On the equivalence between the Godard and Shalvi-Weinstein schemes of blind equalization

Certain equivalences between the Godard and Shalvi—Weinstein schemes have been previously noted under special circumstances. We present here a simple proof for real signals that an equivalence can be established assuming little more than stationarity to fourth order of the equalizer input; the exact nature of the input sequence proves otherwise irrelevant to the validity of the equivalence. The equivalence also carries over to complex signals, but subject to more restrictive circularity conditions. In a communication context, the equivalence implies that many performance issues, such as susceptibility to local minima, the ability (or lack thereof) to open the eye, or mean performance degradations due to channel noise and/or source correlation properties, are common to the two, even when applied with nonlinear channels. Our equivalence also indicates a simple modification to the Godard algorithm to render it applicable to leptokurtic sources. ( 1999 Elsevier Science B.V. All rights reserved.