Local Convergence of the Sato Blind Equalizer and Generalizations Under Practical Constraints

An early use of recursive identification in blind adaptive channel equalization is an algorithm developed by Sato. An important generalization of the Sato algorithm with extensive analysis appears in the work of Benveniste, Goursat, and Ruget. These generalized algorithms have been shown to possess a desirable global convergence property under two idealized conditions. The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied. Results show that, in practice, when either the equalizer is finite-dimensional and/or the input is discrete (as in digital communications) the equalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse. It is also shown, that a center spike initialization is insufficient to guarantee avoiding such ill-convergence. Simulations verify the analytical results.