Auxiliary Factor Method to Remove ISI of Nyquist Filters

TL;DR

This paper introduces auxiliary factors to completely eliminate ISI in Nyquist filters with finite window lengths, improving performance even with timing jitter, and provides a closed-form solution validated by simulations.

Contribution

A novel auxiliary factor method that compensates for Fourier transform truncation, enabling zero-ISI in practical FIR Nyquist filters regardless of window size.

Findings

Complete ISI removal achieved with auxiliary factors

Significant performance improvement under timing jitter

Closed-form solution validated by simulations

Abstract

As has been known, the Nyquist first condition promises no intersymbol interference (ISI) as derived in the frequency domain. However, the practical implementation using the FIR filter truncates the Fourier transform by its window and prevents the mathematical calculation from reaching the ideal solution at zero-ISI. For obtaining better results, an increase in the window's length is required in general. To address this problem, a new approach is presented by using auxiliary factors (AFs) to compensate shortcomings of the truncated Fourier transform and remove the ISI completely, regardless of the window's length. In addition, the performance in the presence of the timing jitter is also improved significantly. The closed-form solution of the AFs is derived and the effectiveness is confirmed by the simulation results. Finally, the problems of the transmission delay and additional calculation complexity are analysed.