Robust equalisation for inter symbol interference communication channels

The problem of equalisation for communication channels with inter symbol interference (ISI) is investigated in this study. One practical yet challenging constraint for a channel with high transmission rate is incorporated into the modelling of the equalisation system: the communication channel is subject to uncertainties, which are assumed to be within a polytope with finite vertices. By using the augmentation method, the filtering error system of the equalisation problem is also characterised as a system with polytopic uncertainties. Sufficient conditions on the stability and the H_∞ performance for the filtering error system are obtained. A design method for the equaliser is proposed such that the filtering error system can achieve minimal H_∞ performance index even with the channel uncertainties. Two illustrative design examples demonstrate the design procedure and the effectiveness of the proposed method.