SOME CONVERGENCE PROPERTIES OF GODARDS 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 p oint of the average performance function, From this result, we can det ermine the adaptation gain and compare the convergence rate with that of the decision directed (DD) algorithm. It is shown that the converge nce rate of the GQ algorithm is faster than that of the DD equalizatio n algorithm. The second main result is a description of the geometry o f the average performance function: the region of attraction is observ ed to depend on the characteristics of the channel as well as the stat istics 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 t he geometry of the average performance function.