Reduced adaptive modeling: case of long impulse response channels

Some real signals are driven by process filters that have normal order but reduced structure. It follows that only some coefficients of the process filter are significant whereas the others coefficients are almost zero. Such signals, and their process filters, are said to be naturally reduced. To study these reduced models, we derive in this paper a mathematical formulation generalizing the classic case. We also show and quantify the advantages of reduced filters in an adaptive context. We found that, contrary to what can be inferred by intuition, reduced modeling could be of great interest even if the filter is not naturally reduced. In this case the filter has to be with a sufficiently long impulse response. Such a result could resolve an important problem encountered in communications where channels, such as radio-mobile channels, have long impulse response. The first part of this paper deals with naturally reduced signals. We provide a theoretical as well as experimental comparative study between our reduced model and the classical model. We clearly show the superiority of our model for this class of signals. The second part focuses on the study of a particular class of signals, namely signals with process filters that have long impulse response. For these signals, our model exhibits a conditional superiority. This condition is mainly related to the allowed amount of fluctuations in the LMS algorithm.