Pulses with Minimum Residual Intersymbol Interference for Faster than Nyquist Signaling

TL;DR

This paper introduces optimized pulses for faster than Nyquist signaling that significantly reduce residual intersymbol interference, enabling simpler equalizers and improved bit error rates at higher transmission speeds.

Contribution

It develops a numerical optimization method using prolate spheroidal wave functions to design pulses with minimal residual interference, outperforming traditional root raised cosine pulses.

Findings

Residual interference decreased by 32 dB with new pulses.

New pulses enable simpler equalizers for faster transmission.

Bit error rate improved using optimized pulses with fewer states.

Abstract

Faster than Nyquist signaling increases the spectral efficiency of pulse amplitude modulation by accepting intersymbol interference, where an equalizer is needed at the receiver. Since the complexity of an optimal equalizer increases exponentially with the number of the interfering symbols, practical truncated equalizers assume shorter memory. The power of the resulting residual interference depends on the transmit filter and limits the performance of truncated equalizers. In this paper, we use numerical optimizations and the prolate spheroidal wave functions to find optimal time-limited pulses that achieve minimum residual interference. Compared to root raised cosine pulses, the new pulses decrease the residual interference by an order of magnitude, for example, a decrease by 32 dB is achieved for an equalizer that considers four interfering symbols at 57% faster transmissions. As a proof of concept, for the 57% faster transmissions of binary symbols, we showed that using the new pulse with a 4-state equalizer has better bit error rate performance compared to using a root raised cosine pulse with a 128-state equalizer.