Godard blind equalizer error surface characteristics: White, zero‐mean, binary source case

Abstract

We study the Godard/CMA error surface in adapting the impulse response coefficients of a finite‐length, tapped‐delay‐line filter to equalize a white, zero‐mean, binary (± 1) source that suffers ISI due to a linear channel. Our results arise primarily from examination of the expressions for the gradient and the Hessian in the baud‐spaced equalizer parameter space of the cost‐function in this particular setting. This paper presents results useful in topological assessment of predures for initializing a gradient descent algorithm on this multimodal surface in the equalizer parameter space.