An estimation-based approach to multiple-input multiple-output (MIMO) channel equalization

The purpose of this paper is to propose and investigate a new approach to implementing a spatio-temporal decision feedback equalizer (DFE) for MIMO (multiple-input multiple-output) channels. A system with an array of n transmit and m receiver antennas where (m⩾n) is assumed. Both finite-length (finite horizon) and infinite-length (infinite horizon) MIMO decision feedback equalizers are considered. We also assume an ISI (inter-symbol-interference) MIMO channel, which means the channel matrix elements are frequency selective. For the infinite-length case the DFE problem leads to solving a matrix spectral factorization. For the finite-length case the DFE problem leads to solving a corresponding Cholesky factorization. Using the estimation-based spectral factorization we have shown that the solution to the infinite-length MIMO DFE is not unique. In the finite-length case the estimation-based approach leads to a recursive algorithm to perform the Cholesky factorization. The proposed recursive algorithm has low complexity and is also simple to implement. Moreover it leads to a closed form solution for the MIMO DFE matrices