Matrix inversion using multiple-input multiple-output adaptive filtering

Abstract

A new approach for matrix inversion is introduced. The approach is based on vector representation of multiple-input multiple-output (MIMO) channel matrix, in which the channel matrix is described by a linear combination of channel vectors weighted by their respective system inputs. The MIMO system output is then fed into a bank of adaptive filters, wherein the response of a given adaptive filter is iteratively minimized to match its output to the given system input. In doing so, adaptive filters equalize the impact of respective channel vectors on the MIMO channel output, while simultaneously orthogonalizing themselves from all other channel vectors, forming the channel matrix inverse. The method demonstrates satisfactory convergence and accuracy in Monte Carlo simulations conducted with varying signal-to-noise ratios (SNRs) and matrix conditioning scenarios. The suggested approach, by virtue of its adaptable characteristics, can also be employed for time-varying linear equation systems.