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. We derive upper bounds for the average squared parameter estimation error (ASPE) of the blind identification scheme that depend on the mean-squared error of the Wiener equalizer, the kurtoses of the desired and interfering sources, and the channel impulse response. The effects of finite data length and stochastic gradient equalizer design on ASPE are also investigated. All results are derived in a general multiuser vector-channel context.