Wireless Networks

, Volume 24, Issue 7, pp 2699–2704 | Cite as

Approaches of approximating matrix inversion for zero-forcing pre-coding in downlink massive MIMO systems

  • Lin Shao
  • Yunxiao ZuEmail author


Several approximation approaches including the Gauss–Seidel (GS) method have been proposed to reduce the complexity of matrix inversion for zero-forcing pre-coding in massive multiple-input–multiple-output systems. However, extra computation is required to obtain the matrix inversion from the iteration result of the GS method. In this paper, we propose a new GS-based matrix inversion approximation (GSBMIA) approach. Unlike the traditional GS method, the GSBMIA approach approximates the matrix inversion, which will simplify further calculations. Furthermore, in order to speed up convergence, we propose a joint algorithm based on the GSBMIA and Newton iteration method where the GSBMIA approach is employed to provide an efficient searching direction for the following Newton iterations. Compared with other approximation methods, the joint algorithm can accommodate more single antenna users for the same base station antenna number. Simulation results demonstrate that the joint algorithm and the GSBMIA approach converge faster than the Neumann series and Newton iteration method.


Massive MIMO ZF pre-coding Matrix inversion GS method Newton iteration 



This work is supported by “Beijing Key Laboratory of Work Safety Intelligent Monitoring (Beijing University of Posts and Telecommunications)”.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of Electronic EngineeringBeijing University of Posts and TelecommunicationsBeijingChina

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