Approximate Matrix Inversion Methods for Massive MIMO Detectors

Abstract

Building a practical detector to achieve the attractive merits of large-scale multiple-input multiple-output (MIMO) is not a trivial task. However, low-complexity linear detectors could achieve a satisfactory performance for uplink massive MIMO, but such detectors involve unfavorable matrix inversions, whose not a hardware friendly. This paper considers several approximate matrix inversion methods to avoid a direct matrix inversion, namely, the Neumann method, the Gauss-Seidel (GS), the successive over-relaxation (SOR), the Jacobi method, the Richardson method, the optimized coordinate descent (OCD), and the conjugate gradients (CG) method. This paper shows that the MMSE detector based on the SOR and GS methods outperform the other detectors when the ratio between the number of BS antennas and user terminal antennas (s) varies from small to large values. It also investigates the selection of ω for both Richardson and SOR methods. The optimum performance can be achieved when $\omega=\frac{2}{\lambda}$ in the Richardson method. This paper shows that not every iteration has a positive impact on the performance.