  This paper considers the problem of constant envelope (CE) precoder designs
for multiuser massive MISO downlink channels. The use of CE signals allows one
to employ low-cost radio frequency chains and thereby facilitates the
implementation of massive MIMO. However, the subsequent CE precoder designs are
usually challenging owing to the non-convex CE constraints. The existing CE
precoder designs consider minimization of some measures on the distortion
levels of the received symbols, and they usually aim at improving the
symbol-error rate (SER) performances. In this paper we formulate a minimum
SER-based design for CE precoding. The design formulation is non-convex and we
propose two low-complexity first-order algorithms using gradient projection.
Curiously, our simulation results show that the proposed designs can achieve
bit-error rate performance close to that of zero-forcing beamforming without CE
signaling restrictions.
