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We consider the multi-user MIMO broadcast channel with M single-antenna users and N transmit antennas under the constraint that each antenna emits signals having constant envelope (CE). The motivation for this is that CE signals facilitate the use of power-efficient RF power amplifiers. Analytical and numerical results show that, under certain mild conditions on the channel gains, for a fixed M , an array gain is achievable even under the stringent per-antenna CE constraint. Essentially, for adoi:10.1109/tcomm.2013.012913.110827 fatcat:rhcrbnvbvnfbne32yafvd3pta4