Closed form expression of EMSE for Bussgang equalization with spatio-temporal diversity

Bussgang algorithms are a class of simple stochastic gradient type solutions for blind channel equalization. We investigate the degradation of performance in the source estimation resulting from the stochastic jitter around stationary points of Bussgang algorithms (which correspond to the equalizers of the channel). More precisely, we derive a closed form approximation of the excess mean square error (EMSE) defined as the variance of the jitter which depends on the effects of the channel characteristics, the source distribution and the non-linearity used in the update equation. The analysis is performed in a context of spatiotemporal channel diversity involving a single-input/multiple outputs data model.