A deterministic approach to optimal linear digital equalizers

This paper presents a new method for the optimal design of linear nonrecursive and recursive digital equalizers using a quadratic performance index. The nonrecursive and recursive digital equalizers are designed from the deterministic point of view. The proposed equalizers are based on pseudoinverse systems. It is known that an inverse system with delay can be designed under certain conditions. However, the condition for the existence of the inverse system is so severe that quite often it becomes unrealizable. On the other hand, it is always possible to design the pseudoinverse systems if the original system is asymptotically stable. Since the transmission channels are asymptotically stable, optimal nonrecursive and recursive digital equalizers can be designed by using the proposed pseudoinverse systems. Furthermore, the order of the nonrecursive and recursive digital equalizers can be assigned arbitrarily, whereas it is not arbitrary in the case when the inverse system is used as an equalizer. If the inverse system is possible to realize, then it can be obtained as a special case of the proposed pseudoinverse system.