FIR H∞ equalization

We approach FIR equalization problem from an H∞ perspective. First, we formulate the calculation of the optimal H∞ performance for a given equalization setting as a semidefinite programming (SDP) problem. H∞ criterion provides a set of FIR equalizers with different optimality properties. Among these, we formulate the calculation of risk sensitive or minimum entropy FIR filter as the constrained analytic centring problem and mixed H2/H" problem as another SDP. We provide an example to il- lustrate the procedures we described

MIMO linear equalization with an H∞ criterion

In this paper, we study the problem of linearly equalizing the multiple-input multiple-output (MIMO) communications channels from an H∞ point of view. H∞ estimation theory has been recently introduced as a method for designing filters that have acceptable performance in the face of model uncertainty and lack of statistical information on the exogenous signals. In this paper, we obtain a closed-form solution to the square MIMO linear H∞ equalization problem and parameterize all possible H∞-optimal equalizers. In particular, we show that, for minimum phase channels, a scaled version of the zero-forcing equalizer is H∞-optimal. The results also indicate an interesting dichotomy between minimum phase and nonminimum phase channels: for minimum phase channels the best causal equalizer performs as well as the best noncausal equalizer, whereas for nonminimum phase channels, causal equalizers cannot reduce the estimation error bounds from their a priori values. Our analysis also suggests certain remedies in the nonminimum phase case, namely, allowing for finite delay, oversampling, or using multiple sensors. For example, we show that H∞ equalization of nonminimum phase channels requires a time delay of at least l units, where l is the number of nonminimum phase zeros of the channel

FIR H∞ Equalization

We approach "nite impulse response (FIR) equalization problem from an H# perspective. First, we formulate the calculation of the optimal H# performance for a given equalization setting as a semide"nite programming (SDP) problem. H# criterion provides a set of FIR equalizers with di!erent optimality properties. Among these, we formulate the calculation of risk-sensitive or minimum entropy FIR "lter as the constrained analytic centring problem and mixed H#/H# problem as another SDP. We provide examples to illustrate the procedures we described. # 2001 Elsevier Science B.V. All rights reserved