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 l₀ norm minimization problem and relaxes it into a quadratic programming with the l 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.