Performance analysis of Godard-based blind channel identification

We analyze a blind channel impulse response identification scheme based on the cross-correlation of blind symbol estimates with the received signal. The symbol estimates specified are those minimizing the Godard (1980) (or constant modulus) criterion, for which mean-squared symbol estimation error bounds have been derived previously. We derive upper bounds for the average squared parameter estimation error of the blind identification scheme which depend on the mean-squared error of the Wiener symbol estimator, the kurtoses of the desired and interfering sources, and the channel impulse response. All results are derived in a general multi-user vector-channel context.