An Optimum Linear Receiver for Multiple Channel Digital Transmission Systems

An optimum linear receiver for multiple channel digital transmission systems is developed for the minimum P
e
and for the zero-forcing criterion. A multidimensional Nyquist criterion is defined together with a theorem on the optimality of a finite lenght multiple tapped delay line. Furthermore an algorithm is given to calculate the tap settings of this multiple tapped delay line. This algorithm simplifies in those cases where the noise is so small that it can be neglected. Finally as an example the transmission of binary data over a cable, consisting of four identical wires, symmetrically situated inside a cylindrical shield, is considered.