  In this letter, we develop an $\ell_2$-box maximum likelihood (ML)
formulation for massive multiple-input multiple-output (MIMO) quadrature
amplitude modulation (QAM) signal detection and customize an alternating
direction method of multipliers (ADMM) algorithm to solve the nonconvex
optimization model. In the $\ell_2$-box ADMM implementation, all variables are
solved analytically. Moreover, several theoretical results related to
convergence, iteration complexity, and computational complexity are presented.
Simulation results demonstrate the effectiveness of the proposed $\ell_2$-box
ADMM detector in comparison with state-of-the-arts approaches.
