Multiband Unlimited Sampling: Super-Nyquist or Sub-Nyquist, That is the Question!

Abstract

The problem of sub-Nyquist multiband sensing has numerous applications across various fields. Despite substantial algorithmic pursuits, the practical implementation of these methods is subject to limitations of digital acquisition via analog-to-digital converters (ADCs). Multiband reconstruction for high-dynamic-range signals that may saturate the ADC is a practical yet challenging problem in many applications. From a different perspective, the Unlimited Sensing Framework (USF) focuses on reconstructing large signals from folded samples yet requires oversampling. The key challenge of multiband reconstruction via sub-Nyquist USF lies in the fundamental stalemate between sub-Nyquist acquisition and the oversampling assumptions required for unfolding. In this paper, we propose a hardware-software co-design approach that enables multiband reconstruction from folded samples at sub-Nyquist rates. The key insight here is to trade the channel redundancy for temporal sampling rate. We extend the multi-coset sampling strategy to the USF context and design a novel reconstruction algorithm. We demonstrate the robustness of our method via Monte-Carlo experiments. Beyond numerical experiments, we build customized hardware and validate our approach through lab experiments. This demonstrates the capabilities of our method in real-world scenarios while creating new avenues and opportunities for the field.