Fast techniques for computing finite-length MIMO MMSE decision feedback equalizers

Multiple-input multiple-output (MIMO) digital communication systems have received great attention due to their potential of increasing the overall system throughput. In such systems, MIMO decision feedback equalization (DFE) schemes are often used to mitigate intersymbol interference (ISI) resulting from channel multipath propagation. In this context, the existing computationally efficient methods for exact estimation of the DFE filters under minimum mean-square-error criteria (MMSE-DFE) rely on fast Cholesky decomposition and backsubstitution or Levinson techniques. These methods may still present several difficulties in implementation as the demand on higher transmission rates increases, and thus a simple solution is necessary. In this paper, new procedures for fast computation of the MIMO-MMSE-DFE are presented. The new algorithms are obtained from a simple observation, namely, that the optimal feedforward filter (FFF) is related to the well-known Kalman gain matrix, commonly encountered in fast recursive least squares adaptive algorithms-for which fast recursions exist and are readily applicable. Moreover, the feedback filter can be easily computed via stable fast MIMO convolution techniques. As a result, the proposed method is less complex, more structured, and can be as reliable in finite precision as known approaches in the literature.