Some convergence properties of Godard's quartic algorithm

Convergence analysis on Godard's quartic (GQ) algorithm used for blind equalization is accomplished. The first main result is an explanation of the local behavior of the GQ algorithm around the global minimum point of the average performance function. From this result, we can determine the adaptation gain and compare the convergence rate with that of the decision directed (DD) algorithm. It is shown that the convergence rate of the GQ algorithm is faster than that of the DD equalization algorithm. The second main result is a description of the geometry of the average performance function: the region of attraction is observed to depend on the characteristics of the channel as well as the statistics of the input signal. It is shown that a good initial parameter vector of the GQ algorithm can be chosen based on the information of the geometry of the average performance function.