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

Certain equivalences between the Godard and Shalvi-Weinstein schemes have b een previously noted under special circumstances. We present here a simple proof for real signals that an equivalence can be established assuming litt le more than stationarity to fourth order of the equalizer input; the exact nature of the input sequence proves otherwise irrelevant to the validity o f the equivalence. The equivalence also carries over to complex signals, bu t subject to more restrictive circularity conditions. In a communication co ntext, the equivalence implies that many performance issues, such as suscep tibility to local minima, the ability (or lack there of) to open the eye, o r mean performance degradations due to channel noise and/or source correlat ion properties, are common to the two, even when applied with nonlinear cha nnels. Our equivalence also indicates a simple modification to the Godard a lgorithm to render it applicable to leptokurtic sources. (C) 1999 Elsevier Science B.V. All rights reserved.