Low-Complexity MMSE Signal Detection Based on Richardson Method for Large-Scale MIMO Systems

Minimum mean square error (MMSE) signal detection is near-optimal for uplink multi-user large-scale MIMO systems with hundreds of antennas at the base station, but involves matrix inversion with high complexity. In this paper, we first prove that the filtering matrix of the MMSE algorithm in large-scale MIMO is symmetric positive definite, based on which we propose a low-complexity signal detection algorithm by exploiting the Richardson method to avoid the complicated matrix inversion. The proof of the convergence of the proposed scheme is also provided. We then propose a zone-based initial solution by simply checking the values of the received signals, which can accelerate the convergence rate of the Richardson method for high-order modulations to reduce the complexity further. The analysis shows that the complexity can be reduced from O(K³) to O(K²) by the proposed signal detection algorithm, where K is the number of users. Simulation results indicate that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm and achieves the near-optimal performance of the classical MMSE algorithm.