On the nonvanishing stability of undesirable equilibria for FIR Godard blind equalizers

The existence of undesirable equilibria of Godard (1980) or constant modulus algorithms (CMA) is demonstrated for all finite-dimensional FIR equalizers. Sufficient stability conditions are presented for these equilibria. It is shown that for the Godard-2 algorithm, these undesirable equilibria are locally stable as long as the equalizer length remains finite. Results indicate that merely increasing the equalizer length does not necessarily nullify the potential for local convergence by Godard algorithms