  Constant envelope (CE) precoding is an appealing transmission technique which
enables the realization of high power amplifier (PA) efficiency. For CE
precoding in a single-user multiple-input single-output (MISO) channel, a
desired constellation is feasible at the receiver if and only if it can be
scaled to lie in an annulus, whose boundaries are characterized by the
instantaneous channel realization. Therefore, if a fixed receiver constellation
is used for CE precoding in a fading channel, where the annulus is
time-varying, there is in general a non-zero probability of encountering a
channel that makes CE precoding infeasible, thereby causing a high probability
of error. To tackle this problem, this paper studies the adaptive receiver
constellation design for CE precoding in a single-user MISO flat-fading channel
with an arbitrary number of antennas at the transmitter. We first investigate
the fixed-rate adaptive receiver constellation design to minimize the symbol
error rate (SER). Specifically, an efficient algorithm is proposed to find the
optimal amplitude-and-phase shift keying (APSK) constellation with two rings
that is both feasible and of the maximum minimum Euclidean distance (MED), for
any given constellation size and instantaneous channel realization. Numerical
results show that by using the optimized fixed-rate adaptive receiver
constellation, our proposed scheme achieves significantly improved SER
performance over CE precoding with a fixed receiver constellation. Furthermore,
based on the family of optimal fixed-rate adaptive two-ring APSK constellation
sets, a variable-rate CE transmission scheme is proposed and numerically
examined.
