Fast Converging Iterative Precoding for Massive MIMO Systems: An Accelerated Weighted Neumann Series-Steepest Descent Approach

For massive multiple-input multiple-output (MIMO) systems, linear precoding is preferable to nonlinear precoding for better performance-complexity trade-off. However, linear precoding is still difficult to implement in practice for such large systems, because the precoding matrix involves the complicated matrix inversion that must be rapidly computed in real-time. In this paper, we use the large-scale property of massive MIMO systems, the excellent characteristics of the weighted Neumann series (WNS) matrix, and steepest descent (SD) method to devise a new iterative precoding for massive MIMO systems. First, by exploiting the characteristics of WNS iteration, we proposed a weighted Neumann series-steepest descent (WNS-SD) iterative algorithm to perform precoding with low-complexity, and the convergence condition is always met in underloaded scenarios. Second, by devising a novel first iterative step of the aforementioned WNS-SD iterative algorithm, we proposed an accelerated iterative algorithm, named the accelerated weighted Neumann series-steepest descent (AWNS-SD) algorithm. Furthermore, in the first iterative step of the AWNS-SD algorithm, we designed a promising preconditioning matrix for the SD algorithm based on the WNS matrix. Subsequently, via merger with the WNS iterative method, the AWNS-SD iterative precoding not only greatly improves the convergence rate of WNS-SD and other competitive precoding algorithms while maintaining low-complexity, but also guarantees a wide range of convergence. Finally, simulation results verify the validity of the theoretical analysis and show that without additional iteration steps, the proposed AWNS-SD precoding achieves near-optimal performance of the exact zero forcing (ZF) precoding in just one iterative step for typical massive MIMO system configurations. Furthermore, the diagonal matrix concept is applied to the preconditioning technique to further reduce the overall complexity.