Removal of Intersymbol Interference

Abstract

To remove the intersymbol interference I(k) defined in (1.42), we may not impose any constraint on the symbol sequence a(k), because the system design should hold for any sequence given by the user at the transmitter. Therefore we can only touch upon the impulse response h(k). Looking at (1.38) the system is prepared already with two degrees of freedom, $g_{I}(t)$ and $g_{R}(t)$. Hence, for a given impulse response $g_{C}(t)$ of the physical channel we can design the overall impulse response in such a way that

$$\begin{aligned} h(k-m)=h_{e}\left( t_{0}+(k-m)T\right) ={\left\{ \begin{array}{ll} \begin{array}{ccc} 0 &{} ; &{} m\,\epsilon \,\mathbb {Z}\,\,;\,\,m\ne k\\ h(0)=h_{e}(t_{0})\ne 0 &{} ; &{} m=k \end{array}\end{array}\right. } \end{aligned}$$

(2.1) is called Nyquist’s first criterion in the time domain [1] and the corresponding impulse is referred to as Nyquist impulse. An example of a real-valued impulse response satisfying (2.1) is depicted in Fig. 2.1. Obviously, $h_{e}(t)$ owns equidistant zeros except at $t=t_{0}$.