Time Localization and Capacity of Faster-Than-Nyquist Signaling

TL;DR

This paper investigates the limits of faster-than-Nyquist (FTN) signaling, showing that signals are not necessarily well localized in time, which challenges previous capacity claims, and proposes a precoding scheme for non-sinc pulses.

Contribution

It clarifies the time localization properties of FTN signals and introduces a low-complexity precoding method for non-sinc pulses to improve spectral efficiency.

Findings

FTN signals are generally not well localized in time.

Mazo's capacity results do not hold under realistic localization assumptions.

A low-complexity precoding scheme effectively removes inter-symbol interference.

Abstract

In this paper, we consider communication over the bandwidth limited analog white Gaussian noise channel using non-orthogonal pulses. In particular, we consider non-orthogonal transmission by signaling samples at a rate higher than the Nyquist rate. Using the faster-than-Nyquist (FTN) framework, Mazo showed that one may transmit symbols carried by sinc pulses at a higher rate than that dictated by Nyquist without loosing bit error rate. However, as we will show in this paper, such pulses are not necessarily well localized in time. In fact, assuming that signals in the FTN framework are well localized in time, one can construct a signaling scheme that violates the Shannon capacity bound. We also show directly that FTN signals are in general not well localized in time. Therefore, the results of Mazo do not imply that one can transmit more data per time unit without degrading performance in terms of error probability. We also consider FTN signaling in the case of pulses that are different from the sinc pulses. We show that one can use a precoding scheme of low complexity to remove the inter-symbol interference. This leads to the possibility of increasing the number of transmitted samples per time unit and compensate for spectral inefficiency due to signaling at the Nyquist rate of the non sinc pulses. We demonstrate the power of the precoding scheme by simulations.