On the (Non)Existence of Undesirable Equilibria of
Zhi Jun Ding, C.R. Johnson, Rodney A. Kennedy · 1992
Existing results in the literature have proved that particular blind equalization algorithms, including Godard al- gorithms, are globally convergent in an ideal and nonimple- mentable setting where a doubly infinite dimensional equalizer is available for adaptation. Contrary to popular conjectures, we show that implementable finite dimensional equalizers which attempt to approximate the ideal setting generally fail to have global convergence to acceptable equalizer parameter settings without the use of special remedial measures. We present a the- ory based on the channel convolution matrix nullspace to ex- plain the failure of Godard algorithms for such practical blind equalization situations. We support our nullspace theory by a simple example showing ill convergence of the Godard algo- rithm.