Low-Complexity Implicit Detection for Massive MIMO Using Neumann Series
Xiaohui Zhang, Huacheng Zeng, Baofeng Ji, Gaoyuan Zhang
Abstract
In massive MIMO systems, the high complexity of signal detection comes mainly from computing a Gram matrix and its inversion. In this correspondence, we propose a low-complexity MIMO detection method based on the Neumann series (NS), which does not require explicitly computing the Gram matrix and its inversion. The proposed method leverages the statistical information of the Gram matrix to compute an initialization matrix, which guarantees the convergence of NS expansion. The signal detection is conducted implicitly by transforming matrix inversion and product operations into matrix-vector multiplication operations. By doing so, it reduces the computational complexity of MIMO signal detection from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(BU^{2}+U^{3})$</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">$\mathcal {O}(BUN)$</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">$B$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$U$</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">$N$</tex-math></inline-formula> are the numbers of antennas at the base station, at the user equipment, and NS terms, respectively. Simulation results show that, compared with existing approaches, the proposed method can significantly reduce the signal detection complexity while achieving similar performance.