An efficient quadratic programming relaxation based algorithm for large-scale mimo detection

Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient quadratic programming (QP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as a sparse QP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the sparse QP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve small-scale problems, the proposed algorithm is demonstrated to be competitive with the state-of-the-art approaches in terms of detection accuracy and solution efficiency; when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power method.