In this paper, we address the problem of underdetermined massive MIMO detection for QAM constellations. In [1], the authors showed the utility of projecting the signal in a basis of the modulation alphabet, looking for the sparsest vector representation. As an extension of this work and in order to reduce the detection complexity, we present first an equivalent real-valued formulation of the optimization problem, all the more interesting as the modulation order is high. Then we consider an outer forward error correcting (FEC) code and we propose a turbo detection scheme. We focus on the medium SNR value range where detection errors involve adjacent symbols. Based on this hypothesis, we propose a sparse vector formulation to be treated as a soft detection output that can be directly exploited in a symbol-to-binary conversion to feed the FEC decoder with reliable soft input. The FEC decoder output will be exploited to provide a priori information within the detection criterion based on a regularization approach. Simulation results show the efficiency of the proposed scheme in comparison with reference schemes of the state-of-art.