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The authors consider downlink cellular multi-user communication between a Base Station (BS) having N antennas and M single-antenna users, i.e., an N ?M Gaussian Broadcast Channel (GBC). Under an Average only total transmit Power Constraint (APC), large antenna arrays at the BS (having tens to a few hundred antennas) have been recently shown to achieve remarkable Multi-User Interference (MUI) suppression with simple pre-coding techniques. However, building large arrays in practice, would require cheap/power-efficient Radio-Frequency (RF) electronic components. The type of transmitted signal that facilitates the use of most power-efficient RF components is a Constant Envelope (CE) signal (i.e., the amplitude of the signal transmitted from each antenna is constant for every channel use and every channel realization).
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