Joint Newton Iteration and Neumann Series Method of Convergence-Accelerating Matrix Inversion Approximation in Linear Precoding for Massive MIMO Systems

Lin Shao,Yunxiao Zu

doi:10.1155/2016/1745808

Abstract

Due to large numbers of antennas and users, matrix inversion is complicated in linear precoding techniques for massive MIMO systems. Several approximated matrix inversion methods, including the Neumann series, have been proposed to reduce the complexity. However, the Neumann series does not converge fast enough. In this paper, to speed up convergence, a new joint Newton iteration and Neumann series method is proposed, with the first iteration result of Newton iteration method being employed to reconstruct the Neumann series. Then, a high probability convergence condition is established, which can offer useful guidelines for practical massive MIMO systems. Finally, simulation examples are given to demonstrate that the new joint Newton iteration and Neumann series method has a faster convergence rate compared to the previous Neumann series, with almost no increase in complexity when the iteration number is greater than or equal to 2.

Highlights

Massive multiple-input multiple-output (MIMO) [1,2,3] is one of the promising technologies for the fifth-generation communication system
We propose a new joint Newton iteration and Neumann series method, where Newton iteration method is utilized to provide an efficient searching direction for the Neumann series
Richardson method [7] was applied in minimum mean square error (MMSE) signal detection, but the relaxation parameter of the method still remains unknown for ZF precoding

Summary

Introduction

Massive multiple-input multiple-output (MIMO) [1,2,3] is one of the promising technologies for the fifth-generation communication system. Conjugate gradient method was applied to reduce the complexity of data detection and precoding in the massive MIMO system with realistic antenna configurations [8]. Newton iteration method converges fast and the complexity can be controlled just by the number of iterations [10]. Truncated Neumann series in [11, 12] was proposed to obtain near-optimal performance. The first iteration result of Newton iteration method is employed to reconstruct the Neumann series expansion to accelerate convergence. A high probability convergence condition is derived to guarantee the convergence of the new approach This condition is expected to contribute to the massive MIMO system in practice.

Background

Joint Newton Iteration and Neumann Series Method

Numerical Results

Conclusions