Asymptotic series expansion for the probability density function of the interference due to Faster-Than-Nyquist signaling

Abstract

A follow-up on a recent analytical investigation into the statistical characteristics of the Intersymbol Interference (ISI) due to Faster-Than-Nyquist (FTN) signaling is presented. An asymptotic series expansion for the ISI Probability Density Function (PDF) is provided based on the Edgeworth expansion. The non-trivial Petrov’s formula (a compact form of the Edgeworth series) is expanded into a simpler-to-use form accurate up to the 14th-order statistics. The ISI cumulants used in this expansion are compactly expressed in terms of power series of the FTN base signaling pulse. Using computer simulations, we illustrate the merits and limitations of the Edgeworth-Petrov (EP) expansion in comparison to its previously-used Gram-Charlier (GC) counterpart. Namely, while the former has a better convergence profile when ISI is due to FTN with a negligible phase jitter, the latter seems to be more computationally desirable for FTN with larger phase-jitters. Some application notes are provided to further illustrate the use of these expansion results.

Keywords

• Faster-Than-Nyquist (FTN) signaling
• Intersymbol Interference (ISI)
• Edgeworth-Petrov expansion
• Gram-Charlier expansion
• Root Raised Cosine (RRC)
• Bit Error Rate (BER)