Realizable MIMO decision feedback equalizers

A general MMSE decision feedback equalizer (DFE) for multiple input-multiple output channels is presented. It is derived under the constraint of realizability, requiring finite smoothing lag and causal filters both in the forward and feedback link. The proposed DFE, which provides an optimal structure as well as optimal filter degrees, is obtained as an explicit solution in terms of the channel and noise description. A generalization of the scalar zero-forcing DFE is also presented. Conditions for the existence of such an equalizer are discussed. We argue that when no zero-forcing equalizer exists, poor near-far resistance of the corresponding optimal minimum mean square error DFE can be expected. A numerical example indicates the potential advantages of using a decision feedback equalizer with appropriate structure. The main improvements are obtained at moderate to high signal-to-noise ratios.