A fast and low-complexity matrix inversion scheme based on CSM method for massive MIMO systems

Yue Xu,Liutong Du,Weixia Zou

doi:10.1186/s13638-016-0749-3

Abstract

Massive multiple-input-multiple-output (MIMO), also known as very-large MIMO systems, is an attracting technique in 5G and can provide higher rates and power efficiency than 4G. Linear-precoding schemes are able to achieve the near optimal performance, and thus are more attractive than non-linear precoding schemes. However, conventional linear precoding schemes in massive MIMO systems, such as regularized zero-forcing (RZF) precoding, have near-optimal performance but suffer from high computational complexity due to the required matrix inversion of large size. To solve this problem, we utilize the Cholesky-decomposition and Sherman-Morrison lemma and propose CSM (Cholesky and Sherman-Morrison strategy)-based precoding scheme to the matrix inversion by exploiting the asymptotically orthogonal channel property in massive MIMO systems. Results are evaluated numerically in terms of bit-error-rate (BER)and average sum rate. Comparing with the Neumann series approximation of inversing matrix, it is concluded that, with fewer operations, the performance of CSM-based precoding is better than conventional methods in massive MIMO configurations.

Highlights

Massive multiple-input multiple-output(MIMO), i.e., MIMO with large numbers of transmit and/or receive antennas, is widely accepted as one of the key enabling technologies for generation(e.g., 5G) wireless communication systems [1, 2]
This is motivated by the fact that the matrix which needs to be inversed in regularized zero-forcing (RZF) or MMSE precoding is a positive definite Hermitian matrix and tends to be diagonal dominant in massive MIMO systems [1], which provides the potential to utilize the Cholesky-Decomposition [11] and ShermanMorrison lemma [12]
4 Simulation result We provide the simulation results of average sum rate and BER of the proposed CSM-based precoding in a 256 × 16 massive MIMO system and a 256 × 32 massive MIMO system

Summary

Introduction

Massive multiple-input multiple-output(MIMO), i.e., MIMO with large numbers of transmit and/or receive antennas (massive MIMO technology), is widely accepted as one of the key enabling technologies for generation(e.g., 5G) wireless communication systems [1, 2]. [8–10] proposed SOR-based, LSQR-based, and TPE based schemes, respectively, which are all based Neumann serise. These algorithms’ the reduction in complexity is not obvious and do not consider the property of positive defined Hermitian matrix. We propose CSM-based precoding to reduce the complexity of matrix inversion for classical RZF or MMSE precoding. This is motivated by the fact that the matrix which needs to be inversed in RZF or MMSE precoding is a positive definite Hermitian matrix and tends to be diagonal dominant in massive MIMO systems [1], which provides the potential to utilize the Cholesky-Decomposition [11] and ShermanMorrison lemma [12]. Notation: lower-case and upper-case boldface letters denote vectors and matrices, respectively; (·)T , (·)H , (·)−1, det(·) and tr(·) denote the transpose, conjugate transpose, matrix inversion, determinant and trace, respectively; C denotes the set of complex numbers, IN is the N × N identity matrix

System model

Low-complexity linear-precoding scheme in massive MIMO

Conventional RZF and MMSE precoding

1: INPUT: matrix W

Conclusions