  We consider downlink cellular multi-user communication between a base station
(BS) having N antennas and M single-antenna users, i.e., an N X 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 precoding 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. Under certain
mild channel conditions (including i.i.d. fading), we analytically show that,
even under the stringent per-antenna CE transmission constraint (compared to
APC), MUI suppression can still be achieved with large antenna arrays. Our
analysis also reveals that, with a fixed M and increasing N, the total
transmitted power can be reduced while maintaining a constant
signal-to-interference-noise-ratio (SINR) level at each user. We also propose a
novel low-complexity CE precoding scheme, using which, we confirm our
analytical observations for the i.i.d. Rayleigh fading channel, through
Monte-Carlo simulations. Simulation of the information sum-rate under the
per-antenna CE constraint, shows that, for a fixed M and a fixed desired
sum-rate, the required total transmit power decreases linearly with increasing
N, i.e., an O(N) array power gain. Also, in terms of the total transmit power
required to achieve a fixed desired information sum-rate, despite the stringent
per-antenna CE constraint, the proposed CE precoding scheme performs close to
the GBC sum-capacity (under APC) achieving scheme.
