Nyquist Signaling Modulation (NSM): An FTN-Inspired Paradigm Shift in Modulation Design for 6G and Beyond

2025-11-11

AI Summary

In 6G communications, modulation design faces the conflicting requirements of flexibility, interference resilience, and energy efficiency. Method: We propose a novel modulation paradigm inspired by Faster-Than-Nyquist (FTN) signaling, employing a configurable FIR filter to introduce controlled inter-symbol interference (ISI), enabling multi-dimensional and hybrid-dimensional signal construction while preserving minimum Euclidean distance and optimizing energy efficiency. We unify modulation and coding by embedding an analog LDGM framework into the modulator, supporting joint source-channel modulation or co-design with LDPC codes, and enhancing synergy via graph-based message passing. Contribution/Results: We derive a closed-form optimal real-valued one-dimensional filter and adopt rational-coefficient taps to drastically reduce complexity. Theoretical analysis and simulations exhibit excellent agreement across a wide SNR range, confirming superior trade-offs among flexibility, error-rate performance, and implementation efficiency.

Technology Category

Machine Learning: Multimodal LearningSearch and Optimization: Sampling/Simulation-based SearchGame Theory and Economic Paradigms: Mechanism Design

Application Category

Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAGSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsUser Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Nyquist Signaling Modulations (NSMs) are a new signaling paradigm inspired by faster-than-Nyquist principles but based on a distinct approach that enables controlled inter-symbol interference through carefully designed finite-impulse-response filters. NSMs can operate in any number of dimensions, including mixed-dimensional configurations, offering wide flexibility in filter design, optional energy balancing, and preservation of the 2-ASK minimum squared Euclidean distance (MSED). Both real and rational tapped filters are investigated, and closed-form expressions are derived for the optimal real-tap filters in the one-dimensional case (MS-PRS), providing analytical insight and strong agreement with simulated bit-error behavior across wide SNR ranges. The paradigm is conceptually expanded through an analog Low-Density Generator Matrix (LDGM) formulation, which broadens the NSM family and unifies modulation and coding within a single, structurally coherent framework. When combined with LDPC coding, it enables efficient and naturally synergistic interaction between the analog modulation and the digital LDPC code. Alternatively, when analog LDGM is employed for both source coding and modulation, a simple and harmonious joint source-channel-modulation structure emerges. In both configurations, the constituent blocks exhibit dual graph-based architectures suited to message passing, achieving high flexibility and complexity-efficient operation. Collectively, these results establish promising physical-layer directions for future 6G communication systems.

Problem

• Developing a new modulation paradigm using controlled inter-symbol interference filters
• Unifying modulation and coding within a single coherent framework structure
• Establishing efficient physical-layer architectures for future 6G communication systems

Innovation

• NSMs use finite-impulse-response filters for controlled interference
• Analog LDGM formulation unifies modulation and coding
• Graph-based architectures enable efficient message passing