Matrix inversion-less signal detection using SOR method for uplink large-scale MIMO systems

For uplink large-scale MIMO systems, linear minimum mean square error (MMSE) signal detection algorithm is near-optimal but involves matrix inversion with high complexity. In this paper, we propose a low-complexity signal detection algorithm based on the successive overrelaxation (SOR) method to avoid the complicated matrix inversion. We first prove a special property that the MMSE filtering matrix is symmetric positive definite for uplink large-scale MIMO systems, which is the premise for the SOR method. Then a low-complexity iterative signal detection algorithm based on the SOR method as well as the convergence proof is proposed. The analysis shows that the proposed scheme can reduce the computational complexity from O(K
³
) to O(K
²
), where K is the number of users. Finally, we verify through simulation results that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm, and achieves the near-optimal performance of the classical MMSE algorithm with a small number of iterations.