Spectrum Blind Unlimited Sampling of Multi-Band Signals

Recovering multiband spectra from sub-Nyquist sampling is a prominent research area in signal processing, driven by its wide range of applications and the technical challenges it presents. These challenges demand novel algorithmic approaches tailored to specific scenarios. The problem becomes even more complex when spectral locations are unknown, leading to the development of Blind Multi-Band Sampling techniques. Despite several proposed solutions, a notable research gap persists. Signals with varying energies across different spectral bands often exhibit high-dynamic-range (HDR) features, and with a fixed bit budget, there is a trade-off between optimizing digital resolution and spanning HDR. In this paper, we address this challenge by leveraging the Unlimited Sensing Framework (USF). The interaction between modulo non-linearity and sub-Nyquist sampling induces aliasing in both the domain and range of the signal, further complicating the recovery process, especially with unknown spectral locations. To tackle these challenges, we propose a novel algorithm for blind multiband spectrum recovery from folded samples at sub-Nyquist rates. Importantly, we provide a theoretically guaranteed, perfect recovery at sub-Nyquist sampling rates. Our proof is constructive and leads to an efficient algorithm supported by a novel multi-channel sampling architecture. We validate our approach through numerical experiments, opening up new directions in theory, algorithms, and real-world applications for the field.