  Consider the following problem: A multi-antenna base station (BS) sends
multiple symbol streams to multiple single-antenna users via precoding.
However, unlike conventional multiuser precoding, the transmitted signals are
subjected to binary, unit-modulus, or even discrete unit-modulus constraints.
Such constraints arise in the one-bit and constant-envelope (CE) massive MIMO
scenarios, wherein high-resolution digital-to-analog converters (DACs) are
replaced by one-bit DACs and phase shifters, respectively, for cutting down
hardware cost and energy consumption. Multiuser precoding under one-bit and CE
restrictions poses significant design difficulty. In this paper we establish a
framework for designing multiuser precoding under the one-bit, continuous CE
and discrete CE scenarios---all within one theme. We first formulate a
precoding design that focuses on minimizations of symbol-error probabilities
(SEPs), assuming quadrature amplitude modulation (QAM) constellations. We then
devise an algorithm for our SEP-based design. The algorithm combines i) a novel
penalty method for handling binary, unit-modulus and discrete unit-modulus
constraints; and ii) a first-order non-convex optimization recipe custom-built
for the design. Specifically, the latter is an inexact
majorization-minimization method via accelerated projected gradient, which, as
shown by simulations, runs very fast and can handle a large number of decision
variables. Simulation results indicate that the proposed design offers
significantly better bit-error rate performance than the existing designs.
