  In this letter, we propose a novel manifold-based algorithm to solve the
constant envelope (CE) precoding problem with interference exploitation. For a
given power budget, we design the precoded symbols subject to the CE
constraints, such that the constructive effect of the multi-user interference
(MUI) is maximized. While the objective for the original problem is
non-differentiable on the complex plane, we consider the smooth approximation
of its real representation, and map it onto a Riemannian manifold. By using the
Riemmanian conjugate gradient (RCG) algorithm, a local minimizer can be
efficiently found for the problem. The complexity of the algorithm is
analytically derived in terms of floating-points operations (flops) per
iteration. Numerical results show that the proposed algorithm outperforms the
conventional methods on both symbol error rate and computational complexity.
