Robust Design of Adaptive Equalizers

Abstract

Although equalizers promise to improve the signal- to-noise energy ratio, zero forcing equalizers are derived classically in a deterministic setting minimizing intersymbol interference, while minimum mean square error (MMSE) equalizer solutions are derived in a stochastic context based on quadratic Wiener cost functions. In this paper, we show that it is possible-and in our opinion even simpler-to derive the classical results in a purely deterministic setup, interpreting both equalizer types as least squares solutions. This, in turn, allows the introduction of a simple linear reference model for equalizers, which supports the exact derivation of a family of iterative and recursive algorithms with robust behavior. The framework applies equally to multiuser transmissions and multiple-input multiple-output (MIMO) channels. A major contribution is that due to the reference approach the adaptive equalizer problem can equivalently be treated as an adaptive system identification problem for which very precise statements are possible with respect to convergence, robustness and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -stability. Robust adaptive equalizers are much more desirable as they guarantee a much stronger form of stability than conventional in the mean square sense convergence. Even some blind channel estimation schemes can now be included in the form of recursive algorithms and treated under this general framework.