We give a simple yet efficient Alternating Direction Method of Multipliers algorithm for solving sparse-modeling-based detectors [7, 9] for massive MIMO systems. Our solution relies on a special reformulation of the associated optimization problem by describing the constraints as a Cartesian power of the probability simplex. Simulation results show that the proposed algorithm is as accurate as the best known solvers (interior point methods), while its complexity remains linear with respect to the size of the system.