  Quantized constant envelope (QCE) precoding, a new transmission scheme that
only discrete QCE transmit signals are allowed at each antenna, has gained
growing research interests due to its ability of reducing the hardware cost and
the energy consumption of massive multiple-input multiple-output (MIMO)
systems. However, the discrete nature of QCE transmit signals greatly
complicates the precoding design. In this paper, we consider the QCE precoding
problem for a massive MIMO system with phase shift keying (PSK) modulation and
develop an efficient approach for solving the constructive interference (CI)
based problem formulation. Our approach is based on a custom-designed
(continuous) penalty model that is equivalent to the original discrete problem.
Specifically, the penalty model relaxes the discrete QCE constraint and
penalizes it in the objective with a negative $\ell_2$-norm term, which leads
to a non-smooth non-convex optimization problem. To tackle it, we resort to our
recently proposed alternating optimization (AO) algorithm. We show that the AO
algorithm admits closed-form updates at each iteration when applied to our
problem and thus can be efficiently implemented. Simulation results demonstrate
the superiority of the proposed approach over the existing algorithms.
