Equivalence of Several 6G Modulation Schemes for Doubly-Selective Channels

2025-11-12

AI Summary

Conventional time-frequency modulation suffers severe performance degradation in doubly selective channels characterized by large delay and Doppler spreads. Method: This paper introduces a novel evaluation framework centered on “non-selectivity” and “predictability,” formally establishing them as fundamental robustness criteria for modulation schemes in time-varying channels. By unifying signal representations in the delay-Doppler, chirp, and time-sequency domains, we rigorously prove the mathematical equivalence of three modulation families under doubly selective fading. Leveraging delay-Doppler analysis, linear canonical transforms (for chirp processing), and Walsh–Hadamard time-sequency transforms, we demonstrate that modulation designs adhering to this framework achieve both strong diversity gain and high spectral efficiency. Contribution/Results: The work provides foundational modeling tools and a new design paradigm for modulation theory in non-stationary channels—critical for 6G wireless systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Multimodal Learning
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems
• User Modeling, Personalization and Recommendation: User model development and evaluation

Abstract

There is significant recent interest in designing new modulation schemes for doubly-selective channels with large delay and Doppler spreads, where legacy modulation schemes based on time-frequency signal representations do not perform well. In this paper, we develop a framework for analyzing such modulations using two characteristics -- non-selectivity and predictability -- which directly relate to the diversity and spectral efficiency that the modulations achieve. We show that modulations in the delay-Doppler, chirp and time-sequency domains are non-selective, predictable and equivalent to one another, whereas time-frequency modulations are selective and non-predictable.

Problem

• Analyzing modulation schemes for doubly-selective channels
• Comparing diversity and spectral efficiency of 6G modulations
• Establishing equivalence between delay-Doppler and chirp domains

Innovation

• Framework analyzes modulations via non-selectivity and predictability
• Shows delay-Doppler, chirp, time-sequency modulations are equivalent
• Proves these outperform traditional time-frequency modulation schemes