Low Complexity Zero Forcing Detector Based on Newton-Schultz Iterative Algorithm for Massive MIMO Systems

Abstract

Linear detectors, such as zero forcing (ZF) and minimum mean-square error (MMSE), can achieve near-optimum performance due to the favorable channel propagation of massive multiple-input multiple-output systems. However, these detectors employ, in general, exact matrix inversion, which is computationally complex for such huge systems. Thus, in order to avoid the computation of the exact matrix inversion of ZF or MMSE, Newton–Schultz iterative (NSI) algorithm for obtaining an approximate matrix inversion is proposed, which yields similar performance of the exact matrix inversion. Besides, in order to further accelerate the convergence rate and reduce the complexity, we propose a novel initial matrix inversion solution for NSI algorithm based on Tchebychev polynomial, which is much closer to the final exact matrix inverse than the traditional initial matrix inversion solutions. Simulation results show that NSI algorithm with the proposed initial matrix inversion solution achieves the near-optimum ZF performance in just two iterations. Finally, the band matrix concept is employed in order to reduce the computational complexity from $O\left(N_T^3 \right)$ to $O\left(N_T^2 \right)$ , especially when the number of transmitting antennas, $N_T$ , is large.