Reduced-rank transform-domain LMS algorithm for stabilizing fractionally-spaced channel equalizers

Fractionally-spaced channel equalizers suffer from stability problems due to ill-conditioning of the input signal. Pulse shaping is the root cause of signal ill-conditioning, which manifests itself as lack of persistent excitation, poor convergence and coefficient drifts. The traditional solutions to ill-conditioning involve regularization of the input signal autocorrelation matrix using a tap-leakage adaptive filter, which improves the eigenvalue spread of the input signal at the expense of increased steady-state mean-squared error (MSE). In this paper we propose a new solution based on the transform-domain least-mean-square (TD-LMS) algorithm. The proposed algorithm exploits the unitary transform of TD-LMS to identify and update only the equalizer coefficients that fall within the passband of the pulse shape. The new algorithm improves the eigenvalue spread of the input signal without compromising the MSE performance, which in turn eliminates stability problems and produces a much improved convergence performance.