  In this paper, we design an efficient quadrature amplitude modulation (QAM)
signal detector for massive multiple-input multiple-output (MIMO) communication
systems via the penalty-sharing alternating direction method of multipliers
(PS-ADMM). Its main content is as follows: first, we formulate QAM-MIMO
detection as a maximum-likelihood optimization problem with bound relaxation
constraints. Decomposing QAM signals into a sum of multiple binary variables
and exploiting introduced binary variables as penalty functions, we transform
the detection optimization model to a non-convex sharing problem; second, a
customized ADMM algorithm is presented to solve the formulated non-convex
optimization problem. In the implementation, all variables can be solved
analytically and in parallel; third, it is proved that the proposed PS-ADMM
algorithm converges under mild conditions. Simulation results demonstrate the
effectiveness of the proposed approach.
