Abstract :
This correspondence presents, from the stochastic point of view, a new method for the optimal design of linear digital equalizers using a quadratic performance index. It is well known that a Kalman filter can be used as an equalizer for a digital communication system. If the Kalman filter is applied, then it is useful that an optimal linear equalizer, which minimizes the mean-square error, can be obtained. However, the most disadvantageous point in the Kalman filter is that a great deal of computation is needed to obtain the estimates. Furthermore, the order of the Kalman filter is always equal to the sample number of the impulse response of a transmission channel. Therefore, a high-order equalizer becomes necessary if the sample number is large. Usually, however, it is not necessary to use such a high-order equalizer. Considering this fact, an optimal equalizer is presented under the condition that the order can be assigned arbitrarily by the designer. The proposed equalizer is optimal in the sense that it minimizes the mean-square error subject to this condition.
