Sub-Nyquist Sampling for Reaching Theoretical Minimal Sampling Rate Boundary

2026-04-27

AI Summary

This work addresses the challenge of blind wideband spectrum sensing when subband locations are unknown, a scenario where existing sub-Nyquist sampling methods require at least twice the theoretically minimal sampling rate, hindering efficient implementation. The paper proposes the Dual-Aliasing Wideband Converter (DAWC), which achieves perfect subband localization and signal reconstruction at the theoretical minimum sampling rate without prior knowledge of subband positions. This is accomplished through non-uniform spectral segmentation and selective subband sampling. Key innovations include a dual-aliasing sampling architecture, a side-information-assisted subspace pursuit algorithm (MSSP) leveraging the common support structure among column submatrices of the signal, and rigorous theoretical guarantees based on the Restricted Isometry Property (RIP). Simulations demonstrate that the proposed method significantly outperforms state-of-the-art approaches in both reconstruction accuracy and noise robustness.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Online Learning & Bandits
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Wideband spectrum sensing motivates sub-Nyquist sampling architectures that exploit spectral sparsity, yet in blind scenarios where subband locations are unknown, existing schemes require sampling rates at least twice the theoretical minimum. To this end, we propose a dual-frequency aliasing wideband converter (DAWC), which partitions the multiband spectrum into non-uniform frequency intervals and selectively samples only a subset of them, requiring no prior knowledge of subband locations. We demonstrate that under mild conditions on the signal and the system, DAWC achieves perfect subband localization and waveform reconstruction at the theoretical minimum rate. Moreover, we introduce an innovative side-information-aided subspace pursuit (MSSP) algorithm exploiting the common support structure inherent in the signal column submatrices for exact recovery of the spectrum support set. Based on the restricted isometry property (RIP), we provide stable recovery guarantees for MSSP in the presence of noise. Numerical simulations show that the proposed scheme achieves superior spectrum recovery accuracy compared to state-of-the-art methods.

Problem

• sub-Nyquist sampling
• wideband spectrum sensing
• spectral sparsity
• blind scenario
• theoretical minimal sampling rate

Innovation

• sub-Nyquist sampling
• spectral sparsity
• blind spectrum sensing
• restricted isometry property
• wideband signal reconstruction