Adaptive Conjugate Gradient DFEs for Wideband MIMO Systems Using Galerkin Projections

Three new adaptive equalization algorithms for wireless systems operating over frequency selective MIMO channels are proposed. The problem of the MIMO DFE design is formulated as a set of linear equations with multiple right-hand sides (RHS) evolving in time. By applying an adaptive modified conjugate gradient algorithm, originally proposed for a single linear system, to the problem at hand, we arrive at an equalizer of performance identical to RLS, numerically robust, but of higher computational cost. To reduce its complexity, two updating strategies of the equalizer filters are derived based on Galerkin projection in time and space respectively. The two alternative schemes exhibit a complexity lower than RLS while offering slightly inferior convergence properties.