This paper considers the downlink precoding for physical layer multicastingin massive multiple-input-multiple-output (MIMO) systems. We study the max-minfairness (MMF) problem, where channel state information (CSI) at thetransmitter is used to design precoding vectors that maximize the minimumspectral efficiency (SE) of the system, given fixed power budgets for uplinktraining and downlink transmission. Our system model accounts for channelestimation, pilot contamination, arbitrary pathlosses, and multi-groupmulticasting. We consider six scenarios with different transmissiontechnologies (unicast and multicast), different pilot assignment strategies(dedicated or shared pilot assignments), and different precoding schemes(maximum ratio transmission and zero forcing), and derive achievable spectralefficiencies for all possible combinations. Then we solve the MMF problem foreach of these scenarios and for any given pilot length we find the SEmaximizing uplink pilot and downlink data transmission policies, all inclosed-forms. We use these results to draw a general guideline for massive MIMOmulticasting design, where for a given number of base station antennas, numberof users, and coherence interval length, we determine the multicasting schemethat shall be used.
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