Iterative Matrix Inversion Methods for Precoding in Cell-Free Massive MIMO Systems

Cell-free massive multiple-input multiple-output (mMIMO) systems are an alternative topology for mMIMO deployment, wherein a large number of access points are distributed over the coverage area to jointly serve users. Linear precoding methods such as zero-forcing are sufficient to achieve near-optimal performance in mMIMO systems. However, a key challenge in implementing these precoders can be a channel matrix inversion operation, which results in significant computational complexity in systems with large-scale antenna arrays. Hence, instead of direct matrix inversion, we examine several iterative methods to calculate the precoding matrix in a cell-free mMIMO system. We investigate their computational complexity and convergence rate in the presence of small- and large-scale fading and spatial correlation between antennas. Notably, we demonstrate that some iterative methods previously proposed for conventional (co-located) mMIMO do not always converge for cell-free mMIMO. Our main focus is the hyper-power iterative inversion method, which can be applied to both matrix inverses and pseudoinverses with guaranteed convergence; its factorized version also reduces its computational complexity. Although the hyper-power method does not reduce the complexity compared to direct matrix inversion, it converges quickly with high accuracy and strong numerical stability, and is conducive to parallel computation. These qualities make it a good candidate for matrix inversion in cell-free mMIMO system precoders.