Asynchronous Multi-Channel USF: Modified CRT for Modulo Unfolding

2026-06-18

AI Summary

This work addresses the practical limitations of multi-channel unlimited sampling frameworks (MC-USF), which rely on strict channel synchronization and are thus vulnerable to timing mismatches, jitter, and drift. To overcome this challenge, the authors propose an asynchronous multi-channel USF architecture that eliminates the need for synchronized sampling by abandoning the conventional Chinese Remainder Theorem (CRT) requirement of temporal alignment. For the first time, modulo-based analog-to-digital unfolding is achieved without inter-channel synchronization. The approach formulates spatio-temporal signal reconstruction as a smoothness constraint over a graph representing the sensing channels, integrating an enhanced CRT with graph signal processing techniques to substantially improve robustness and practicality. Numerical experiments demonstrate that the proposed method accurately recovers signals even under severe timing misalignments, offering a viable pathway toward real-world deployment of MC-USF systems.

Abstract

The Unlimited Sampling Framework (USF) overcomes the traditional trade-off between dynamic range and digital resolution, achieving performance unattainable with standard ADCs. Its multi-channel extension (MC-USF) enables reconstruction from multiple folded measurements at critical sampling rates. Existing MC-USF methods typically rely on Chinese Remainder Theorem (CRT)-based unfolding, which requires strict channel-level sampling synchronization and is therefore vulnerable to timing mismatch, jitter, and drift. This paper introduces an asynchronous MC-USF architecture that eliminates the need for synchronization. By viewing spatial-temporal signal lifting as inducing smoothness over a graph of sensing channels, we develop a reconstruction strategy robust to temporal misalignment. Numerical experiments validate the approach, demonstrating accurate recovery and enabling more practical multi-channel USF implementations.

Problem

• Unlimited Sampling Framework
• Multi-Channel USF
• Chinese Remainder Theorem
• Asynchronous Sampling
• Modulo Unfolding

Innovation

• asynchronous multi-channel USF
• modulo unfolding
• graph smoothness
• timing mismatch robustness
• unlimited sampling