  Massive multiuser multiple-input multiple-output (MU-MIMO) systems are
expected to be the core technology in fifth-generation wireless systems because
they significantly improve spectral efficiency. However, the requirement for a
large number of radio frequency (RF) chains results in high hardware costs and
power consumption, which obstruct the commercial deployment of massive MIMO
systems. A potential solution is to use low-resolution digital-to-analog
converters (DAC)/analog-to-digital converters for each antenna and RF chain.
However, using low-resolution DACs at the transmit side directly limits the
degree of freedom of output signals and thus poses a challenge to the precoding
design. In this study, we develop efficient and universal algorithms for a
downlink massive MU-MIMO system with finite-alphabet precodings. Our algorithms
are developed based on the alternating direction method of multipliers (ADMM)
framework. The original ADMM does not converge in a nonlinear discrete
optimization problem. The primary cause of this problem is that the alternating
(update) directions in ADMM on one side are biased, and those on the other side
are unbiased. By making the two updates consistent in an unbiased manner, we
develop two algorithms called iterative discrete estimation (IDE) and IDE2: IDE
demonstrates excellent performance and IDE2 possesses a significantly low
computational complexity. Compared with state-of-the-art techniques, the
proposed precoding algorithms present significant advantages in performance and
computational complexity.
