On the design of Massive MIMO-QAM detector via ${\mathrm{\ell }}_2$-Box ADMM approach

In this letter, we develop an ${\mathrm{\ell }}_2$-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 ${\mathrm{\ell }}_2$-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 ${\mathrm{\ell }}_2$-box ADMM detector in comparison with state-of-the-arts approaches.