In the last decade the work on linear tapped delay line equalizers has proved successful in reducing intersymbol interferenceone of the largest problems in data communication systems. An adjoining problem is the selection of a sampling time reference. An equalizer structure less sensitive to sampling time reference is studied for adaptive equalization. The equalization is simply done by means of tap coefficient adjustment. The equalizer consists of two parallel branches, each containing a transversal filter with adjustable tap coefficients. The branches are connected by a fixed filter, the transfer function of which is selected such that the equalizer can perform a sampling time reference displacement and a cancellation of intersymbol interference simultaneously. The criterion of goodness is the conventional meansquare error (including noise) between the actual output and a desired output. The equalizer is applied in two examples showing-in contrast to a conventional equalizer with the same total number of tap coefficients-the insensitivity of the minimum mean-square error (MMSE) to how the the sampling time reference is selected. Thus no extra circuits are needed for this purpose, while a mean-square error that is as low as the best that can be obtained with a conventional equalizer is adaptively maintained.

Optimization in the mean-square sense of a transmitter and receiver filter for a time-discrete pulse-amplitude modulation (PAM) system is considered, assuming a situation of realizable filters. This means a general departure from the common matched filter-periodic filter receiver structure. The minimization is carried out with respect to both intersymbol interference and noise, assuming that both transmitter and receiver filters consist of a limited number of basic filters. It is shown that, in general, few basic filters need to be used and that, in general, it is inefficient to use a matched filter and equalizer as a receiver if the transmitter filter is not optimized.