Realizable MIMO decision feedback equalizers: Structure and design

We present and discuss the structure and design of optimum multivariable de cision feedback equalizers (DFEs), The equalizers are derived under the con straint of realizability, that is, causal and stable filters and finite dec ision delay. The design is based on a known dispersive discrete-time multiv ariable channel model with infinite impulse response. The additive noise is described by a multivariate ARMA model. Equations for obtaining minimum me an square error (MMSE) and zero-forcing DFEs are derived under the assumpti on of correct past decisions. Design of a realizable MMSE DFE requires the solution of a linear system of equations in the model parameters, No spectr al factorization is required. We derive novel necessary and sufficient conditions for the existence of ze ro-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 indica te that the performance improvement obtained with an IIR DFE is reduced mor e than for a (suboptimal) FIR DFE when error propagation is taken into acco unt since the use of IIR feedback filters tends to worsen the error propaga tion.