Realizable MIMO decision feedback equalizers: structure and design

We present and discuss the structure and design of optimum multivariable decision feedback equalizers (DFEs). The equalizers are derived under the constraint of realizability, that is, causal and stable filters and finite decision delay. The design is based on a known dispersive discrete-time multivariable channel model with infinite impulse response. The additive noise is described by a multivariate ARMA model. Equations for obtaining minimum mean square error (MMSE) and zero-forcing DFEs are derived under the assumption of correct past decisions. The design of a realizable MMSE DFE requires the solution of a linear system of equations in the model parameters. No spectral factorization is required. We derive novel necessary and sufficient conditions for the existence of zero-forcing DFEs and point out the significance of these conditions for the design of multiuser detectors. An optimal MMSE DFE will contain IIR filters in general. Simulations indicate that the performance improvement obtained with an IIR DFE is reduced more than for a (suboptimal) FIR DFE when error propagation is taken into account since the use of IIR feedback filters tends to worsen the error propagation.