Faster-than-Nyquist Signaling in the Finite Time-Bandwidth Product Regime

TL;DR

The paper addresses latency-constrained communications by analyzing faster-than-Nyquist signaling in a fixed time-bandwidth product regime and deriving tight bounds on the maximum channel coding rate $R$.It formulates FTN as an $N$-parallel Gaussian channel through a discrete-time model, diagonalizes the channel, and introduces the folded-spectrum framework to express capacity under finite TBP.Key contributions include a capacity expression $C_{FTN}$, normal and nonasymptotic bounds (NA, MC, RCU), and practical design criteria for the signaling rate, pulse shaping under OOB/OOI constraints, and a turbo-equalization coding scheme that closely approaches the MCCR.The results demonstrate sizable rate gains over Nyquist signaling in finite TBP settings, with design guidelines that enable near-optimal performance in short-packet regimes and potential extensions to fading, MIMO, and multi-user channels.

Abstract

This paper analyzes faster-than-Nyquist (FTN) signaling within a consistent framework based on a fixed time-bandwidth product (TBP), resolving potential ambiguities present in finite blocklength analysis. A key feature of FTN is its ability to increase the number of transmitted symbols in a given time and frequency resource, which can lower the rate penalties inherent in short packet communications. We derive tight bounds on the maximum channel coding rate (MCCR) and demonstrate that FTN's rate gains over Nyquist signaling can be higher in the finite TBP regime than in the asymptotic case. Performance is benchmarked against the theoretical optimum of transmitting prolate spheroidal wave functions, showing that a well-designed FTN system can closely approach this limit. We present practical design criteria, including the optimal time-acceleration factor for maximizing signaling dimensions, an optimized pulse shape that meets strict out-of-band constraints, and a turbo-equalization-based coding scheme that performs near the derived MCCR bounds. These findings establish FTN as a practical and near-optimal technique for enhancing the rate and reliability of latency-constrained communications.

Figures (7)

• Figure 1: $N$-parallel Gaussian channel formulation of FTN signaling, where the noise in the $n$-th channel has variance $\sigma_n^2 = (\rho\frac{\Omega}{N}\lambda_n)^{-1}$. The SNR of the $n$-th channel is $1/\sigma_n^2$.
• Figure 2: MCCR of FTN signaling in the finite TBP regime using RRC pulses with roll-off $\beta=1$ for $\Omega<50$, $\beta=0.3$ for $\Omega=(50,200$), and $\beta=0.1$ for $\Omega=(200,500)$.
• Figure 3: Percentage MCCR gain, $\frac{R_\text{NA}(\tau)-R_\text{NA}(1)}{R_\text{NA}(1)}\times100\%$, versus $\tau$ at various TBPs for truncated RRC pulses with roll-off $\beta$.
• Figure 4: OOB energy of various pulse shapes in terms of $c=2WT_p$
• Figure 5: Normalized SNRs of the parallel channels ($\sigma_n^{-2}/\rho$) with truncated RRC pulses with $\beta=.5$ and $\epsilon_W=10^{-4}$.

Theorems & Definitions (20)

• Proposition 1: Normal approximation for FTN
• Remark 1
• Remark 2
• Remark 3
• Theorem 1: MC polyanskiy2010channel, erseghe2016coding
• proof
• Theorem 2: MC for FTN
• proof
• Remark 4
• Theorem 3: RCU polyanskiy2010channel, erseghe2016coding