A Generalized Nyquist Criterion and an Optimum Linear Receiver for a Pulse Modulation System

A pulse modulation system is modeled with M waveforms {sm(t)} , each of which is amplitude scaled and simultaneously transmitted over a single physical channel. An infinite pulse train is assumed with signal interval T, which is determined by bandwidth consideration of the channel. We restrict the receiver to be linear with M outputs, one for each signal wavefoim. At a high signal-to-noise ratio the main sources of interference at the input to the receiver are the intersymbol interference and crosstalk; by crosstalk we mean the interference between the different waveforms. It is desirable, therefore, for the receiver to eliminate both types of interference and to minimize the remaining error due to additive noise in the channel. This constraint on the intersymbol interference and crosstalk is defined as the generalized Nyquist criterion. The receiver which accomplishes the above is determined for a mean square error criterion. Finally, some examples are presented which demonstrate the ease with which the generalized Nyquist criterion can be used to design waveforms without intersymbol interference or crosstalk.