L1 Norm Minimization approach to MIMO detector

This paper deals with the quadrature amplitude modulation (QAM) problem for the multiple-input multiple-output (MIMO) channel. Based on the maximum likelihood estimation, the QAM detection problem is formulated as an integer quadratic programming, which is a combinatorial problem and difficult to obtain exact solutions. In order to overcome combinatorial difficulties, this paper formulates the QAM detection problem as the l(o) norm minimization problem and relaxes it into a quadratic programming with the l(1) norm regularization. Utilizing and modifying the forward-backward splitting (FOBOS) algorithm, a new QAM detection algorithm is proposed. This algorithm has a trade-off between the computational cost and the detection accuracy, which depends on a parameter of the algorithm. Numerical simulations show that the proposed algorithm works well and achieves a good detection performance with less computational cost comparing with the semidefinite relaxation (SDR) based algorithm.