FTN Signaling: Spectral Efficiency from BPSK to 16-QAM

2026-10-08

AI Summary

This study addresses the lack of a quantified relationship between constellation order and the optimal acceleration factor in faster-than-Nyquist (FTN) signaling. To bridge this gap, the authors compute finite-alphabet symbol-level achievable information rates (AIR) for BPSK through 16-QAM within an MMSE framework, cross-validated against Ungerboeck BCJR benchmarks, thereby establishing a quantitative model linking modulation order to temporal compression. The work reveals an intrinsic principle that higher-order modulations must approach the Nyquist limit to sustain spectral efficiency. Furthermore, it identifies the optimal acceleration factors at 6 dB for each modulation scheme—0.65 for BPSK and 0.90 for 16-QAM—and demonstrates their robustness across coded systems and varying detector memory lengths. These findings provide a theoretical foundation for operating point design in FTN systems.

Abstract

Faster-than-Nyquist (FTN) signaling can improve spectral efficiency by transmitting symbols closer together than the Nyquist limit, at the cost of additional inter-symbol interference (ISI). In this letter, we study the finite-alphabet symbol-wise achievable information rate (AIR) of FTN signaling for BPSK, QPSK, and 16-QAM under a transmit-power constraint and a common minimum mean square error (MMSE) channel-shortening (CS) detection framework, cross-validated for BPSK against an independent reduced-state Ungerboeck Bahl-Cocke-Jelinek-Raviv (BCJR) benchmark. Our results show a clear trend. Lower-order constellations can benefit from more aggressive time acceleration, while higher-order constellations become less tolerant of acceleration and achieve their best spectral efficiency closer to the Nyquist limit. At a reference signal-to-noise ratio (SNR) of 6 dB the optimum acceleration factor shifts from $τ^\star\approx0.65$ for BPSK to 0.75 for QPSK and 0.90 for 16-QAM. We further show that this trend is preserved in coded systems and remains robust to the detector memory. The impact of FTN operation on the instantaneous-to-average power ratio (IAPR) is also examined. Overall, the results highlight how constellation order should be considered when selecting the operating point for FTN signaling.

Problem

• Faster-than-Nyquist signaling
• achievable information rate
• spectral efficiency
• constellation order
• inter-symbol interference

Innovation

• Faster-than-Nyquist signaling
• Achievable information rate
• Channel shortening
• Constellation order
• Spectral efficiency