A Low Complex Sparse Formulation of Semidefinite Relaxation Detector for Large-MIMO Systems Employing BPSK Constellations

Semidefinite relaxation detector is a promising approach to large-MIMO detection but for its computational complexity. The major computational cost is incurred in solving the semidefinite program (SDP). In this paper, we propose a sparse semidefinite relaxation (S-SDR) detector by reformulating the SDP problem thereby reducing the computational complexity. We formulate the system model using a sparse approach and further introduce a regularization term inducing sparsity into the semidefinite programming model. We provide a sparse formulation requiring approximately 50 % of the computations compared to the conventional semidefinite programming approach. We apply the proposed semidefinite relaxation detector in large-MIMO channels upto 100×100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$100 \times 100$$\end{document} systems and compare its BER performance and complexity. We observe that the BER performance is similar to the conventional semidefinite relaxation with the proposed S-SDR detector requiring relatively fewer computations.