On Approximate Matrix Inversion Methods for Massive MIMO Detectors
Massive multiple-input multiple-output (MIMO) systems have been proposed to meet the user demands in terms of performance and quality of service (QoS). Due to the large number of antennas, detectors in massive MIMO are playing a crucial role in guaranteeing a satisfactory performance, while their complexity is also being increased. This paper considers several approximate algorithms to avoid direct matrix inversion, namely the Neumann method, the Gauss-Seidel (GS) method, the successive over-relaxation (SOR) method, the Jacobi method, the Richardson method, the optimized coordinate descent (OCD), and the conjugate gradients (CG) method. Also, this paper presents a comparison among the approximate matrix inversion methods and the minimum mean square error (MMSE). Simulation of 16×128, and 16×32 MIMO systems shows that a detector based on the GS method outperforms other detectors when the ratio of base station (BS) antennas to user terminal antennas, β, is small. On the other hand, the detector based on the SOR method outperforms the other approximate matrix inversion methods when β is large. In addition, this paper studies and recommends the setting values of relaxation parameter (ω) in the SOR and Richardson methods. It also provides a comparison among the approximate matrix inversion methods in the number of multiplications. Simulation results show that the Neumann method, the OCD method, and the CG method achieve the lowest number of multiplications while the CG method outperforms the Neumann and the OCD methods. This paper also shows that not every iteration improves the performance.