Low-complexity MMSE detector based on the first-order Neumann series expansion for massive MIMO systems

Abstract

In massive multiple-input multiple-output (MIMO) systems, with the increase of the number of received antennas at base station (BS), the linear detectors, as minimum mean-square error (MMSE), are able to achieve the near-optimal performance. However, these detectors involve matrix inversion with high complexity. Thus, in order to reduce the complexity, Neumann Series (NS) expansion has been proposed to find an approximate inverse matrix, because of its suitability for massive MIMO systems and its advantages in hardware implementation. In this paper, the basic idea is to carry out an approximate matrix inversion using a small number of NS terms, which allows one to achieve near-optimal performance at low complexity for the MMSE detector, in particular, the scale factor needed in NS expansion is optimized for the first-order NS expansion for which the post-detection signal-to-interference plus noise ratio (SINR) is maximized. Our result reveals that the low-complexity MMSE detector based on the first-order NS expansion has bit error rate (BER) equivalent to the one that employs matrix inversion and outperforms earlier approaches reported in the literature.