Fast Computation of Constrained Decision Feedback Equalizers

Constrained formulations of decision feedback equalizer (DFE) schemes arise whenever its intrinsic error propagation phenomenon must be reduced. This is the case when linear or a quadratic norm limits are enforced in the formulation of the usual minimum mean-square-error (mmse) DFE problem, so that superior performance can be achieved when compared to its unconstrained version. This paper solves the problem of designing fast algorithms for computing the DFE filters under the so-called magnitude and energy limiting norm criteria. The former is obtained by developing new updates in addition to the ones efficiently computed via a fast Kalman based method recently introduced. In a constrained energy formulation, however, it turns out that the desired shift structure of the channel convolution matrix that allows for a fast Kalman algorithm no longer exists. Still, we shall show how to properly correct for this discrepancy in structure in order to provide a fast recursion for computing the DFE coefficients in the constrained energy scenario. We verify the accuracy of the new algorithms under finite precision via computer simulations