Digital Transmission Over the RC Channel

Abstract

This work evaluates the performance of digital transmission links over a lumped RC channel when one of three static equalization schemes is utilized: 1. Use of a Sidelobe Transmitter 2. Transversal Filter at the Receiver 3. Frequency Compensation of the Transfer Characteristics to form a rectangular Nyquist Channel. The effect on the probability of error of thermal noise and intersymbol interference is considered. In each of the equalization schemes, the intersymbol interference is reduced to zero, and the waveshape at the transmitter which maximizes the SNR at the receiver decision instant is transmitted. It is found that the performance of the Sidelobe Transmitter and the Transversal Filter Receiver are equal theoretically and that Frequency Compensation provides the poorest results. The comparisons carried out in this work have utilized the RC channel as an example. Detailed generalization of the comparative performance as a function of the impulse response of the channel utilized would be desirable but cannot be made readily. An analysis of the coaxial line is planned for the future. The eigenfunctions and corresponding eigenvalues of the system are required in order to evaluate the optimal performance of the Sidelobe Transmitter and Transversal Filter Receiver. For arbitrary impulse responses, these eigenfunctions are usually complex to obtain. However, one is able to state in general that since the Sidelobe Transmitter or Transversal Filter combined with transmission of the optimum waveshape represent the best linear filter, their performance will not be inferior to the Frequency Compensated rectangular Nyquist channel. This follows since frequency compensation networks fall into the class of linear filters.