposed scheme also leads to a greater SNR for a randomly chosen user, and it reduces the variance of the required bandwidth, which eases the implementation in real networks.