Asynchronous Multi-Channel USF: Modified CRT for Modulo Unfolding
For practitioners of multi-channel USF, this work removes a key practical barrier (synchronization) but is incremental as it adapts existing graph-based smoothness ideas to a specific sensing problem.
The paper tackles the synchronization requirement in multi-channel Unlimited Sampling Framework (MC-USF) by proposing an asynchronous architecture that eliminates the need for channel-level timing alignment. Numerical experiments validate accurate recovery, enabling more practical implementations.
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.