Convergence characteristics of the kalman-type equalizer in decision-directed mode

In general, in the adjustment of its tap weight, the automatic equalizer requires the reference signal in addition to the input to the equalizer. For the convergence to be correct, the reference signal should be the equalizer output after the convergence is completed correctly. Since this is impossible in practice, a decision-directed operation occurs wherein the equalizer output during tap weight adjustment is given to the decision part and the output of the decision part is used as the reference signal. In such a case, the adjustment of the tap weight is not exactly correct. This paper shows first that the characteristics of the cascade system (which consists of the transfer characteristics of a Kalman-type automatic equalizer after tap weight adjustment, operating by following the reference signal from the decision part) and the characteristics of the transmission channel can be determined directly from the signal type and the characteristics of the transmission channel and the characteristics of the decision part. In the above reasoning, the characteristics of the cascade system are obtained as the cross correlation between the transmitted signal and the output signal from the decision part. Then the mechanism to arrive at the correct convergence is described for the automatic equalizer, based on the knowledge obtained in the analysis of the cascade system. Finally, a Karhunen-Loeve type decision-assist fixed equalizer is proposed, which compensates the frequencygain characteristics of the transmission channel and assists the correct decision of the decision part.