Fast-Converging and Low-Complexity Linear Massive MIMO Detection With L-BFGS Method

Abstract

In massive multiple-input multiple-output (MIMO) uplink, linear minimum mean square error (MMSE) detection achieves near-optimal performance but suffers from undesirable computational burden due to the high-dimensional matrix inversion involved. To address this issue, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is introduced in this paper to realize free-matrix-inversion MMSE detection in an iterative way with significant reduction in computational complexity from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(K^{3})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(L K^{2})$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> denote the number of user antennas and iterations, respectively. For the better performance and complexity trade-off, three low-complexity L-BFGS based linear MMSE detection algorithms (namely E-LBFGS, I-LBFGS and S-LBFGS) are proposed successively. Furthermore, an efficient initialization strategy for the L-BFGS method based MMSE detection is devised, which helps to accelerate convergence and improve performance with acceptable complexity overhead added compared to the conventional L-BFGS based detection algorithms. Simulation results finally validate that the proposed detection scheme based on the L-BFGS method can closely approach to the MMSE accuracy with a small number of iterations even in poor propagation environments and provide attractive trade-offs between performance and complexity.